Question 1/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद (p(x)) का शून्यक ज्यामितीय रूप से क्या दर्शाता है?
What does a zero of a polynomial (p(x)) represent geometrically?
#polynomials
#zeroes
#geometrical-meaning
#x-axis
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A वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis
B वह बिंदु जहाँ ग्राफ (y)-अक्ष को काटता है / The point where the graph cuts the (y)-axis
C ग्राफ का सबसे ऊँचा बिंदु / The highest point of the graph
D ग्राफ का सबसे निचला बिंदु / The lowest point of the graph
Explanation opens after your attempt
Correct Answer
A. वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis
Step 1
Concept
A zero is the (x)-value for which (p(x)=0). On the graph, it is shown where the curve meets the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis. A zero is the (x)-value for which (p(x)=0). On the graph, it is shown where the curve meets the (x)-axis.
Step 3
Exam Tip
किसी बहुपद का शून्यक वह (x)-मान होता है जहाँ (p(x)=0) होता है। ग्राफ में यह (x)-अक्ष पर मिलने वाला बिंदु बताता है।
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Question 2/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x)-अक्ष को (x=3) पर काटता है, तो उसका शून्यक क्या होगा?
If the graph of a polynomial cuts the (x)-axis at (x=3), what is its zero?
#polynomials
#graph
#zero
#x-intercept
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A (3)
B (-3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-value where the graph cuts the (x)-axis is the zero. Hence the zero is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The (x)-value where the graph cuts the (x)-axis is the zero. Hence the zero is (3).
Step 3
Exam Tip
जहाँ ग्राफ (x)-अक्ष को काटता है वही (x)-मान शून्यक होता है। इसलिए यहाँ शून्यक (3) है।
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Question 3/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((-2,0)) और ((4,0)) पर काटता है, तो बहुपद के शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at ((-2,0)) and ((4,0)), what are the zeroes of the polynomial?
#x-intercepts
#zeroes
#polynomial-graph
#class-10
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A (-2) और (4) / (-2) and (4)
B (2) और (-4) / (2) and (-4)
C (0) और (4) / (0) and (4)
D (-2) और (0) / (-2) and (0)
Explanation opens after your attempt
Correct Answer
A. (-2) और (4) / (-2) and (4)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph meets the (x)-axis. So the zeroes are (-2) and (4).
Step 2
Why this answer is correct
The correct answer is A. (-2) और (4) / (-2) and (4). Zeroes are the (x)-coordinates of the points where the graph meets the (x)-axis. So the zeroes are (-2) and (4).
Step 3
Exam Tip
शून्यक हमेशा (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-2) और (4) हैं।
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Question 4/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी रैखिक बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो उसके कितने शून्यक होंगे?
If the graph of a linear polynomial cuts the (x)-axis only once, how many zeroes will it have?
#linear-polynomial
#zeroes
#graph
#easy
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A एक / One
B दो / Two
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The graph of a linear polynomial is a line and usually cuts the (x)-axis once. Therefore it has one zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The graph of a linear polynomial is a line and usually cuts the (x)-axis once. Therefore it has one zero.
Step 3
Exam Tip
रैखिक बहुपद का ग्राफ एक रेखा होता है और सामान्यतः (x)-अक्ष को एक बार काटता है। इसलिए उसका एक शून्यक होता है।
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Question 5/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस बिंदु से बहुपद का शून्यक सीधे मिल सकता है?
From which point can the zero of a polynomial be directly found?
#zeroes
#graphical-meaning
#x-axis
#polynomials
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A जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis
B जहाँ ग्राफ (y)-अक्ष को काटता है / Where the graph cuts the (y)-axis
C जहाँ ग्राफ ऊपर जाता है / Where the graph goes upward
D जहाँ ग्राफ नीचे जाता है / Where the graph goes downward
Explanation opens after your attempt
Correct Answer
A. जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis
Step 1
Concept
For a zero, (y=0), and this happens on the (x)-axis. So look at the points where the graph meets the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis. For a zero, (y=0), and this happens on the (x)-axis. So look at the points where the graph meets the (x)-axis.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए और यह स्थिति (x)-अक्ष पर होती है। इसलिए (x)-अक्ष से मिलने वाले बिंदु देखें।
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Question 6/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x)-अक्ष को नहीं काटता और नहीं छूता, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a polynomial neither cuts nor touches the (x)-axis, how many real zeroes does it have?
#real-zeroes
#no-intersection
#polynomial-graph
#easy
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A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 3
Exam Tip
वास्तविक शून्यक तभी दिखते हैं जब ग्राफ (x)-अक्ष से मिले। यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो वास्तविक शून्यक नहीं होंगे।
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Question 7/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है, तो द्विघात बहुपद के कितने शून्यक होंगे?
If a parabola cuts the (x)-axis at two distinct points, how many zeroes does the quadratic polynomial have?
#quadratic-polynomial
#parabola
#two-zeroes
#x-axis
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A दो / Two
B एक / One
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.
Step 3
Exam Tip
द्विघात बहुपद का ग्राफ परवलय होता है। (x)-अक्ष पर दो अलग-अलग कटाव दो वास्तविक शून्यक बताते हैं।
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Question 8/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को केवल छूता है, काटता नहीं है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola only touches the (x)-axis and does not cut it, how many real zeroes does the quadratic polynomial have?
#parabola
#touching-x-axis
#one-zero
#quadratic
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A एक / One
B दो / Two
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 3
Exam Tip
जब परवलय (x)-अक्ष को केवल एक बिंदु पर छूता है, तो एक वास्तविक शून्यक होता है। परीक्षा में छूना भी (x)-अक्ष से मिलना माना जाता है।
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Question 9/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय पूरा (x)-अक्ष के ऊपर है, तो द्विघात बहुपद के कितने वास्तविक शून्यक होंगे?
If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-graph
#no-real-zero
#parabola
#easy
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A कोई नहीं / None
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. कोई नहीं / None
Step 1
Concept
If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. कोई नहीं / None. If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 3
Exam Tip
यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो (p(x)=0) का कोई वास्तविक मान नहीं मिलता। इसलिए वास्तविक शून्यक (0) होंगे।
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Question 10/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद (p(x)) के शून्यक ज्ञात करने के लिए ग्राफ पर कौन-से बिंदु देखे जाते हैं?
Which points on the graph are observed to find the zeroes of a polynomial (p(x))?
#zeroes
#graph-reading
#x-axis
#polynomials
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A (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis
B (y)-अक्ष से मिलने वाले बिंदु / Points meeting the (y)-axis
C ग्राफ के सभी मोड़ / All turns of the graph
D केवल मूल बिंदु / Only the origin
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis
Step 1
Concept
For a zero, (p(x)=0), which means (y=0). Points with (y=0) lie on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis. For a zero, (p(x)=0), which means (y=0). Points with (y=0) lie on the (x)-axis.
Step 3
Exam Tip
शून्यक के लिए (p(x)=0), यानी (y=0) होना चाहिए। (y=0) वाले बिंदु (x)-अक्ष पर होते हैं।
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Question 11/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((0,0)) पर काटता है, तो बहुपद का एक शून्यक क्या होगा?
If a graph cuts the (x)-axis at ((0,0)), what is one zero of the polynomial?
#origin
#zero-of-polynomial
#x-intercept
#easy
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A (0)
B (1)
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of ((0,0)) is (0). Therefore (0) is one zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). The (x)-coordinate of ((0,0)) is (0). Therefore (0) is one zero of the polynomial.
Step 3
Exam Tip
बिंदु ((0,0)) का (x)-निर्देशांक (0) है। इसलिए (0) बहुपद का एक शून्यक होगा।
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Question 12/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को (x=-5) पर काटता है, तो कौन-सा कथन सही है?
If a graph cuts the (x)-axis at (x=-5), which statement is correct?
#negative-zero
#x-intercept
#graph
#polynomials
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A (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial
B (5) बहुपद का शून्यक है / (5) is a zero of the polynomial
C (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
A. (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial
Step 1
Concept
The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 2
Why this answer is correct
The correct answer is A. (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial. The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 3
Exam Tip
जहाँ ग्राफ (x)-अक्ष को काटता है वही (x)-मान शून्यक होता है। ऋण चिह्न को अनदेखा न करें।
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Question 13/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी ग्राफ के (x)-अक्ष से मिलने वाले बिंदु ((1,0)), ((2,0)), और ((5,0)) हैं, तो शून्यकों की संख्या क्या है?
If the points where a graph meets the (x)-axis are ((1,0)), ((2,0)), and ((5,0)), how many zeroes are there?
#number-of-zeroes
#x-intercepts
#graph-reading
#easy
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A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
Each distinct intersection with the (x)-axis gives one zero. Here there are three distinct points, so there are three zeroes.
Step 2
Why this answer is correct
The correct answer is A. (3). Each distinct intersection with the (x)-axis gives one zero. Here there are three distinct points, so there are three zeroes.
Step 3
Exam Tip
हर अलग (x)-अक्ष कटाव एक शून्यक देता है। यहाँ तीन अलग बिंदु हैं, इसलिए तीन शून्यक हैं।
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Question 14/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी स्थिर अशून्य बहुपद जैसे (p(x)=5) के ग्राफ से शून्यकों के बारे में क्या पता चलता है?
What does the graph of a non-zero constant polynomial like (p(x)=5) show about its zeroes?
#constant-polynomial
#no-zero
#graph
#easy
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A कोई शून्यक नहीं / No zero
B एक शून्यक / One zero
C दो शून्यक / Two zeroes
D अनंत शून्यक / Infinite zeroes
Explanation opens after your attempt
Correct Answer
A. कोई शून्यक नहीं / No zero
Step 1
Concept
The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 2
Why this answer is correct
The correct answer is A. कोई शून्यक नहीं / No zero. The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 3
Exam Tip
(p(x)=5) का ग्राफ (x)-अक्ष के समानांतर रेखा है जो (x)-अक्ष को नहीं काटती। इसलिए इसका कोई शून्यक नहीं है।
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Question 15/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-4) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक क्या होगा?
If the graph of (p(x)=x-4) cuts the (x)-axis, what is the zero?
#linear-polynomial
#zero
#graphical-meaning
#class-10
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A (4)
B (-4)
C (0)
D (1)
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Step 1
Concept
For the zero, (x-4=0), so (x=4). The graph also cuts the (x)-axis at (x=4).
Step 2
Why this answer is correct
The correct answer is A. (4). For the zero, (x-4=0), so (x=4). The graph also cuts the (x)-axis at (x=4).
Step 3
Exam Tip
शून्यक के लिए (x-4=0), इसलिए (x=4)। ग्राफ भी (x)-अक्ष को (x=4) पर काटेगा।
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Question 16/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x+2) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक कौन-सा है?
If the graph of (p(x)=x+2) cuts the (x)-axis, which is the zero?
#linear-polynomial
#negative-zero
#x-intercept
#easy
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A (2)
B (-2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
For the zero, (x+2=0), so (x=-2). The graph cuts the (x)-axis at (x=-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). For the zero, (x+2=0), so (x=-2). The graph cuts the (x)-axis at (x=-2).
Step 3
Exam Tip
शून्यक के लिए (x+2=0), इसलिए (x=-2)। ग्राफ (x)-अक्ष को (x=-2) पर काटेगा।
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Question 17/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
ग्राफ पर ((3,0)) बिंदु बहुपद के लिए क्या दर्शाता है?
What does the point ((3,0)) on a polynomial graph represent?
#coordinate-point
#x-axis
#zeroes
#graph
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A (3) बहुपद का शून्यक है / (3) is a zero of the polynomial
B (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
C (3) बहुपद का गुणांक है / (3) is a coefficient of the polynomial
D ग्राफ का अधिकतम मान है / It is the maximum value of the graph
Explanation opens after your attempt
Correct Answer
A. (3) बहुपद का शून्यक है / (3) is a zero of the polynomial
Step 1
Concept
In ((3,0)), (y=0) and (x=3). Therefore (3) is the zero.
Step 2
Why this answer is correct
The correct answer is A. (3) बहुपद का शून्यक है / (3) is a zero of the polynomial. In ((3,0)), (y=0) and (x=3). Therefore (3) is the zero.
Step 3
Exam Tip
((3,0)) में (y=0) है और (x=3) है। इसलिए (3) शून्यक होगा।
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Question 18/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
ग्राफ पर ((0,4)) बिंदु मिलने से क्या (0) शून्यक होगा?
Does the point ((0,4)) on a graph mean that (0) is a zero?
#common-mistake
#y-intercept
#zeroes
#graph
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A नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\)
B हाँ, क्योंकि (x=0) है / Yes, because (x=0)
C हाँ, क्योंकि बिंदु (y)-अक्ष पर है / Yes, because the point is on the (y)-axis
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\)
Step 1
Concept
For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\). For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए। ((0,4)) में (y=4) है, इसलिए (0) शून्यक नहीं है।
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Question 19/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ के (x)-अक्ष से दो कटाव हैं, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph has two intersections with the (x)-axis, how many real zeroes does it have?
#real-zeroes
#x-axis-intersections
#polynomial-graph
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से प्रत्येक अलग कटाव एक वास्तविक शून्यक देता है। दो कटाव होने पर दो वास्तविक शून्यक होंगे।
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Question 20/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस स्थिति में (x=2) बहुपद (p(x)) का शून्यक कहलाएगा?
In which situation will (x=2) be called a zero of polynomial (p(x))?
#definition
#zero-of-polynomial
#value-test
#easy
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A जब (p(2)=0) हो / When (p(2)=0)
B जब (p(0)=2) हो / When (p(0)=2)
C जब (p(2)=2) हो / When (p(2)=2)
D जब (p(x)=2) हो / When (p(x)=2)
Explanation opens after your attempt
Correct Answer
A. जब (p(2)=0) हो / When (p(2)=0)
Step 1
Concept
A value is called a zero only when the polynomial value at that point is (0). So for (x=2), (p(2)=0) is required.
Step 2
Why this answer is correct
The correct answer is A. जब (p(2)=0) हो / When (p(2)=0). A value is called a zero only when the polynomial value at that point is (0). So for (x=2), (p(2)=0) is required.
Step 3
Exam Tip
किसी मान को शून्यक तभी कहते हैं जब उस पर बहुपद का मान (0) हो। इसलिए (x=2) के लिए (p(2)=0) होना चाहिए।
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Question 21/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(-1)=0), तो ग्राफ किस बिंदु से गुजरेगा?
If (p(-1)=0), through which point will the graph pass?
#function-value
#graph-point
#zeroes
#polynomials
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A ((-1,0))
B ((1,0))
C ((0,-1))
D ((0,1))
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Correct Answer
A. ((-1,0))
Step 1
Concept
(p(-1)=0) means (y=0) at (x=-1). So the graph passes through ((-1,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)). (p(-1)=0) means (y=0) at (x=-1). So the graph passes through ((-1,0)).
Step 3
Exam Tip
(p(-1)=0) का अर्थ है (x=-1) पर (y=0)। इसलिए ग्राफ ((-1,0)) से गुजरेगा।
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Question 22/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(6)=0), तो बहुपद के ग्राफ का (x)-अक्ष से कौन-सा कटाव होगा?
If (p(6)=0), what will be the (x)-axis intersection of the polynomial graph?
#x-intercept
#function-value
#zeroes
#easy
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A ((6,0))
B ((0,6))
C ((-6,0))
D ((6,6))
Explanation opens after your attempt
Correct Answer
A. ((6,0))
Step 1
Concept
(p(6)=0) means (y=0) when (x=6). Hence the graph cuts the (x)-axis at ((6,0)).
Step 2
Why this answer is correct
The correct answer is A. ((6,0)). (p(6)=0) means (y=0) when (x=6). Hence the graph cuts the (x)-axis at ((6,0)).
Step 3
Exam Tip
(p(6)=0) बताता है कि (x=6) पर (y=0) है। इसलिए ग्राफ (x)-अक्ष को ((6,0)) पर काटता है।
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Question 23/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को ((2,0)) और ((7,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of a quadratic polynomial cuts the (x)-axis at ((2,0)) and ((7,0)), what are the zeroes?
#quadratic-polynomial
#x-intercepts
#zeroes
#graph
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A (2) और (7) / (2) and (7)
B (-2) और (-7) / (-2) and (-7)
C (0) और (7) / (0) and (7)
D (2) और (0) / (2) and (0)
Explanation opens after your attempt
Correct Answer
A. (2) और (7) / (2) and (7)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).
Step 2
Why this answer is correct
The correct answer is A. (2) और (7) / (2) and (7). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).
Step 3
Exam Tip
शून्यक (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (2) और (7) हैं।
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Question 24/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी परवलय का शीर्ष (x)-अक्ष पर है और वह (x=4) पर है, तो वास्तविक शून्यक क्या होगा?
If the vertex of a parabola lies on the (x)-axis at (x=4), what is the real zero?
#parabola
#vertex
#touching-x-axis
#one-zero
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A (4)
B (0)
C (-4)
D दो शून्यक होंगे / There will be two zeroes
Explanation opens after your attempt
Step 1
Concept
When a parabola touches the (x)-axis at its vertex, it has one real zero. Its (x)-coordinate is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). When a parabola touches the (x)-axis at its vertex, it has one real zero. Its (x)-coordinate is (4).
Step 3
Exam Tip
जब परवलय (x)-अक्ष को शीर्ष पर छूता है, तो एक ही वास्तविक शून्यक होता है। उसका (x)-निर्देशांक (4) है।
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Question 25/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस ग्राफ से शून्यक (-3) और (2) मिलेंगे?
Which graph will give zeroes (-3) and (2)?
#graph-from-zeroes
#x-intercepts
#polynomials
#easy
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A जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0))
B जो (y)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (y)-axis at ((-3,0)) and ((2,0))
C जो (x)-अक्ष को ((0,-3)) और ((0,2)) पर काटे / One that cuts the (x)-axis at ((0,-3)) and ((0,2))
D जो मूल बिंदु से न गुजरे / One that does not pass through origin
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0))
Step 1
Concept
If the zeroes are (-3) and (2), the graph cuts the (x)-axis at those (x)-values. So the points are ((-3,0)) and ((2,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0)). If the zeroes are (-3) and (2), the graph cuts the (x)-axis at those (x)-values. So the points are ((-3,0)) and ((2,0)).
Step 3
Exam Tip
शून्यक (-3) और (2) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((-3,0)) और ((2,0)) होंगे।
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Question 26/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ केवल (y)-अक्ष को ((0,3)) पर काटता है और (x)-अक्ष को नहीं काटता, तो वास्तविक शून्यक कितने होंगे?
If a polynomial graph cuts only the (y)-axis at ((0,3)) and does not cut the (x)-axis, how many real zeroes are there?
#y-intercept
#no-real-zero
#common-mistake
#graph
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 3
Exam Tip
शून्यक (x)-अक्ष से मिलने पर मिलते हैं, (y)-अक्ष से नहीं। इसलिए (x)-अक्ष से कटाव न होने पर वास्तविक शून्यक (0) होंगे।
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Question 27/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
बहुपद (p(x)) के ग्राफ में (y=p(x)) होता है। शून्यक पर (y) का मान क्या होगा?
In the graph of polynomial (p(x)), (y=p(x)). What is the value of (y) at a zero?
#definition
#y-value
#zeroes
#graph
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A (0)
B (1)
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
At a zero, the value of the polynomial is (0). Therefore the (y)-value at that point on the graph is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). At a zero, the value of the polynomial is (0). Therefore the (y)-value at that point on the graph is (0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। इसलिए ग्राफ पर उस बिंदु का (y)-मान (0) होगा।
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Question 28/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि रेखा (y=2x-6) (x)-अक्ष को काटती है, तो संबंधित रैखिक बहुपद का शून्यक क्या है?
If the line (y=2x-6) cuts the (x)-axis, what is the zero of the related linear polynomial?
#linear-graph
#x-intercept
#zero
#polynomial
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A (3)
B (-3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (2x-6=0) gives (x=3). This is the graphical zero.
Step 2
Why this answer is correct
The correct answer is A. (3). On the (x)-axis, (y=0), so (2x-6=0) gives (x=3). This is the graphical zero.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (2x-6=0) से (x=3) मिलता है। यही ग्राफीय शून्यक है।
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Question 29/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि रेखा (y=x+7) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक क्या होगा?
If the graph of the line (y=x+7) cuts the (x)-axis, what is the zero?
#linear-polynomial
#zero
#x-intercept
#easy
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A (7)
B (-7)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (x+7=0) gives (x=-7). Watch the negative sign carefully.
Step 2
Why this answer is correct
The correct answer is B. (-7). On the (x)-axis, (y=0), so (x+7=0) gives (x=-7). Watch the negative sign carefully.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (x+7=0) से (x=-7) मिलता है। ऋण चिह्न को ध्यान से देखें।
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Question 30/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x)-अक्ष को ((5,0)) पर केवल छूता है, तो कौन-सा कथन सही है?
If the graph of a polynomial only touches the (x)-axis at ((5,0)), which statement is correct?
#touching-x-axis
#zeroes
#graphical-meaning
#easy
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A (5) शून्यक है / (5) is a zero
B (0) शून्यक है / (0) is a zero
C कोई शून्यक नहीं है / There is no zero
D (-5) शून्यक है / (-5) is a zero
Explanation opens after your attempt
Correct Answer
A. (5) शून्यक है / (5) is a zero
Step 1
Concept
Touching the (x)-axis also shows (p(x)=0). Therefore (x=5) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (5) शून्यक है / (5) is a zero. Touching the (x)-axis also shows (p(x)=0). Therefore (x=5) is a zero.
Step 3
Exam Tip
ग्राफ का (x)-अक्ष को छूना भी (p(x)=0) को दिखाता है। इसलिए (x=5) शून्यक है।
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Question 31/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि बहुपद के ग्राफ में (x)-अक्ष से कटाव की संख्या (4) है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If the number of intersections of a polynomial graph with the (x)-axis is (4), how many real zeroes are there?
#number-of-zeroes
#x-axis
#graph-reading
#polynomials
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A (4)
B (3)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
Each distinct (x)-axis intersection represents one real zero. Therefore (4) intersections give (4) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (4). Each distinct (x)-axis intersection represents one real zero. Therefore (4) intersections give (4) real zeroes.
Step 3
Exam Tip
प्रत्येक अलग (x)-अक्ष कटाव एक वास्तविक शून्यक बताता है। इसलिए (4) कटावों से (4) वास्तविक शून्यक मिलेंगे।
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Question 32/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(2)=5), तो क्या (2) बहुपद का शून्यक है?
If (p(2)=5), is (2) a zero of the polynomial?
#value-test
#not-zero
#polynomials
#easy
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A नहीं / No
B हाँ / Yes
C केवल द्विघात में / Only in quadratic
D केवल रैखिक में / Only in linear
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For (2) to be a zero, (p(2)=0) must hold. Here (p(2)=5), so (2) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For (2) to be a zero, (p(2)=0) must hold. Here (p(2)=5), so (2) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(2)=0) होना चाहिए। यहाँ (p(2)=5), इसलिए (2) शून्यक नहीं है।
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Question 33/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(a)=0), तो ग्राफ किस बिंदु से अवश्य गुजरेगा?
If (p(a)=0), through which point must the graph pass?
#general-zero
#coordinate
#graph
#polynomials
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A ((a,0))
B ((0,a))
C ((a,a))
D ((-a,0))
Explanation opens after your attempt
Correct Answer
A. ((a,0))
Step 1
Concept
(p(a)=0) means (y=0) at (x=a). Therefore the graph passes through ((a,0)).
Step 2
Why this answer is correct
The correct answer is A. ((a,0)). (p(a)=0) means (y=0) at (x=a). Therefore the graph passes through ((a,0)).
Step 3
Exam Tip
(p(a)=0) का अर्थ है (x=a) पर (y=0)। इसलिए ग्राफ ((a,0)) से गुजरेगा।
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Question 34/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को (x=1), (x=3), और (x=6) पर काटता है, तो शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at (x=1), (x=3), and (x=6), what are the zeroes?
#x-values
#zeroes
#graph-reading
#easy
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A (1), (3), (6)
B (0), (3), (6)
C (1), (0), (6)
D (-1), (-3), (-6)
Explanation opens after your attempt
Correct Answer
A. (1), (3), (6)
Step 1
Concept
Zeroes are the (x)-values where the graph cuts the (x)-axis. So the zeroes are (1), (3), and (6).
Step 2
Why this answer is correct
The correct answer is A. (1), (3), (6). Zeroes are the (x)-values where the graph cuts the (x)-axis. So the zeroes are (1), (3), and (6).
Step 3
Exam Tip
शून्यक वही (x)-मान होते हैं जहाँ ग्राफ (x)-अक्ष को काटता है। इसलिए शून्यक (1), (3), और (6) हैं।
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Question 35/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को ((-1,0)) और ((5,0)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at ((-1,0)) and ((5,0)), how many real zeroes are there?
#parabola
#two-zeroes
#x-intercepts
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 3
Exam Tip
दो अलग-अलग (x)-अक्ष कटाव दो वास्तविक शून्यक बताते हैं। यहाँ शून्यक (-1) और (5) हैं।
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Question 36/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को ((2,0)) पर छूकर ऊपर लौट जाता है, तो शून्यकों की संख्या क्या होगी?
If a parabola touches the (x)-axis at ((2,0)) and turns upward, how many zeroes does it have?
#touching-parabola
#one-zero
#quadratic
#easy
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A एक / One
B दो / Two
C कोई नहीं / None
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
The parabola meets the (x)-axis at only one point. Therefore it has one real zero, (2).
Step 2
Why this answer is correct
The correct answer is A. एक / One. The parabola meets the (x)-axis at only one point. Therefore it has one real zero, (2).
Step 3
Exam Tip
परवलय (x)-अक्ष से केवल एक बिंदु पर मिलता है। इसलिए उसका एक वास्तविक शून्यक (2) होगा।
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Question 37/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस स्थिति में द्विघात बहुपद के दो वास्तविक शून्यक होंगे?
In which case will a quadratic polynomial have two real zeroes?
#quadratic-zeroes
#parabola
#x-axis
#concept
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A जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
B जब उसका ग्राफ (y)-अक्ष को एक बार काटे / When its graph cuts the (y)-axis once
C जब उसका ग्राफ (x)-अक्ष को न काटे / When its graph does not cut the (x)-axis
D जब उसका ग्राफ केवल ऊपर हो / When its graph is only above
Explanation opens after your attempt
Correct Answer
A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
Step 1
Concept
Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points. Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 3
Exam Tip
द्विघात बहुपद के वास्तविक शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। दो अलग कटाव दो वास्तविक शून्यक देते हैं।
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Question 38/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस स्थिति में द्विघात बहुपद का कोई वास्तविक शून्यक नहीं होगा?
In which case will a quadratic polynomial have no real zero?
#no-real-zero
#quadratic-graph
#parabola
#easy
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A जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis
B जब उसका ग्राफ (x)-अक्ष को दो बार काटे / When its graph cuts the (x)-axis twice
C जब उसका ग्राफ (x)-अक्ष को एक बार छुए / When its graph touches the (x)-axis once
D जब उसका ग्राफ मूल बिंदु से गुजरे / When its graph passes through origin
Explanation opens after your attempt
Correct Answer
A. जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis
Step 1
Concept
For real zeroes, the graph must meet the (x)-axis. If it does not meet the (x)-axis, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis. For real zeroes, the graph must meet the (x)-axis. If it does not meet the (x)-axis, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो कोई वास्तविक शून्यक नहीं होगा।
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Question 39/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद के ग्राफ में (x)-अक्ष से कटावों की संख्या क्या बताती है?
What does the number of intersections with the (x)-axis tell in a polynomial graph?
#graph-reading
#number-of-zeroes
#x-axis
#concept
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A वास्तविक शून्यकों की संख्या / Number of real zeroes
B गुणांकों की संख्या / Number of coefficients
C घातांक का मान हमेशा / Always the degree
D (y)-अक्ष का कटाव / (y)-intercept
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या / Number of real zeroes
Step 1
Concept
The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या / Number of real zeroes. The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 3
Exam Tip
ग्राफ जितनी बार (x)-अक्ष से अलग-अलग मिलता है, उतने वास्तविक शून्यक होते हैं। इसे ग्राफ पढ़ते समय सबसे पहले देखें।
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Question 40/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((-4,0)) पर काटता है, तो कौन-सा मान बहुपद को शून्य बनाता है?
If a graph cuts the (x)-axis at ((-4,0)), which value makes the polynomial zero?
#negative-x-intercept
#zeroes
#graph
#easy
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A (-4)
B (4)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of the intersection point is (-4). Therefore the polynomial value is (0) at (x=-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). The (x)-coordinate of the intersection point is (-4). Therefore the polynomial value is (0) at (x=-4).
Step 3
Exam Tip
कटाव बिंदु का (x)-निर्देशांक (-4) है। इसलिए (x=-4) पर बहुपद का मान (0) होगा।
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Question 41/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(0)=0), तो ग्राफ किस विशेष बिंदु से गुजरेगा?
If (p(0)=0), through which special point will the graph pass?
#origin
#zero
#p-of-zero
#graph
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A मूल बिंदु / Origin
B केवल ((1,0)) / Only ((1,0))
C केवल ((0,1)) / Only ((0,1))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. मूल बिंदु / Origin
Step 1
Concept
(p(0)=0) means (y=0) at (x=0). So the graph passes through the origin ((0,0)).
Step 2
Why this answer is correct
The correct answer is A. मूल बिंदु / Origin. (p(0)=0) means (y=0) at (x=0). So the graph passes through the origin ((0,0)).
Step 3
Exam Tip
(p(0)=0) का अर्थ है (x=0) पर (y=0)। इसलिए ग्राफ मूल बिंदु ((0,0)) से गुजरेगा।
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Question 42/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस बहुपद का ग्राफ (x)-अक्ष को (x=0) पर काटेगा?
Which polynomial graph will cut the (x)-axis at (x=0)?
#condition-for-zero
#origin
#x-axis
#polynomial
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A जिसके लिए (p(0)=0) / One for which (p(0)=0)
B जिसके लिए (p(0)=5) / One for which (p(0)=5)
C जिसके लिए (p(1)=0) / One for which (p(1)=0)
D जिसके लिए (p(-1)=1) / One for which (p(-1)=1)
Explanation opens after your attempt
Correct Answer
A. जिसके लिए (p(0)=0) / One for which (p(0)=0)
Step 1
Concept
To cut the (x)-axis at (x=0), the (y)-value must be (0). Hence (p(0)=0) is required.
Step 2
Why this answer is correct
The correct answer is A. जिसके लिए (p(0)=0) / One for which (p(0)=0). To cut the (x)-axis at (x=0), the (y)-value must be (0). Hence (p(0)=0) is required.
Step 3
Exam Tip
(x=0) पर (x)-अक्ष से कटने के लिए (y=0) होना चाहिए। इसलिए (p(0)=0) होना जरूरी है।
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Question 43/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि बहुपद का ग्राफ (x)-अक्ष को ((a,0)) पर काटता है, तो शून्यक क्या होगा?
If the graph of a polynomial cuts the (x)-axis at ((a,0)), what is the zero?
#general-coordinate
#zeroes
#x-intercept
#easy
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A (a)
B (0)
C (-a)
D \(a^2\)
Explanation opens after your attempt
Step 1
Concept
The zero is the (x)-coordinate of the intersection point. In ((a,0)), the (x)-coordinate is (a).
Step 2
Why this answer is correct
The correct answer is A. (a). The zero is the (x)-coordinate of the intersection point. In ((a,0)), the (x)-coordinate is (a).
Step 3
Exam Tip
शून्यक कटाव बिंदु का (x)-निर्देशांक होता है। ((a,0)) में (x)-निर्देशांक (a) है।
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Question 44/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
बहुपद के शून्यकों को ग्राफ में किस नाम से भी समझा जा सकता है?
By what name can the zeroes of a polynomial also be understood on a graph?
#x-intercepts
#zeroes
#terminology
#graph
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A (x)-अवरोध / (x)-intercepts
B (y)-अवरोध / (y)-intercepts
C ढाल / Slope
D शीर्ष / Vertex
Explanation opens after your attempt
Correct Answer
A. (x)-अवरोध / (x)-intercepts
Step 1
Concept
Zeroes are the (x)-values where the graph cuts or touches the (x)-axis. Hence they are linked with (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. (x)-अवरोध / (x)-intercepts. Zeroes are the (x)-values where the graph cuts or touches the (x)-axis. Hence they are linked with (x)-intercepts.
Step 3
Exam Tip
शून्यक वही (x)-मान हैं जहाँ ग्राफ (x)-अक्ष को काटता या छूता है। इसलिए इन्हें (x)-अवरोध से जोड़ा जाता है।
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Question 45/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x)-अक्ष को एक बार काटता और एक बार छूता है, तो अलग-अलग वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph cuts the (x)-axis once and touches it once, how many distinct real zeroes will it have?
#distinct-zeroes
#touching-cutting
#x-axis
#polynomials
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching count as meeting the (x)-axis. If the two points are distinct, there are two distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Both cutting and touching count as meeting the (x)-axis. If the two points are distinct, there are two distinct real zeroes.
Step 3
Exam Tip
कटना और छूना दोनों (x)-अक्ष से मिलना है। यदि दोनों बिंदु अलग हैं, तो दो अलग वास्तविक शून्यक होंगे।
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Question 46/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((8,0)) पर काटता है, तो (p(8)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((8,0)), what is the value of (p(8))?
#function-value
#x-axis
#zeroes
#easy
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A (0)
B (8)
C (-8)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((8,0)), (p(8)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((8,0)), (p(8)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((8,0)) पर (p(8)=0) होगा।
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Question 47/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(-6)=0), तो कौन-सा बिंदु ग्राफ पर होगा?
If (p(-6)=0), which point will lie on the graph?
#graph-point
#function-value
#negative-zero
#easy
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A ((-6,0))
B ((6,0))
C ((0,-6))
D ((0,6))
Explanation opens after your attempt
Correct Answer
A. ((-6,0))
Step 1
Concept
(p(-6)=0) means (y=0) at (x=-6). So the point ((-6,0)) lies on the graph.
Step 2
Why this answer is correct
The correct answer is A. ((-6,0)). (p(-6)=0) means (y=0) at (x=-6). So the point ((-6,0)) lies on the graph.
Step 3
Exam Tip
(p(-6)=0) बताता है कि (x=-6) पर (y=0) है। इसलिए बिंदु ((-6,0)) ग्राफ पर होगा।
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Question 48/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी ग्राफ का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो शून्यकों के बारे में क्या निष्कर्ष है?
If a graph has no common point with the (x)-axis, what is the conclusion about its zeroes?
#no-common-point
#no-real-zero
#graph
#polynomials
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A कोई वास्तविक शून्यक नहीं / No real zero
B एक वास्तविक शून्यक / One real zero
C दो वास्तविक शून्यक / Two real zeroes
D अनंत वास्तविक शून्यक / Infinite real zeroes
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक शून्यक नहीं / No real zero
Step 1
Concept
Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zero. Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक ग्राफ और (x)-अक्ष के साझा बिंदुओं से मिलते हैं। साझा बिंदु न हो तो वास्तविक शून्यक नहीं होगा।
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Question 49/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
एक बहुपद का ग्राफ (x)-अक्ष को केवल ((-2,0)) पर छूता है। अलग वास्तविक शून्यक कौन-सा है?
A polynomial graph only touches the (x)-axis at ((-2,0)). What is the distinct real zero?
#touching-point
#distinct-zero
#graph
#easy
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A (-2)
B (2)
C (0)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
A touching point also gives (p(x)=0). Therefore the distinct real zero is (-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). A touching point also gives (p(x)=0). Therefore the distinct real zero is (-2).
Step 3
Exam Tip
छूने वाला बिंदु भी (p(x)=0) देता है। इसलिए अलग वास्तविक शून्यक (-2) है।
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Question 50/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((r,0)) और ((s,0)) पर काटता है, जहाँ \(r\neq s\), तो शून्यक क्या होंगे?
If a graph cuts the (x)-axis at ((r,0)) and ((s,0)), where \(r\neq s\), what are the zeroes?
#general-zeroes
#x-intercepts
#polynomial-graph
#easy
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A (r) और (s) / (r) and (s)
B (0) और (0) / (0) and (0)
C (-r) और (-s) / (-r) and (-s)
D (r+s) और (rs) / (r+s) and (rs)
Explanation opens after your attempt
Correct Answer
A. (r) और (s) / (r) and (s)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (r) and (s).
Step 2
Why this answer is correct
The correct answer is A. (r) और (s) / (r) and (s). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (r) and (s).
Step 3
Exam Tip
शून्यक (x)-अक्ष के कटाव बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (r) और (s) हैं।
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Question 51/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी बहुपद के ग्राफ पर शून्यक पहचानने के लिए कौन-सा मान शून्य होना चाहिए?
Which value must be zero to identify a zero on the graph of a polynomial?
#polynomials
#zeroes
#graph
#value-test
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A बहुपद का मान / Value of the polynomial
B चर का गुणांक / Coefficient of the variable
C घात का मान / Value of the degree
D स्थिर पद / Constant term
Explanation opens after your attempt
Correct Answer
A. बहुपद का मान / Value of the polynomial
Step 1
Concept
At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 2
Why this answer is correct
The correct answer is A. बहुपद का मान / Value of the polynomial. At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। ग्राफ पढ़ते समय (y=0) वाले बिंदु देखें।
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Question 52/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((-4,0)) और ((1,0)) पर काटता है, तो शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at ((-4,0)) and ((1,0)), what are the zeroes?
#x-intercepts
#zeroes
#graph-reading
#polynomials
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A (-4) और (1) / (-4) and (1)
B (4) और (-1) / (4) and (-1)
C (-4) और (0) / (-4) and (0)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (-4) और (1) / (-4) and (1)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (-4) and (1).
Step 2
Why this answer is correct
The correct answer is A. (-4) और (1) / (-4) and (1). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (-4) and (1).
Step 3
Exam Tip
शून्यक (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-4) और (1) हैं।
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Question 53/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद के ग्राफ का (x)-अक्ष से केवल एक साझा बिंदु ((6,0)) है, तो अलग वास्तविक शून्यक क्या होगा?
If a polynomial graph has only one common point with the (x)-axis at ((6,0)), what is the distinct real zero?
#distinct-zero
#x-axis
#graph
#easy
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A (6)
B (-6)
C (0)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The common point ((6,0)) has (x)-coordinate (6). So the distinct real zero is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The common point ((6,0)) has (x)-coordinate (6). So the distinct real zero is (6).
Step 3
Exam Tip
एक साझा बिंदु ((6,0)) का (x)-निर्देशांक (6) है। इसलिए अलग वास्तविक शून्यक (6) होगा।
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Question 54/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(9)=0), तो ग्राफ किस बिंदु से गुजरेगा?
If (p(9)=0), through which point will the graph pass?
#function-value
#graph-point
#zeroes
#class-10
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A ((9,0))
B ((0,9))
C ((-9,0))
D ((9,9))
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Correct Answer
A. ((9,0))
Step 1
Concept
(p(9)=0) means (y=0) when (x=9). Therefore the graph passes through ((9,0)).
Step 2
Why this answer is correct
The correct answer is A. ((9,0)). (p(9)=0) means (y=0) when (x=9). Therefore the graph passes through ((9,0)).
Step 3
Exam Tip
(p(9)=0) का अर्थ है (x=9) पर (y=0)। इसलिए ग्राफ ((9,0)) से गुजरेगा।
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Question 55/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-3)=0), तो बहुपद का कौन-सा शून्यक है?
If (p(-3)=0), which value is a zero of the polynomial?
#zero-definition
#function-value
#negative-zero
#easy
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A (-3)
B (3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (-3). The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 3
Exam Tip
जिस (x)-मान पर (p(x)=0) हो वही शून्यक होता है। इसलिए (-3) बहुपद का शून्यक है।
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Question 56/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी ग्राफ का (y)-अक्ष से कटना शून्यक क्यों नहीं बताता?
Why does the intersection of a graph with the (y)-axis not directly give a zero?
#common-mistake
#y-intercept
#x-intercept
#zeroes
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A क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0)
B क्योंकि शून्यक के लिए (x=0) चाहिए / Because a zero needs (x=0)
C क्योंकि हर बिंदु शून्यक होता है / Because every point is a zero
D क्योंकि (y)-अक्ष पर ग्राफ नहीं बनता / Because graphs are not drawn on the (y)-axis
Explanation opens after your attempt
Correct Answer
A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0)
Step 1
Concept
Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0). Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 3
Exam Tip
शून्यक (x)-अक्ष से जुड़े होते हैं जहाँ (y=0) होता है। (y)-अक्ष से कटाव केवल (x=0) पर बहुपद का मान बताता है।
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Question 57/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at three distinct points, how many real zeroes will it have?
#real-zeroes
#x-axis
#graph-reading
#easy
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A तीन / Three
B दो / Two
C एक / One
D कोई नहीं / None
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Correct Answer
A. तीन / Three
Step 1
Concept
Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 3
Exam Tip
हर अलग (x)-अक्ष कटाव एक वास्तविक शून्यक देता है। इसलिए तीन अलग कटावों से तीन वास्तविक शून्यक मिलेंगे।
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Question 58/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो द्विघात बहुपद के वास्तविक शून्यक कितने होंगे?
If a parabola has no common point with the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-polynomial
#parabola
#no-real-zero
#graph
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 3
Exam Tip
वास्तविक शून्यक तभी मिलते हैं जब ग्राफ (x)-अक्ष से मिले। साझा बिंदु न होने पर वास्तविक शून्यक (0) होंगे।
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Question 59/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि परवलय (x)-अक्ष को ((3,0)) पर केवल छूता है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या है?
If a parabola only touches the (x)-axis at ((3,0)), how many real zeroes does the quadratic polynomial have?
#touching-x-axis
#one-zero
#parabola
#easy
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A एक / One
B दो / Two
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 3
Exam Tip
छूना भी (x)-अक्ष से मिलना है, लेकिन बिंदु केवल एक है। इसलिए एक वास्तविक शून्यक होगा।
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Question 60/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि परवलय (x)-अक्ष को ((-5,0)) और ((2,0)) पर काटता है, तो शून्यक कौन-से होंगे?
If a parabola cuts the (x)-axis at ((-5,0)) and ((2,0)), what will be the zeroes?
#parabola
#two-zeroes
#x-intercepts
#easy
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A (-5) और (2) / (-5) and (2)
B (5) और (-2) / (5) and (-2)
C (-5) और (0) / (-5) and (0)
D (0) और (2) / (0) and (2)
Explanation opens after your attempt
Correct Answer
A. (-5) और (2) / (-5) and (2)
Step 1
Concept
Zeroes are the (x)-coordinates of the intersection points. Hence the zeroes are (-5) and (2).
Step 2
Why this answer is correct
The correct answer is A. (-5) और (2) / (-5) and (2). Zeroes are the (x)-coordinates of the intersection points. Hence the zeroes are (-5) and (2).
Step 3
Exam Tip
शून्यक कटाव बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-5) और (2) हैं।
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Question 61/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
ग्राफ में (x)-अक्ष से कटाव बिंदु ((a,0)) हो, तो (p(a)) का मान क्या होगा?
If ((a,0)) is an intersection point with the (x)-axis on the graph, what is the value of (p(a))?
#general-point
#p-of-a
#zeroes
#x-axis
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A (0)
B (a)
C (-a)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((a,0)), (p(a)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((a,0)), (p(a)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((a,0)) पर (p(a)=0) होगा।
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Question 62/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(0)=4), तो क्या (0) बहुपद का शून्यक है?
If (p(0)=4), is (0) a zero of the polynomial?
#value-test
#not-zero
#origin
#polynomials
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A नहीं / No
B हाँ / Yes
C केवल रैखिक बहुपद में / Only in a linear polynomial
D केवल द्विघात बहुपद में / Only in a quadratic polynomial
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For (0) to be a zero, (p(0)=0) must be true. Here (p(0)=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For (0) to be a zero, (p(0)=0) must be true. Here (p(0)=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(0)=0) होना चाहिए। यहाँ (p(0)=4), इसलिए (0) शून्यक नहीं है।
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Question 63/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
रेखा (y=3x-12) का (x)-अक्ष से कटाव किस (x)-मान पर होगा?
At which (x)-value will the line (y=3x-12) cut the (x)-axis?
#linear-polynomial
#x-intercept
#zero
#easy
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A (4)
B (-4)
C (12)
D (3)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (3x-12=0) gives (x=4). This is the zero.
Step 2
Why this answer is correct
The correct answer is A. (4). On the (x)-axis, (y=0), so (3x-12=0) gives (x=4). This is the zero.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (3x-12=0) से (x=4) मिलता है। यही शून्यक है।
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Question 64/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
रेखा (y=x-8) का शून्यक कौन-सा है?
What is the zero of the line (y=x-8)?
#linear-graph
#zero
#x-axis
#easy
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A (8)
B (-8)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
For the zero, (y=0), so (x-8=0) gives (x=8). The graph cuts the (x)-axis at (8).
Step 2
Why this answer is correct
The correct answer is A. (8). For the zero, (y=0), so (x-8=0) gives (x=8). The graph cuts the (x)-axis at (8).
Step 3
Exam Tip
शून्यक के लिए (y=0), इसलिए (x-8=0) से (x=8) मिलता है। ग्राफ (x)-अक्ष को (8) पर काटता है।
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Question 65/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
रेखा (y=x+9) का शून्यक क्या होगा?
What will be the zero of the line (y=x+9)?
#linear-polynomial
#negative-zero
#x-intercept
#polynomials
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A (9)
B (-9)
C (0)
D (18)
Explanation opens after your attempt
Step 1
Concept
For the zero, (x+9=0), so (x=-9). Do not make a sign error.
Step 2
Why this answer is correct
The correct answer is B. (-9). For the zero, (x+9=0), so (x=-9). Do not make a sign error.
Step 3
Exam Tip
शून्यक के लिए (x+9=0), इसलिए (x=-9)। चिह्न बदलने की गलती न करें।
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Question 66/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=2x+6), तो ग्राफ का (x)-अक्ष से कटाव किस (x)-मान पर होगा?
If (p(x)=2x+6), at which (x)-value will the graph cut the (x)-axis?
#linear-polynomial
#graphical-zero
#value-test
#easy
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A (-3)
B (3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (p(x)=0), so (2x+6=0) gives (x=-3). This is the graphical zero.
Step 2
Why this answer is correct
The correct answer is A. (-3). On the (x)-axis, (p(x)=0), so (2x+6=0) gives (x=-3). This is the graphical zero.
Step 3
Exam Tip
(x)-अक्ष पर (p(x)=0), इसलिए (2x+6=0) से (x=-3)। यही ग्राफीय शून्यक है।
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Question 67/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((10,0)) पर काटता है, तो कौन-सा कथन सही है?
If a graph cuts the (x)-axis at ((10,0)), which statement is correct?
#x-intercept
#zero
#coordinate
#graph
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A (10) शून्यक है / (10) is a zero
B (0) शून्यक है / (0) is a zero
C (-10) शून्यक है / (-10) is a zero
D (10) स्थिर पद है / (10) is the constant term
Explanation opens after your attempt
Correct Answer
A. (10) शून्यक है / (10) is a zero
Step 1
Concept
The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (10) शून्यक है / (10) is a zero. The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 3
Exam Tip
कटाव बिंदु का (x)-निर्देशांक (10) है। इसलिए (10) बहुपद का शून्यक है।
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Question 68/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ ((0,7)) से गुजरता है, तो क्या इससे (0) शून्यक सिद्ध होता है?
If a graph passes through ((0,7)), does it prove that (0) is a zero?
#common-mistake
#y-intercept
#zeroes
#graph
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A नहीं, क्योंकि (y=7) है / No, because (y=7)
B हाँ, क्योंकि (x=0) है / Yes, because (x=0)
C हाँ, क्योंकि यह (y)-अक्ष पर है / Yes, because it is on the (y)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. नहीं, क्योंकि (y=7) है / No, because (y=7)
Step 1
Concept
For a zero, (y=0) is needed. In ((0,7)), (y=7), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि (y=7) है / No, because (y=7). For a zero, (y=0) is needed. In ((0,7)), (y=7), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) चाहिए। ((0,7)) में (y=7) है, इसलिए (0) शून्यक नहीं है।
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Question 69/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि बहुपद का ग्राफ (x)-अक्ष को ((-7,0)), ((0,0)), और ((4,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of a polynomial cuts the (x)-axis at ((-7,0)), ((0,0)), and ((4,0)), what are the zeroes?
#multiple-zeroes
#x-axis
#coordinates
#easy
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A (-7), (0), (4)
B (7), (0), (-4)
C (-7), (4), (7)
D (0), (0), (4)
Explanation opens after your attempt
Correct Answer
A. (-7), (0), (4)
Step 1
Concept
The zeroes are the (x)-coordinates of these points. Hence the zeroes are (-7), (0), and (4).
Step 2
Why this answer is correct
The correct answer is A. (-7), (0), (4). The zeroes are the (x)-coordinates of these points. Hence the zeroes are (-7), (0), and (4).
Step 3
Exam Tip
शून्यक इन बिंदुओं के (x)-निर्देशांक हैं। इसलिए शून्यक (-7), (0), और (4) होंगे।
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Question 70/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी स्थिर अशून्य बहुपद (p(x)=-3) का ग्राफ (x)-अक्ष को क्यों नहीं काटता?
Why does the graph of the non-zero constant polynomial (p(x)=-3) not cut the (x)-axis?
#constant-polynomial
#no-zero
#x-axis
#easy
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A क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
B क्योंकि (x) हमेशा (-3) रहता है / Because (x) always remains (-3)
C क्योंकि ग्राफ पर कोई बिंदु नहीं होता / Because the graph has no point
D क्योंकि यह परवलय है / Because it is a parabola
Explanation opens after your attempt
Correct Answer
A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
Step 1
Concept
For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3). For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 3
Exam Tip
(p(x)=-3) का (y)-मान कभी (0) नहीं होता। इसलिए ग्राफ (x)-अक्ष को नहीं काटता और कोई शून्यक नहीं है।
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Question 71/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(c)=0), तो (c) को क्या कहते हैं?
If (p(c)=0), what is (c) called?
#definition
#zero-of-polynomial
#p-of-c
#easy
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A बहुपद का शून्यक / Zero of the polynomial
B बहुपद का घातांक / Degree of the polynomial
C बहुपद का स्थिर पद / Constant term of the polynomial
D बहुपद का गुणांक / Coefficient of the polynomial
Explanation opens after your attempt
Correct Answer
A. बहुपद का शून्यक / Zero of the polynomial
Step 1
Concept
The value for which the polynomial becomes (0) is called a zero. Therefore (c) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. बहुपद का शून्यक / Zero of the polynomial. The value for which the polynomial becomes (0) is called a zero. Therefore (c) is a zero of the polynomial.
Step 3
Exam Tip
जिस मान पर बहुपद का मान (0) हो, वह शून्यक कहलाता है। इसलिए (c) बहुपद का शून्यक है।
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Question 72/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
ग्राफ में बिंदु ((-8,0)) दिखने पर बहुपद का कौन-सा मान शून्य होगा?
If the point ((-8,0)) appears on the graph, which value of the polynomial input gives zero?
#negative-zero
#coordinate-reading
#x-intercept
#polynomials
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A (x=-8)
B (x=8)
C (x=0)
D (x=-1)
Explanation opens after your attempt
Step 1
Concept
The point ((-8,0)) means (y=0) at (x=-8). So (x=-8) makes the polynomial zero.
Step 2
Why this answer is correct
The correct answer is A. (x=-8). The point ((-8,0)) means (y=0) at (x=-8). So (x=-8) makes the polynomial zero.
Step 3
Exam Tip
((-8,0)) का अर्थ है (x=-8) पर (y=0)। इसलिए (x=-8) बहुपद को शून्य बनाता है।
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Question 73/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को (x=2) और (x=9) पर काटता है, तो (p(2)) और (p(9)) के मान क्या होंगे?
If a graph cuts the (x)-axis at (x=2) and (x=9), what will be the values of (p(2)) and (p(9))?
#function-values
#x-intercepts
#zeroes
#easy
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A दोनों (0) / Both (0)
B दोनों (1) / Both (1)
C (p(2)=2) और (p(9)=9) / (p(2)=2) and (p(9)=9)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. दोनों (0) / Both (0)
Step 1
Concept
On the (x)-axis, (y=0). Therefore the polynomial value at both these (x)-values is (0).
Step 2
Why this answer is correct
The correct answer is A. दोनों (0) / Both (0). On the (x)-axis, (y=0). Therefore the polynomial value at both these (x)-values is (0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए इन दोनों (x)-मानों पर बहुपद का मान (0) होगा।
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Question 74/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का शीर्ष ((-2,0)) पर है और वह (x)-अक्ष को वहीं छूता है, तो शून्यक क्या होगा?
If the vertex of a parabola is at ((-2,0)) and it touches the (x)-axis there, what is the zero?
#vertex
#parabola
#touching-x-axis
#zero
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A (-2)
B (2)
C (0)
D दो शून्यक होंगे / There will be two zeroes
Explanation opens after your attempt
Step 1
Concept
The parabola meets the (x)-axis only at ((-2,0)). Hence its real zero is (-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). The parabola meets the (x)-axis only at ((-2,0)). Hence its real zero is (-2).
Step 3
Exam Tip
परवलय (x)-अक्ष से केवल ((-2,0)) पर मिलता है। इसलिए उसका वास्तविक शून्यक (-2) है।
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Question 75/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किस ग्राफ से शून्यक (1) और (-6) मिलेंगे?
Which graph will give zeroes (1) and (-6)?
#graph-from-zeroes
#x-intercepts
#polynomial-graph
#easy
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A जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0))
B जो (y)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (y)-axis at ((1,0)) and ((-6,0))
C जो (x)-अक्ष को ((0,1)) और ((0,-6)) पर काटे / One that cuts the (x)-axis at ((0,1)) and ((0,-6))
D जो (x)-अक्ष को न काटे / One that does not cut the (x)-axis
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0))
Step 1
Concept
If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0)). If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 3
Exam Tip
शून्यक (1) और (-6) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((1,0)) और ((-6,0)) होंगे।
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Question 76/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि कोई ग्राफ (x)-अक्ष को केवल छूता है, तो क्या वह बिंदु शून्यक देगा?
If a graph only touches the (x)-axis, will that point give a zero?
#touching-x-axis
#zeroes
#concept
#easy
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A हाँ / Yes
B नहीं / No
C केवल रेखा में / Only for a line
D केवल तब जब (y=1) हो / Only when (y=1)
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Even when the graph touches, the point lies on the (x)-axis and (y=0). Therefore that point gives a zero.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Even when the graph touches, the point lies on the (x)-axis and (y=0). Therefore that point gives a zero.
Step 3
Exam Tip
छूने पर भी बिंदु (x)-अक्ष पर होता है और (y=0) होता है। इसलिए वह बिंदु शून्यक देता है।
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Question 77/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष के नीचे पूरा बना है और (x)-अक्ष को नहीं छूता, तो वास्तविक शून्यक कितने हैं?
If a graph lies completely below the (x)-axis and does not touch it, how many real zeroes does it have?
#no-real-zero
#below-x-axis
#graph
#easy
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A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। नीचे रहने और न छूने पर कोई वास्तविक शून्यक नहीं होगा।
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Question 78/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(5)\neq 0), तो (5) के बारे में क्या कहा जाएगा?
If (p(5)\neq 0), what can be said about (5)?
#not-zero
#value-test
#polynomial
#easy
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A (5) शून्यक नहीं है / (5) is not a zero
B (5) शून्यक है / (5) is a zero
C (5) हमेशा दोहरा शून्यक है / (5) is always a repeated zero
D जानकारी अपूर्ण है / Information is incomplete
Explanation opens after your attempt
Correct Answer
A. (5) शून्यक नहीं है / (5) is not a zero
Step 1
Concept
For (5) to be a zero, (p(5)=0) is necessary. If (p(5)\neq 0), then (5) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. (5) शून्यक नहीं है / (5) is not a zero. For (5) to be a zero, (p(5)=0) is necessary. If (p(5)\neq 0), then (5) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(5)=0) जरूरी है। यदि (p(5)\neq 0), तो (5) शून्यक नहीं है।
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Question 79/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-10)=0), तो (x)-अक्ष पर संबंधित बिंदु कौन-सा होगा?
If (p(-10)=0), which corresponding point will be on the (x)-axis?
#x-axis-point
#function-value
#negative-zero
#easy
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A ((-10,0))
B ((10,0))
C ((0,-10))
D ((-10,-10))
Explanation opens after your attempt
Correct Answer
A. ((-10,0))
Step 1
Concept
(p(-10)=0) means (y=0) at (x=-10). Therefore the point on the (x)-axis is ((-10,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-10,0)). (p(-10)=0) means (y=0) at (x=-10). Therefore the point on the (x)-axis is ((-10,0)).
Step 3
Exam Tip
(p(-10)=0) का अर्थ है (x=-10) पर (y=0)। इसलिए (x)-अक्ष पर बिंदु ((-10,0)) होगा।
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Question 80/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी बहुपद के ग्राफ में (x)-अक्ष से अलग-अलग मिलने वाले बिंदुओं की संख्या क्या बताती है?
What does the number of distinct meeting points with the (x)-axis tell in a polynomial graph?
#number-of-zeroes
#x-axis
#graphical-meaning
#concept
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A वास्तविक शून्यकों की संख्या / Number of real zeroes
B केवल स्थिर पद / Only constant term
C केवल (y)-अवरोध / Only (y)-intercept
D गुणांकों का योग / Sum of coefficients
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या / Number of real zeroes
Step 1
Concept
The number of distinct points where the graph meets the (x)-axis gives the number of real zeroes. This is the main graphical rule.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या / Number of real zeroes. The number of distinct points where the graph meets the (x)-axis gives the number of real zeroes. This is the main graphical rule.
Step 3
Exam Tip
ग्राफ जितनी बार अलग-अलग (x)-अक्ष से मिलता है, उतने वास्तविक शून्यक होते हैं। यह ग्राफीय अर्थ का मुख्य नियम है।
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Question 81/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=4) है, तो ग्राफ (x)-अक्ष से कैसा संबंध रखेगा?
If (p(x)=4), how is the graph related to the (x)-axis?
#constant-polynomial
#parallel-line
#no-zero
#easy
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A यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it
B यह (x)-अक्ष को चार बार काटेगा / It cuts the (x)-axis four times
C यह मूल बिंदु से गुजरेगा / It passes through the origin
D यह परवलय होगा / It is a parabola
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it
Step 1
Concept
In (p(x)=4), (y) is always (4) and never (0). Hence it has no zero.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it. In (p(x)=4), (y) is always (4) and never (0). Hence it has no zero.
Step 3
Exam Tip
(p(x)=4) में (y) हमेशा (4) है और कभी (0) नहीं होता। इसलिए इसका कोई शून्यक नहीं है।
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Question 82/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x), तो ग्राफ का शून्यक क्या है?
If (p(x)=x), what is the zero of the graph?
#linear-polynomial
#origin
#zero
#easy
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A (0)
B (1)
C (-1)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
For the zero, (x=0) because (p(x)=x). The graph passes through the origin.
Step 2
Why this answer is correct
The correct answer is A. (0). For the zero, (x=0) because (p(x)=x). The graph passes through the origin.
Step 3
Exam Tip
शून्यक के लिए (x=0) होना चाहिए क्योंकि (p(x)=x)। ग्राफ मूल बिंदु से गुजरता है।
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Question 83/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ के शून्यक (-1), (3), और (8) हैं, तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?
If the zeroes of a graph are (-1), (3), and (8), at which points will it cut the (x)-axis?
#zeroes-to-points
#x-intercepts
#graph
#easy
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A ((-1,0)), ((3,0)), ((8,0))
B ((0,-1)), ((0,3)), ((0,8))
C ((1,0)), ((-3,0)), ((-8,0))
D ((-1,1)), ((3,3)), ((8,8))
Explanation opens after your attempt
Correct Answer
A. ((-1,0)), ((3,0)), ((8,0))
Step 1
Concept
Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)), ((3,0)), ((8,0)). Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 3
Exam Tip
शून्यकों को (x)-निर्देशांक बनाकर (y=0) लिया जाता है। इसलिए कटाव बिंदु ((-1,0)), ((3,0)), और ((8,0)) होंगे।
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Question 84/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय के दो वास्तविक शून्यक हैं, तो वह (x)-अक्ष से कैसे मिलेगा?
If a parabola has two real zeroes, how will it meet the (x)-axis?
#quadratic
#two-real-zeroes
#parabola
#graph
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A दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
B कहीं नहीं मिलेगा / It will not meet anywhere
C एक ही बिंदु पर छुएगा / It will touch at one point
D पूरे (x)-अक्ष पर होगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
Step 1
Concept
Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 2
Why this answer is correct
The correct answer is A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points. Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 3
Exam Tip
दो वास्तविक शून्यक दो अलग (x)-अक्ष कटाव बताते हैं। इसलिए परवलय (x)-अक्ष को दो बिंदुओं पर काटेगा।
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Question 85/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का एक ही वास्तविक शून्यक है, तो ग्राफ (x)-अक्ष से कैसे मिलेगा?
If a parabola has exactly one real zero, how will its graph meet the (x)-axis?
#one-real-zero
#parabola
#tangent-case
#easy
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A एक बिंदु पर छुएगा / It will touch at one point
B दो बिंदुओं पर काटेगा / It will cut at two points
C कहीं नहीं मिलेगा / It will not meet
D चार बिंदुओं पर काटेगा / It will cut at four points
Explanation opens after your attempt
Correct Answer
A. एक बिंदु पर छुएगा / It will touch at one point
Step 1
Concept
One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 2
Why this answer is correct
The correct answer is A. एक बिंदु पर छुएगा / It will touch at one point. One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 3
Exam Tip
एक वास्तविक शून्यक का अर्थ है ग्राफ (x)-अक्ष से केवल एक बिंदु पर मिलता है। परवलय में यह सामान्यतः छूने की स्थिति होती है।
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Question 86/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((2,0)) पर काटता और ((5,0)) पर छूता है, तो अलग वास्तविक शून्यक कितने हैं?
If a graph cuts the (x)-axis at ((2,0)) and touches it at ((5,0)), how many distinct real zeroes are there?
#distinct-real-zeroes
#touching-cutting
#x-axis
#easy
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 3
Exam Tip
कटना और छूना दोनों (x)-अक्ष से मिलना है। दो अलग बिंदु हैं, इसलिए दो अलग वास्तविक शून्यक हैं।
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Question 87/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((r,0)) पर छूता है, तो (r) के बारे में क्या कहा जाएगा?
If a graph touches the (x)-axis at ((r,0)), what can be said about (r)?
#general-touching-point
#zeroes
#x-axis
#easy
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A (r) शून्यक है / (r) is a zero
B (r) स्थिर पद है / (r) is the constant term
C (r) घात है / (r) is the degree
D (r) शून्यक नहीं है / (r) is not a zero
Explanation opens after your attempt
Correct Answer
A. (r) शून्यक है / (r) is a zero
Step 1
Concept
Even when the graph touches, (y=0). Therefore the (x)-coordinate (r) of ((r,0)) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (r) शून्यक है / (r) is a zero. Even when the graph touches, (y=0). Therefore the (x)-coordinate (r) of ((r,0)) is a zero.
Step 3
Exam Tip
छूने पर भी (y=0) होता है। इसलिए ((r,0)) का (x)-निर्देशांक (r) शून्यक है।
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Question 88/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(12)=0), तो (12) को ग्राफ पर कैसे देखा जाएगा?
If (p(12)=0), how will (12) be seen on the graph?
#function-value
#graphical-meaning
#zeroes
#easy
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A ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12)
B ग्राफ (y)-अक्ष को (y=12) पर काटेगा / The graph will cut the (y)-axis at (y=12)
C ग्राफ (x=0) पर ही होगा / The graph will only be at (x=0)
D ग्राफ नहीं बनेगा / No graph will be formed
Explanation opens after your attempt
Correct Answer
A. ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12)
Step 1
Concept
(p(12)=0) means (y=0) at (x=12). So the graph will meet the (x)-axis there.
Step 2
Why this answer is correct
The correct answer is A. ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12). (p(12)=0) means (y=0) at (x=12). So the graph will meet the (x)-axis there.
Step 3
Exam Tip
(p(12)=0) का अर्थ है (x=12) पर (y=0)। इसलिए ग्राफ (x)-अक्ष से वहाँ मिलेगा।
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Question 89/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किस बिंदु पर ग्राफ होने से (x=11) शून्यक सिद्ध होगा?
Which point on the graph proves that (x=11) is a zero?
#point-identification
#zeroes
#x-axis
#graph
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A ((11,0))
B ((0,11))
C ((11,1))
D ((-11,0))
Explanation opens after your attempt
Correct Answer
A. ((11,0))
Step 1
Concept
For (x=11) to be a zero, (y=0) is needed. So the point must be ((11,0)).
Step 2
Why this answer is correct
The correct answer is A. ((11,0)). For (x=11) to be a zero, (y=0) is needed. So the point must be ((11,0)).
Step 3
Exam Tip
(x=11) शून्यक होने के लिए (y=0) चाहिए। इसलिए बिंदु ((11,0)) होना चाहिए।
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Question 90/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किस बिंदु पर ग्राफ होने से (x=-2) शून्यक सिद्ध होगा?
Which point on the graph proves that (x=-2) is a zero?
#negative-zero
#point-reading
#x-intercept
#easy
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A ((-2,0))
B ((2,0))
C ((0,-2))
D ((-2,2))
Explanation opens after your attempt
Correct Answer
A. ((-2,0))
Step 1
Concept
For (x=-2) to be a zero, (y=0) at that point. Hence the correct point is ((-2,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-2,0)). For (x=-2) to be a zero, (y=0) at that point. Hence the correct point is ((-2,0)).
Step 3
Exam Tip
(x=-2) शून्यक होने के लिए उस बिंदु पर (y=0) होना चाहिए। इसलिए सही बिंदु ((-2,0)) है।
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Question 91/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)) का ग्राफ मूल बिंदु से गुजरता है, तो कौन-सा मान शून्यक है?
If the graph of (p(x)) passes through the origin, which value is a zero?
#origin
#zeroes
#graph
#polynomials
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A (0)
B (1
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The origin is ((0,0)), so (p(x)=0) at (x=0). Hence (0) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (0). The origin is ((0,0)), so (p(x)=0) at (x=0). Hence (0) is a zero.
Step 3
Exam Tip
मूल बिंदु ((0,0)) है, इसलिए (x=0) पर (p(x)=0)। अतः (0) शून्यक है।
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Question 92/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि बहुपद के ग्राफ में (x)-अक्ष से मिलने वाले बिंदु ((-9,0)), ((-1,0)), और ((3,0)) हैं, तो वास्तविक शून्यक कितने हैं?
If the points where a polynomial graph meets the (x)-axis are ((-9,0)), ((-1,0)), and ((3,0)), how many real zeroes are there?
#counting-zeroes
#x-intercepts
#graph-reading
#easy
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A तीन / Three
B दो / Two
C एक / One
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 3
Exam Tip
तीन अलग (x)-अक्ष बिंदु तीन अलग वास्तविक शून्यक बताते हैं। उनके (x)-निर्देशांक ही शून्यक हैं।
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Question 93/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ में ((4,2)) बिंदु है, तो क्या (4) शून्यक है?
If a graph has the point ((4,2)), is (4) a zero?
#point-test
#not-zero
#graph
#easy
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A नहीं / No
B हाँ / Yes
C केवल यदि बहुपद द्विघात हो / Only if the polynomial is quadratic
D केवल यदि ग्राफ रेखा हो / Only if the graph is a line
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
In ((4,2)), (y=2), not (0). Therefore (x=4) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. In ((4,2)), (y=2), not (0). Therefore (x=4) is not a zero.
Step 3
Exam Tip
((4,2)) में (y=2) है, (0) नहीं। इसलिए (x=4) शून्यक नहीं है।
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Question 94/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((m,0)) और ((n,0)) पर काटता है, जहाँ \(m\neq n\), तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at ((m,0)) and ((n,0)), where \(m\neq n\), how many real zeroes will it have?
#general-zeroes
#distinct-points
#x-axis
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 3
Exam Tip
दो अलग कटाव बिंदु दो अलग वास्तविक शून्यक देते हैं। यहाँ शून्यक (m) और (n) होंगे।
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Question 95/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
ग्राफ में शून्यक देखने के लिए किस अक्ष पर ध्यान देना चाहिए?
Which axis should be observed to see the zeroes on a graph?
#x-axis
#zeroes
#graphical-meaning
#easy
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A (x)-अक्ष / (x)-axis
B (y)-अक्ष / (y)-axis
C दोनों अक्ष हमेशा / Both axes always
D कोई अक्ष नहीं / No axis
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष / (x)-axis
Step 1
Concept
Zeroes are obtained from the points where the graph meets the (x)-axis. So focus on the (x)-axis while reading the graph.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष / (x)-axis. Zeroes are obtained from the points where the graph meets the (x)-axis. So focus on the (x)-axis while reading the graph.
Step 3
Exam Tip
शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। इसलिए ग्राफ पढ़ते समय (x)-अक्ष पर ध्यान दें।
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Question 96/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((7,0)) पर काटता है, तो (p(7)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((7,0)), what will be the value of (p(7))?
#p-value
#x-axis
#zeroes
#easy
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A (0)
B (7)
C (-7)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((7,0)), (p(7)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((7,0)), (p(7)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((7,0)) पर (p(7)=0) होगा।
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Question 97/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-4)=0), तो ग्राफ (x)-अक्ष से कहाँ मिलेगा?
If (p(-4)=0), where will the graph meet the (x)-axis?
#negative-zero
#function-value
#x-axis
#easy
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A ((-4,0))
B ((4,0))
C ((0,-4))
D ((-4,4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
(p(-4)=0) means (y=0) when (x=-4). Therefore the graph meets the (x)-axis at ((-4,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). (p(-4)=0) means (y=0) when (x=-4). Therefore the graph meets the (x)-axis at ((-4,0)).
Step 3
Exam Tip
(p(-4)=0) बताता है कि (x=-4) पर (y=0) है। इसलिए ग्राफ (x)-अक्ष से ((-4,0)) पर मिलेगा।
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Question 98/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का ग्राफ (x)-अक्ष को बिल्कुल दो बार छूता या काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph touches or cuts the (x)-axis exactly two times, how many real zeroes will it have?
#touch-or-cut
#counting-zeroes
#x-axis
#easy
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से हर अलग मिलन एक वास्तविक शून्यक देता है। दो बार मिलने पर दो वास्तविक शून्यक होंगे।
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Question 99/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का कोई वास्तविक शून्यक नहीं है, तो उसका ग्राफ (x)-अक्ष के साथ क्या करेगा?
If a polynomial has no real zero, what will its graph do with the (x)-axis?
#no-real-zero
#graph
#x-axis
#concept
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A न तो काटेगा न छुएगा / It will neither cut nor touch it
B हमेशा दो बार काटेगा / It will always cut twice
C हमेशा एक बार छुएगा / It will always touch once
D पूरे (x)-अक्ष पर रहेगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. न तो काटेगा न छुएगा / It will neither cut nor touch it
Step 1
Concept
A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. न तो काटेगा न छुएगा / It will neither cut nor touch it. A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष से मिलने पर दिखता है। कोई वास्तविक शून्यक न होने पर ग्राफ (x)-अक्ष से नहीं मिलेगा।
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Question 100/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)) का ग्राफ (x)-अक्ष को ((u,0)), ((v,0)), और ((w,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of (p(x)) cuts the (x)-axis at ((u,0)), ((v,0)), and ((w,0)), what are the zeroes?
#general-zeroes
#coordinates
#x-intercepts
#polynomials
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A (u), (v), (w)
B (0), (0), (0)
C (-u), (-v), (-w)
D (u+v+w)
Explanation opens after your attempt
Correct Answer
A. (u), (v), (w)
Step 1
Concept
Zeroes are the (x)-coordinates of the (x)-axis intersections. Therefore the zeroes are (u), (v), and (w).
Step 2
Why this answer is correct
The correct answer is A. (u), (v), (w). Zeroes are the (x)-coordinates of the (x)-axis intersections. Therefore the zeroes are (u), (v), and (w).
Step 3
Exam Tip
शून्यक (x)-अक्ष कटावों के (x)-निर्देशांक होते हैं। इसलिए शून्यक (u), (v), और (w) हैं।
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Question 101/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद (p(x)) का शून्यक आलेख में किससे दर्शाया जाता है?
What represents a zero of a polynomial (p(x)) on its graph?
#polynomials zeroes graph
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A जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis
B जहाँ आलेख (y)-अक्ष को काटता है / Where the graph cuts the (y)-axis
C आलेख का सबसे ऊँचा बिंदु / The highest point of the graph
D आलेख का कोई भी बिंदु / Any point on the graph
Explanation opens after your attempt
Correct Answer
A. जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis
Step 1
Concept
At a zero (p(x)=0) so the point lies on the (x)-axis. Tip: on the (x)-axis (y=0).
Step 2
Why this answer is correct
The correct answer is A. जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis. At a zero (p(x)=0) so the point lies on the (x)-axis. Tip: on the (x)-axis (y=0).
Step 3
Exam Tip
शून्यक पर (p(x)=0) होता है इसलिए बिंदु (x)-अक्ष पर होता है। टिप: (x)-अक्ष पर (y=0) होता है।
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Question 102/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी रैखिक बहुपद का आलेख (x)-अक्ष को एक बार काटता है तो उसके कितने शून्यक होंगे?
If the graph of a linear polynomial cuts the (x)-axis once then how many zeroes does it have?
#polynomials linear graph
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A एक / One
B दो / Two
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 3
Exam Tip
जितनी बार आलेख (x)-अक्ष को काटता है उतने वास्तविक शून्यक होते हैं। टिप: रैखिक बहुपद का अधिकतम एक शून्यक होता है।
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Question 103/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि द्विघात बहुपद का आलेख (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial cuts the (x)-axis at two distinct points then what is the number of real zeroes?
#quadratic zeroes graph
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A दो / Two
B एक / One
C शून्य / Zero
D चार / Four
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Step 1
Concept
Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 3
Exam Tip
दो कटान बिंदु दो वास्तविक शून्यक बताते हैं। टिप: परवलय (x)-अक्ष को अधिकतम दो बार काट सकता है।
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Question 104/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय (x)-अक्ष को केवल स्पर्श करता है तो बहुपद के कितने वास्तविक शून्यक माने जाते हैं?
If a parabola only touches the (x)-axis then how many real zeroes does the polynomial have?
#quadratic tangent zero
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A एक / One
B दो / Two
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 3
Exam Tip
स्पर्श करने पर केवल एक समान शून्यक मिलता है। टिप: छूना भी (x)-अक्ष से मिलना है।
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Question 105/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि द्विघात बहुपद का आलेख (x)-अक्ष को कहीं नहीं छूता तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial does not meet the (x)-axis anywhere then how many real zeroes does it have?
#quadratic no real zero
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A शून्य / Zero
B एक / One
C दो / Two
D असीमित / Infinite
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Correct Answer
A. शून्य / Zero
Step 1
Concept
There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 3
Exam Tip
कोई (x)-अक्ष कटान नहीं है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: केवल (x)-अक्ष पर मिलने को गिनें।
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Question 106/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद के आलेख पर बिंदु ((4,0)) है। इससे कौन सा कथन सही है?
The point ((4,0)) lies on the graph of a polynomial. Which statement is correct?
#point zero graph
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A (4) बहुपद का शून्यक है / (4) is a zero of the polynomial
B (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
C (4) (y)-अक्ष कटान है / (4) is the (y)-intercept
D बहुपद स्थिर है / The polynomial is constant
Explanation opens after your attempt
Correct Answer
A. (4) बहुपद का शून्यक है / (4) is a zero of the polynomial
Step 1
Concept
The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) बहुपद का शून्यक है / (4) is a zero of the polynomial. The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 3
Exam Tip
((4,0)) का अर्थ है (x=4) पर (p(x)=0)। टिप: ((a,0)) से शून्यक (a) मिलता है।
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Question 107/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि बहुपद का आलेख मूल बिंदु ((0,0)) से गुजरता है तो कौन सा शून्यक अवश्य होगा?
If the graph of a polynomial passes through the origin ((0,0)) then which zero is certain?
#origin zero graph
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A (0)
B (1)
C (-1)
D (2)
Explanation opens after your attempt
Step 1
Concept
At the origin (x=0) and (p(x)=0). Tip: a graph through the origin has (0) as a zero.
Step 2
Why this answer is correct
The correct answer is A. (0). At the origin (x=0) and (p(x)=0). Tip: a graph through the origin has (0) as a zero.
Step 3
Exam Tip
मूल बिंदु पर (x=0) और (p(x)=0) होता है। टिप: origin पर जाने वाला आलेख (0) को शून्यक बनाता है।
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Question 108/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि आलेख (x)-अक्ष को (-2) पर काटता है तो बहुपद का शून्यक क्या है?
If the graph cuts the (x)-axis at (-2) then what is the zero of the polynomial?
#negative zero graph
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A (-2)
B (2)
C (0)
D (-1)
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Step 1
Concept
The (x)-coordinate of the (x)-axis intersection is the zero. Tip: read the sign carefully.
Step 2
Why this answer is correct
The correct answer is A. (-2). The (x)-coordinate of the (x)-axis intersection is the zero. Tip: read the sign carefully.
Step 3
Exam Tip
(x)-अक्ष कटान का (x)-निर्देशांक ही शून्यक होता है। टिप: चिह्न को ध्यान से पढ़ें।
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Question 109/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक आलेख (x)-अक्ष को (-3) और (5) पर काटता है। इसके वास्तविक शून्यक कौन से हैं?
A graph cuts the (x)-axis at (-3) and (5). What are its real zeroes?
#two zeroes intercepts
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A (-3) और (5) / (-3) and (5)
B (3) और (-5) / (3) and (-5)
C (-3) और (-5) / (-3) and (-5)
D (0) और (5) / (0) and (5)
Explanation opens after your attempt
Correct Answer
A. (-3) और (5) / (-3) and (5)
Step 1
Concept
The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 2
Why this answer is correct
The correct answer is A. (-3) और (5) / (-3) and (5). The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 3
Exam Tip
कटान बिंदुओं के (x)-मान शून्यक होते हैं। टिप: (y)-मान यहाँ (0) रहता है।
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Question 110/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी रैखिक बहुपद का आलेख (x)-अक्ष के समांतर है और उसे नहीं काटता तो उसके कितने शून्यक हैं?
If the graph of a linear polynomial is parallel to the (x)-axis and does not cut it then how many zeroes does it have?
#linear no zero
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A शून्य / Zero
B एक / One
C दो / Two
D असीमित / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
On such a line (p(x)) is never (0). Tip: meeting the (x)-axis is necessary.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. On such a line (p(x)) is never (0). Tip: meeting the (x)-axis is necessary.
Step 3
Exam Tip
ऐसी रेखा पर (p(x)) कभी (0) नहीं होता। टिप: (x)-अक्ष से मिलना जरूरी है।
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Question 111/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
बहुपद (p(x)=x-7) का आलेख (x)-अक्ष को किस बिंदु पर काटेगा?
At which point will the graph of (p(x)=x-7) cut the (x)-axis?
#linear polynomial zero
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A ((7,0))
B ((-7,0))
C ((0,7))
D ((0,-7))
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Correct Answer
A. ((7,0))
Step 1
Concept
From (x-7=0) we get (x=7). Tip: write the zero as the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((7,0)). From (x-7=0) we get (x=7). Tip: write the zero as the point ((x,0)).
Step 3
Exam Tip
(x-7=0) से (x=7) मिलता है। टिप: शून्यक को बिंदु ((x,0)) में लिखें।
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Question 112/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
बहुपद (p(x)=x+4) के आलेख का (x)-अक्ष कटान बिंदु कौन सा है?
What is the (x)-axis intersection point of the graph of (p(x)=x+4)?
#linear intercept graph
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A ((-4,0))
B ((4,0))
C ((0,4))
D ((0,-4))
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Correct Answer
A. ((-4,0))
Step 1
Concept
From (x+4=0) we get (x=-4). Tip: on the (x)-axis the second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). From (x+4=0) we get (x=-4). Tip: on the (x)-axis the second coordinate is (0).
Step 3
Exam Tip
(x+4=0) से (x=-4) मिलता है। टिप: (x)-अक्ष पर दूसरा निर्देशांक (0) होता है।
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Question 113/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
बहुपद (p(x)=2x-6) का शून्यक आलेख में किस (x)-मान पर दिखेगा?
At which (x)-value will the zero of (p(x)=2x-6) appear on the graph?
#linear zero value
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A (3)
B (-3)
C (6)
D (2)
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Step 1
Concept
Solving (2x-6=0) gives (x=3). Tip: first put (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (3). Solving (2x-6=0) gives (x=3). Tip: first put (p(x)=0).
Step 3
Exam Tip
(2x-6=0) से (x=3) होता है। टिप: पहले (p(x)=0) रखें।
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Question 114/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि आलेख (x)-अक्ष को ((6,0)) पर काटता है तो (p(6)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((6,0)) then what is the value of (p(6))?
#function value zero
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A (0)
B (6)
C (1)
D (-6)
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Step 1
Concept
On the (x)-axis (y=p(x)=0). Tip: read the function value directly from the intersection point.
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis (y=p(x)=0). Tip: read the function value directly from the intersection point.
Step 3
Exam Tip
(x)-अक्ष पर (y=p(x)=0) होता है। टिप: कटान बिंदु से फलन मान सीधे पढ़ें।
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Question 115/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(-1)=0) है तो बहुपद के आलेख के बारे में कौन सा कथन सही है?
If (p(-1)=0) then which statement about the graph of the polynomial is correct?
#zero point relation
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A आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0))
B आलेख ((0,-1)) से गुजरता है / The graph passes through ((0,-1))
C आलेख (y)-अक्ष को नहीं काटता / The graph does not cut the (y)-axis
D आलेख हमेशा सीधी रेखा है / The graph is always a straight line
Explanation opens after your attempt
Correct Answer
A. आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0))
Step 1
Concept
The value (p(-1)=0) gives the point ((-1,0)). Tip: connect (p(a)=0) with ((a,0)).
Step 2
Why this answer is correct
The correct answer is A. आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0)). The value (p(-1)=0) gives the point ((-1,0)). Tip: connect (p(a)=0) with ((a,0)).
Step 3
Exam Tip
(p(-1)=0) का बिंदु ((-1,0)) है। टिप: (p(a)=0) को ((a,0)) से जोड़ें।
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Question 116/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद के आलेख में (y)-अक्ष कटान ((0,5)) है। क्या (0) उसका शून्यक है?
The graph of a polynomial has (y)-axis intercept ((0,5)). Is (0) its zero?
#y intercept misconception
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A नहीं क्योंकि (p(0)=5) / No because (p(0)=5)
B हाँ क्योंकि (x=0) है / Yes because (x=0)
C हाँ क्योंकि यह अक्ष पर है / Yes because it is on an axis
D नहीं क्योंकि हर बहुपद का शून्यक नहीं होता / No because no polynomial has a zero
Explanation opens after your attempt
Correct Answer
A. नहीं क्योंकि (p(0)=5) / No because (p(0)=5)
Step 1
Concept
For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं क्योंकि (p(0)=5) / No because (p(0)=5). For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 3
Exam Tip
शून्यक के लिए (p(0)) को (0) होना चाहिए। टिप: (y)-अक्ष कटान हमेशा शून्यक नहीं होता।
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Question 117/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
आलेख (x)-अक्ष को केवल ((2,0)) पर स्पर्श करता है। शून्यक कौन सा है?
The graph only touches the (x)-axis at ((2,0)). Which is the zero?
#touching point zero
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A (2)
B (0)
C दो और शून्य / Two and zero
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of the touching point is (2) so the zero is (2). Tip: count a touching point too.
Step 2
Why this answer is correct
The correct answer is A. (2). The (x)-coordinate of the touching point is (2) so the zero is (2). Tip: count a touching point too.
Step 3
Exam Tip
स्पर्श बिंदु का (x)-निर्देशांक (2) है इसलिए शून्यक (2) है। टिप: स्पर्श बिंदु को भी गिनें।
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Question 118/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक परवलय ऊपर की ओर खुलता है और उसका शीर्ष ((0,3)) है। यदि वह (x)-अक्ष को नहीं काटता तो वास्तविक शून्यक कितने हैं?
A parabola opens upward and has vertex ((0,3)). If it does not cut the (x)-axis then how many real zeroes are there?
#parabola above axis
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A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 3
Exam Tip
आलेख पूरा (x)-अक्ष से ऊपर रह सकता है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: कटान न हो तो शून्यक न लिखें।
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Question 119/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी द्विघात बहुपद के वास्तविक शून्यक (1) और (4) हैं तो उसका आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?
If a quadratic polynomial has real zeroes (1) and (4) then at which points will its graph cut the (x)-axis?
#zeroes to points
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A ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
B ((0,1)) और ((0,4)) / ((0,1)) and ((0,4))
C ((1,1)) और ((4,4)) / ((1,1)) and ((4,4))
D ((-1,0)) और ((-4,0)) / ((-1,0)) and ((-4,0))
Explanation opens after your attempt
Correct Answer
A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
Step 1
Concept
A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0)). A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 3
Exam Tip
शून्यक (a) से कटान बिंदु ((a,0)) बनता है। टिप: शून्यक को (y)-निर्देशांक न बनाएं।
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Question 120/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि आलेख (x)-अक्ष को ((-5,0)) और ((2,0)) पर काटता है तो शून्यकों का योग क्या है?
If the graph cuts the (x)-axis at ((-5,0)) and ((2,0)) then what is the sum of zeroes?
#sum of zeroes graph
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A (-3)
B (3)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-5) and (2) so the sum is (-3). Tip: first take the (x)-values from the points.
Step 2
Why this answer is correct
The correct answer is A. (-3). The zeroes are (-5) and (2) so the sum is (-3). Tip: first take the (x)-values from the points.
Step 3
Exam Tip
शून्यक (-5) और (2) हैं इसलिए योग (-3) है। टिप: पहले बिंदुओं से (x)-मान लें।
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Question 121/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि आलेख (x)-अक्ष को ((-2,0)) और ((3,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If the graph cuts the (x)-axis at ((-2,0)) and ((3,0)) then what is the product of zeroes?
#product of zeroes graph
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A (-6)
B (6)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-2) and (3) so the product is (-6). Tip: do not use the (y)-value in the product.
Step 2
Why this answer is correct
The correct answer is A. (-6). The zeroes are (-2) and (3) so the product is (-6). Tip: do not use the (y)-value in the product.
Step 3
Exam Tip
शून्यक (-2) और (3) हैं इसलिए गुणनफल (-6) है। टिप: निर्देशांक का (y)-मान गुणन में न लें।
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Question 122/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
आलेख में बिंदु ((0,0)) और ((3,0)) (x)-अक्ष पर हैं। संभावित शून्यक कौन से हैं?
In a graph the points ((0,0)) and ((3,0)) lie on the (x)-axis. What are the possible zeroes?
#origin and intercepts
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A (0) और (3) / (0) and (3)
B (3) और (1) / (3) and (1)
C (0) और (-3) / (0) and (-3)
D केवल (3) / Only (3)
Explanation opens after your attempt
Correct Answer
A. (0) और (3) / (0) and (3)
Step 1
Concept
The (x)-coordinates of both points give zeroes. Tip: the origin can also give a zero.
Step 2
Why this answer is correct
The correct answer is A. (0) और (3) / (0) and (3). The (x)-coordinates of both points give zeroes. Tip: the origin can also give a zero.
Step 3
Exam Tip
दोनों बिंदुओं के (x)-निर्देशांक शून्यक देते हैं। टिप: मूल बिंदु भी शून्यक दे सकता है।
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Question 123/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी घन बहुपद का आलेख (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a cubic polynomial cuts the (x)-axis at three distinct points. What is the number of real zeroes?
#cubic graph zeroes
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A तीन / Three
B दो / Two
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 3
Exam Tip
तीन कटान बिंदु तीन वास्तविक शून्यक बताते हैं। टिप: प्रत्येक अलग (x)-अक्ष कटान को गिनें।
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Question 124/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
शून्य बहुपद (p(x)=0) का हर (x)-मान क्या कहलाता है?
For the zero polynomial (p(x)=0) what is every (x)-value called?
#zero polynomial concept
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A शून्यक / Zero
B केवल धनात्मक संख्या / Only positive number
C केवल ऋणात्मक संख्या / Only negative number
D कोई शून्यक नहीं / No zero
Explanation opens after your attempt
Correct Answer
A. शून्यक / Zero
Step 1
Concept
For the zero polynomial the value is (0) for every (x). Tip: this is a special case.
Step 2
Why this answer is correct
The correct answer is A. शून्यक / Zero. For the zero polynomial the value is (0) for every (x). Tip: this is a special case.
Step 3
Exam Tip
शून्य बहुपद में हर (x) पर मान (0) होता है। टिप: यह विशेष स्थिति है।
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Question 125/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
अशून्य स्थिर बहुपद (p(x)=5) के आलेख का (x)-अक्ष से संबंध क्या है?
What is the relation of the graph of the non-zero constant polynomial (p(x)=5) with the (x)-axis?
#constant polynomial graph
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A यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
B यह (x)-अक्ष को दो बार काटता है / It cuts the (x)-axis twice
C यह मूल बिंदु से गुजरता है / It passes through the origin
D यह (y)-अक्ष के समांतर है / It is parallel to the (y)-axis
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
Step 1
Concept
The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it. The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 3
Exam Tip
(p(x)=5) कभी (0) नहीं होता इसलिए शून्यक नहीं है। टिप: अशून्य स्थिर बहुपद का शून्यक नहीं होता।
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Question 126/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
बहुपद (p(x)=3x) के आलेख का (x)-अक्ष कटान कौन सा है?
What is the (x)-axis intersection of the graph of (p(x)=3x)?
#linear through origin
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A ((0,0))
B ((3,0))
C ((0,3))
D ((-3,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0))
Step 1
Concept
From (3x=0) we get (x=0). Tip: the coefficient does not change the zero in this case.
Step 2
Why this answer is correct
The correct answer is A. ((0,0)). From (3x=0) we get (x=0). Tip: the coefficient does not change the zero in this case.
Step 3
Exam Tip
(3x=0) से (x=0) मिलता है। टिप: गुणांक बदलने से इस स्थिति में शून्यक नहीं बदलता।
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Question 127/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि रेखा (y=x+2) (x)-अक्ष को काटती है तो कटान का (x)-मान क्या है?
If the line (y=x+2) cuts the (x)-axis then what is the (x)-value of the intersection?
#line x intercept
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A (-2)
B (2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Put (y=0) on the (x)-axis to get (x+2=0). Tip: setting (y=0) is the easiest method.
Step 2
Why this answer is correct
The correct answer is A. (-2). Put (y=0) on the (x)-axis to get (x+2=0). Tip: setting (y=0) is the easiest method.
Step 3
Exam Tip
(x)-अक्ष पर (y=0) रखकर (x+2=0) मिलता है। टिप: (y=0) रखना सबसे आसान तरीका है।
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Question 128/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि रेखा (y=5-x) का आलेख दिया हो तो शून्यक क्या होगा?
If the graph of the line (y=5-x) is given then what is the zero?
#linear equation graph
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A (5)
B (-5)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
From (5-x=0) we get (x=5). Tip: take (y) as (0) for the zero.
Step 2
Why this answer is correct
The correct answer is A. (5). From (5-x=0) we get (x=5). Tip: take (y) as (0) for the zero.
Step 3
Exam Tip
(5-x=0) से (x=5) मिलता है। टिप: शून्यक के लिए (y) को (0) मानें।
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Question 129/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
आलेख में (x)-अक्ष पर केवल बिंदु ((8,0)) दिख रहा है। बहुपद के वास्तविक शून्यक की संख्या क्या है?
Only the point ((8,0)) is visible on the (x)-axis in the graph. What is the number of real zeroes of the polynomial?
#count intersections
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A एक / One
B आठ / Eight
C शून्य / Zero
D दो / Two
Explanation opens after your attempt
Step 1
Concept
Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 3
Exam Tip
केवल एक (x)-अक्ष कटान दिख रहा है इसलिए एक वास्तविक शून्यक है। टिप: संख्या बिंदुओं की गिनती से आती है।
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Question 130/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि बहुपद के आलेख का (x)-अक्ष से कटान ((a,0)) है तो शून्यक क्या होगा?
If the (x)-axis intersection of a polynomial graph is ((a,0)) then what is the zero?
#general intercept rule
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A (a)
B (0)
C (a+0)
D (-a)
Explanation opens after your attempt
Step 1
Concept
In the intersection point ((a,0)) the (x)-value (a) is the zero. Tip: take the first value of the ordered pair.
Step 2
Why this answer is correct
The correct answer is A. (a). In the intersection point ((a,0)) the (x)-value (a) is the zero. Tip: take the first value of the ordered pair.
Step 3
Exam Tip
कटान बिंदु ((a,0)) में (x)-मान (a) ही शून्यक है। टिप: क्रमित युग्म का पहला मान लें।
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Question 131/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(2)=3) है तो बिंदु ((2,3)) आलेख पर है। क्या (2) शून्यक है?
If (p(2)=3) then the point ((2,3)) is on the graph. Is (2) a zero?
#not a zero value
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A नहीं / No
B हाँ / Yes
C केवल द्विघात में हाँ / Yes only in quadratic
D निर्धारित नहीं किया जा सकता / Cannot be decided
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For a zero (p(2)) should be (0). Tip: if (p(a)\neq0) then (a) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For a zero (p(2)) should be (0). Tip: if (p(a)\neq0) then (a) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (p(2)) को (0) होना चाहिए था। टिप: (p(a)\neq0) हो तो (a) शून्यक नहीं है।
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Question 132/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(-4)=0) है तो आलेख किस बिंदु से अवश्य गुजरेगा?
If (p(-4)=0) then through which point must the graph pass?
#function to point
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A ((-4,0))
B ((0,-4))
C ((4,0))
D ((-4,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
The value (p(-4)=0) gives the point ((-4,0)). Tip: treat (p(x)) as the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). The value (p(-4)=0) gives the point ((-4,0)). Tip: treat (p(x)) as the (y)-coordinate.
Step 3
Exam Tip
(p(-4)=0) बिंदु ((-4,0)) देता है। टिप: (p(x)) को (y)-निर्देशांक समझें।
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Question 133/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
कौन सा बिंदु किसी बहुपद के शून्यक को सीधे दिखाता है?
Which point directly shows a zero of a polynomial?
#identify zero point
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A ((9,0))
B ((0,9))
C ((9,9))
D ((0,-9))
Explanation opens after your attempt
Correct Answer
A. ((9,0))
Step 1
Concept
A point showing a zero has (y)-coordinate (0). Tip: choose points lying on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. ((9,0)). A point showing a zero has (y)-coordinate (0). Tip: choose points lying on the (x)-axis.
Step 3
Exam Tip
शून्यक वाले बिंदु का (y)-निर्देशांक (0) होता है। टिप: (x)-अक्ष पर पड़े बिंदु चुनें।
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Question 134/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
आलेख (x)-अक्ष को ((-1,0)) और ((1,0)) पर काटता है। शून्यकों का योग क्या है?
The graph cuts the (x)-axis at ((-1,0)) and ((1,0)). What is the sum of zeroes?
#symmetric zeroes
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A (0)
B (2)
C (-2)
D (1)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-1) and (1) and their sum is (0). Tip: symmetric intersections often give sum (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The zeroes are (-1) and (1) and their sum is (0). Tip: symmetric intersections often give sum (0).
Step 3
Exam Tip
शून्यक (-1) और (1) हैं जिनका योग (0) है। टिप: सममित कटान अक्सर योग (0) देते हैं।
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Question 135/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय (x)-अक्ष को ((0,0)) और ((6,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If a parabola cuts the (x)-axis at ((0,0)) and ((6,0)) then what is the product of zeroes?
#zero product graph
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A (0)
B (6)
C (-6)
D (36)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0) and (6) so the product is (0). Tip: any number multiplied by (0) gives (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The zeroes are (0) and (6) so the product is (0). Tip: any number multiplied by (0) gives (0).
Step 3
Exam Tip
शून्यक (0) और (6) हैं इसलिए गुणनफल (0) है। टिप: किसी भी संख्या से (0) गुणा करने पर (0) मिलता है।
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Question 136/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस आलेख से दो वास्तविक शून्यक मिलेंगे?
Which graph will give two real zeroes?
#two real zeroes
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A जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
B जो (y)-अक्ष को दो बार काटे / One that cuts the (y)-axis twice
C जो (x)-अक्ष के समांतर हो / One that is parallel to the (x)-axis
D जो केवल (y)-अक्ष को छुए / One that only touches the (y)-axis
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
Step 1
Concept
Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points. Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 3
Exam Tip
दो वास्तविक शून्यक के लिए दो अलग (x)-अक्ष कटान चाहिए। टिप: (y)-अक्ष कटान शून्यक नहीं गिनाता।
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Question 137/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस स्थिति में बहुपद का (3) शून्यक होगा?
In which situation will (3) be a zero of the polynomial?
#identify given zero
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A आलेख ((3,0)) से गुजरे / The graph passes through ((3,0))
B आलेख ((0,3)) से गुजरे / The graph passes through ((0,3))
C आलेख ((3,3)) से गुजरे / The graph passes through ((3,3))
D आलेख ((-3,0)) से गुजरे / The graph passes through ((-3,0))
Explanation opens after your attempt
Correct Answer
A. आलेख ((3,0)) से गुजरे / The graph passes through ((3,0))
Step 1
Concept
If (3) is a zero then (p(3)=0). Tip: look for the point ((3,0)).
Step 2
Why this answer is correct
The correct answer is A. आलेख ((3,0)) से गुजरे / The graph passes through ((3,0)). If (3) is a zero then (p(3)=0). Tip: look for the point ((3,0)).
Step 3
Exam Tip
(3) शून्यक होने पर (p(3)=0) होता है। टिप: बिंदु ((3,0)) खोजें।
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Question 138/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस स्थिति में (-6) बहुपद का शून्यक होगा?
In which situation will (-6) be a zero of the polynomial?
#negative zero identify
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A आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0))
B आलेख ((0,-6)) पर (y)-अक्ष को काटे / The graph cuts the (y)-axis at ((0,-6))
C आलेख ((6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((6,0))
D आलेख ((-6,6)) से गुजरे / The graph passes through ((-6,6))
Explanation opens after your attempt
Correct Answer
A. आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0))
Step 1
Concept
For (-6) to be a zero (p(-6)=0). Tip: do not miss the negative sign.
Step 2
Why this answer is correct
The correct answer is A. आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0)). For (-6) to be a zero (p(-6)=0). Tip: do not miss the negative sign.
Step 3
Exam Tip
(-6) शून्यक होने का अर्थ (p(-6)=0) है। टिप: ऋण चिह्न को न छोड़ें।
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Question 139/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी बहुपद के आलेख का कोई भी बिंदु (x)-अक्ष पर नहीं है तो कौन सा कथन सही है?
If no point of a polynomial graph lies on the (x)-axis then which statement is correct?
#no x axis point
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A उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
B उसका एक वास्तविक शून्यक है / It has one real zero
C उसके दो वास्तविक शून्यक हैं / It has two real zeroes
D हर संख्या शून्यक है / Every number is a zero
Explanation opens after your attempt
Correct Answer
A. उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
Step 1
Concept
A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 2
Why this answer is correct
The correct answer is A. उसका कोई वास्तविक शून्यक नहीं है / It has no real zero. A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष पर ही दिखता है। टिप: (x)-अक्ष से दूरी नहीं बल्कि मिलना देखें।
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Question 140/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद का आलेख (x)-अक्ष को (x=10) पर काटता है। कौन सा कथन सही है?
A polynomial graph cuts the (x)-axis at (x=10). Which statement is correct?
#x value zero
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A (p(10)=0)
B (p(0)=10)
C (p(10)=10)
D (p(-10)=0)
Explanation opens after your attempt
Correct Answer
A. (p(10)=0)
Step 1
Concept
An (x)-axis cut at (x=10) means (y=0). Tip: on the (x)-axis the function value is (0).
Step 2
Why this answer is correct
The correct answer is A. (p(10)=0). An (x)-axis cut at (x=10) means (y=0). Tip: on the (x)-axis the function value is (0).
Step 3
Exam Tip
(x=10) पर (x)-अक्ष कटान का अर्थ (y=0) है। टिप: (x)-अक्ष पर फलन मान (0) होता है।
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Question 141/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(5)=0) और (p(-2)=0) है तो आलेख (x)-अक्ष को किन (x)-मानों पर काटेगा?
If (p(5)=0) and (p(-2)=0) then at which (x)-values will the graph cut the (x)-axis?
#two values zero
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A (5) और (-2) / (5) and (-2)
B (0) और (5) / (0) and (5)
C (2) और (-5) / (2) and (-5)
D (5) और (2) / (5) and (2)
Explanation opens after your attempt
Correct Answer
A. (5) और (-2) / (5) and (-2)
Step 1
Concept
The (x)-values where (p(x)=0) give the intersections. Tip: read (p(a)=0) directly as an (x=a) cut.
Step 2
Why this answer is correct
The correct answer is A. (5) और (-2) / (5) and (-2). The (x)-values where (p(x)=0) give the intersections. Tip: read (p(a)=0) directly as an (x=a) cut.
Step 3
Exam Tip
जिन (x)-मानों पर (p(x)=0) है वही कटान देते हैं। टिप: (p(a)=0) को सीधे (x=a) कटान मानें।
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Question 142/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक विद्यार्थी ने ((0,7)) को देखकर (7) को शून्यक कहा। गलती क्या है?
A student saw ((0,7)) and called (7) a zero. What is the mistake?
#common mistake graph
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A यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\)
B (7) हमेशा शून्यक होता है / (7) is always a zero
C हर (y)-अक्ष कटान शून्यक है / Every (y)-axis intercept is a zero
D बिंदु में कोई जानकारी नहीं है / The point has no information
Explanation opens after your attempt
Correct Answer
A. यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\)
Step 1
Concept
For a zero the point must lie on the (x)-axis. Tip: check that the second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\). For a zero the point must lie on the (x)-axis. Tip: check that the second coordinate is (0).
Step 3
Exam Tip
शून्यक के लिए बिंदु (x)-अक्ष पर होना चाहिए। टिप: दूसरे निर्देशांक को (0) जांचें।
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Question 143/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
परवलय (x)-अक्ष को ((2,0)) और ((2,0)) पर ही छूता है। अलग वास्तविक शून्यकों की संख्या क्या है?
A parabola touches the (x)-axis only at ((2,0)). What is the number of distinct real zeroes?
#repeated zero graph
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A एक / One
B दो / Two
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. एक / One. For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 3
Exam Tip
दोहराया शून्यक होने पर अलग (x)-मान केवल (2) है। टिप: अलग शून्यक गिनते समय समान बिंदु दो बार न गिनें।
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Question 144/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि आलेख ((1,0)), ((4,0)) और ((0,6)) से गुजरता है तो शून्यक कौन से हैं?
If a graph passes through ((1,0)), ((4,0)) and ((0,6)) then what are the zeroes?
#select zero points
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A (1) और (4) / (1) and (4)
B (0) और (6) / (0) and (6)
C (1), (4) और (6) / (1), (4) and (6)
D केवल (6) / Only (6)
Explanation opens after your attempt
Correct Answer
A. (1) और (4) / (1) and (4)
Step 1
Concept
Only the points with (y=0) give zeroes. Tip: treat ((0,6)) as a (y)-axis intercept.
Step 2
Why this answer is correct
The correct answer is A. (1) और (4) / (1) and (4). Only the points with (y=0) give zeroes. Tip: treat ((0,6)) as a (y)-axis intercept.
Step 3
Exam Tip
केवल (y=0) वाले बिंदु शून्यक देते हैं। टिप: ((0,6)) को (y)-अक्ष कटान समझें।
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Question 145/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (x)-अक्ष को काटने वाले बिंदु ((-7,0)) और ((-3,0)) हैं तो बड़ा शून्यक कौन सा है?
If the points cutting the (x)-axis are ((-7,0)) and ((-3,0)) then which is the greater zero?
#compare negative zeroes
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A (-3)
B (-7)
C (0)
D (7)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-7) and (-3) and (-3) is greater. Tip: the number to the right on the number line is greater.
Step 2
Why this answer is correct
The correct answer is A. (-3). The zeroes are (-7) and (-3) and (-3) is greater. Tip: the number to the right on the number line is greater.
Step 3
Exam Tip
शून्यक (-7) और (-3) हैं और (-3) बड़ा है। टिप: संख्या रेखा पर दाईं ओर वाली संख्या बड़ी होती है।
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Question 146/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि बहुपद (p(x)=x-2 -9) का आलेख बनाया जाए तो (x)-अक्ष कटान कौन से होंगे?
If the graph of (p(x)=x-2 -9) is drawn then what will be the (x)-axis intersections?
#quadratic simple zeroes
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A ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0))
B ((0,-9)) और ((9,0)) / ((0,-9)) and ((9,0))
C ((3,3)) और ((-3,-3)) / ((3,3)) and ((-3,-3))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0))
Step 1
Concept
Solving \(x^2-9=0\) gives \(x=\pm3\). Tip: recognize \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0)). Solving \(x^2-9=0\) gives \(x=\pm3\). Tip: recognize \(a^2-b^2\).
Step 3
Exam Tip
\(x^2-9=0\) से \(x=\pm3\) मिलता है। टिप: \(a^2-b^2\) को पहचानें।
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Question 147/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
बहुपद (p(x)=x-2 ) का आलेख (x)-अक्ष से कैसे मिलता है?
How does the graph of (p(x)=x-2 ) meet the (x)-axis?
#x square graph
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A मूल बिंदु पर स्पर्श करता है / It touches at the origin
B दो अलग बिंदुओं पर काटता है / It cuts at two distinct points
C कहीं नहीं मिलता / It does not meet anywhere
D (x=1) पर काटता है / It cuts at (x=1)
Explanation opens after your attempt
Correct Answer
A. मूल बिंदु पर स्पर्श करता है / It touches at the origin
Step 1
Concept
From \(x^2=0\) only (x=0) is obtained. Tip: this is a repeated zero.
Step 2
Why this answer is correct
The correct answer is A. मूल बिंदु पर स्पर्श करता है / It touches at the origin. From \(x^2=0\) only (x=0) is obtained. Tip: this is a repeated zero.
Step 3
Exam Tip
\(x^2=0\) से केवल (x=0) मिलता है। टिप: यह एक दोहराया शून्यक है।
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Question 148/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि बहुपद (p(x)=(x-2)(x+5)) है तो आलेख (x)-अक्ष को कहाँ काटेगा?
If the polynomial is (p(x)=(x-2)(x+5)) then where will the graph cut the (x)-axis?
#factor zero graph
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A ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0))
B ((-2,0)) और ((5,0)) / ((-2,0)) and ((5,0))
C ((0,2)) और ((0,-5)) / ((0,2)) and ((0,-5))
D ((2,5)) और ((-5,2)) / ((2,5)) and ((-5,2))
Explanation opens after your attempt
Correct Answer
A. ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0))
Step 1
Concept
Making each factor zero gives (x=2) and (x=-5). Tip: set each factor equal to (0).
Step 2
Why this answer is correct
The correct answer is A. ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0)). Making each factor zero gives (x=2) and (x=-5). Tip: set each factor equal to (0).
Step 3
Exam Tip
कारक शून्य करने पर (x=2) और (x=-5) मिलते हैं। टिप: हर कारक को अलग से (0) रखें।
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Question 149/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद के ग्राफ में (x)-अक्ष कटान की गिनती का मुख्य उपयोग क्या है?
What is the main use of counting (x)-axis intersections in a polynomial graph?
#graph interpretation use
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A वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes
B घात हमेशा जानना / To always know the degree
C स्थिर पद तुरंत जानना / To know the constant term immediately
D रंग तय करना / To decide the color
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes
Step 1
Concept
The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes. The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 3
Exam Tip
(x)-अक्ष कटान वास्तविक शून्यकों की संख्या बताते हैं। टिप: ग्राफ से पहले कटान गिनें।
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Question 150/200
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी बहुपद के आलेख का (x)-अक्ष से केवल एक कटान (x=-8) पर है तो कौन सा कथन सही है?
If a polynomial graph has only one (x)-axis intersection at (x=-8) then which statement is correct?
#single negative intercept
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A उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8)
B उसके आठ वास्तविक शून्यक हैं / It has eight real zeroes
C उसका शून्यक (8) है / Its zero is (8)
D उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
Explanation opens after your attempt
Correct Answer
A. उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8)
Step 1
Concept
There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 2
Why this answer is correct
The correct answer is A. उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8). There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 3
Exam Tip
केवल एक कटान है और उसका (x)-मान (-8) है। टिप: कटान की संख्या और (x)-मान दोनों देखें।
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Question 151/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या अपरिमेय संख्या है?
Which number is an irrational number?
#irrational-numbers
#real-numbers
#classification
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A \(\sqrt{2}\)
B \(\frac{3}{4}\)
C (0.5)
D (7)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\)
Step 1
Concept
\(\sqrt{2}\) cannot be written as \(\frac{p}{q}\). In exams identify roots of non perfect squares.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}\). \(\sqrt{2}\) cannot be written as \(\frac{p}{q}\). In exams identify roots of non perfect squares.
Step 3
Exam Tip
\(\sqrt{2}\) को \(\frac{p}{q}\) के रूप में नहीं लिखा जा सकता। परीक्षा में पूर्ण वर्ग न होने वाली जड़ पहचानें।
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Question 152/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या परिमेय संख्या है?
Which number is a rational number?
#rational-numbers
#real-numbers
#basics
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A \(\frac{5}{8}\)
B \(\sqrt{3}\)
C \(\sqrt{5}\)
D \(\pi\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{8}\)
Step 1
Concept
\(\frac{5}{8}\) is a ratio of two integers. A rational number can be written as \(\frac{p}{q}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{8}\). \(\frac{5}{8}\) is a ratio of two integers. A rational number can be written as \(\frac{p}{q}\).
Step 3
Exam Tip
\(\frac{5}{8}\) दो पूर्णांकों का अनुपात है। परिमेय संख्या को \(\frac{p}{q}\) रूप में लिखा जाता है।
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Question 153/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
सभी परिमेय और अपरिमेय संख्याएँ मिलकर कौन सा समुच्चय बनाती हैं?
All rational and irrational numbers together form which set?
#real-numbers
#sets
#classification
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A वास्तविक संख्याएँ / Real numbers
B प्राकृतिक संख्याएँ / Natural numbers
C केवल पूर्णांक / Integers only
D केवल पूर्ण संख्याएँ / Whole numbers only
Explanation opens after your attempt
Correct Answer
A. वास्तविक संख्याएँ / Real numbers
Step 1
Concept
Real numbers include both rational and irrational numbers. These are placed on the number line.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक संख्याएँ / Real numbers. Real numbers include both rational and irrational numbers. These are placed on the number line.
Step 3
Exam Tip
वास्तविक संख्याओं में परिमेय और अपरिमेय दोनों शामिल होते हैं। संख्या रेखा पर इन्हीं का स्थान होता है।
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Question 154/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
दशमलव (0.333...) किस प्रकार की संख्या है?
What type of number is the decimal (0.333...)?
#decimal-expansion
#rational-numbers
#repeating-decimal
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D न तो परिमेय न अपरिमेय / Neither rational nor irrational
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
A repeating decimal is rational. It can be written as \(\frac{1}{3}\).
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. A repeating decimal is rational. It can be written as \(\frac{1}{3}\).
Step 3
Exam Tip
दोहराने वाला दशमलव परिमेय होता है। इसे \(\frac{1}{3}\) लिखा जा सकता है।
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Question 155/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
दशमलव (0.1010010001...) जिसमें कोई निश्चित आवर्ती क्रम नहीं है किस प्रकार की संख्या है?
The decimal (0.1010010001...) with no fixed repeating pattern is what type of number?
#irrational-decimal
#non-repeating
#real-numbers
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
A non terminating non repeating decimal is irrational. In exams always check the repeating pattern.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. A non terminating non repeating decimal is irrational. In exams always check the repeating pattern.
Step 3
Exam Tip
अनावर्ती और अनंत दशमलव अपरिमेय होता है। परीक्षा में आवर्ती पैटर्न जरूर देखें।
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Question 156/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{49}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{49}\)?
#square-root
#rational-numbers
#perfect-square
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C केवल अपरिमेय वास्तविक संख्या / Only irrational real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(\sqrt{49}=7\) and (7) is rational. The square root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt{49}=7\) and (7) is rational. The square root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{49}=7\) है और (7) परिमेय है। पूर्ण वर्ग की जड़ परिमेय होती है।
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Question 157/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{11}\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(\sqrt{11}\)?
#irrational-root
#square-root
#classification
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A यह अपरिमेय है / It is irrational
B यह पूर्णांक है / It is an integer
C यह प्राकृतिक संख्या है / It is a natural number
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
(11) is not a perfect square so \(\sqrt{11}\) is irrational. Identify such roots in simplest form.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. (11) is not a perfect square so \(\sqrt{11}\) is irrational. Identify such roots in simplest form.
Step 3
Exam Tip
(11) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{11}\) अपरिमेय है। ऐसी जड़ों को सरल रूप में पहचानें।
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Question 158/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
परिमेय संख्या की सही परिभाषा कौन सी है?
Which is the correct definition of a rational number?
#definition
#rational-numbers
#basic-concept
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A जिसे \(\frac{p}{q}\) रूप में लिखा जा सके जहाँ \(q\neq0\) / It can be written as \(\frac{p}{q}\) where \(q\neq0\)
B जिसकी जड़ हमेशा अपरिमेय हो / Its root is always irrational
C जो केवल ऋणात्मक हो / It is only negative
D जो केवल दशमलव में न लिखा जा सके / It cannot be written in decimal form
Explanation opens after your attempt
Correct Answer
A. जिसे \(\frac{p}{q}\) रूप में लिखा जा सके जहाँ \(q\neq0\) / It can be written as \(\frac{p}{q}\) where \(q\neq0\)
Step 1
Concept
A rational number is written as a ratio of two integers. Always remember \(q\neq0\).
Step 2
Why this answer is correct
The correct answer is A. जिसे \(\frac{p}{q}\) रूप में लिखा जा सके जहाँ \(q\neq0\) / It can be written as \(\frac{p}{q}\) where \(q\neq0\). A rational number is written as a ratio of two integers. Always remember \(q\neq0\).
Step 3
Exam Tip
परिमेय संख्या दो पूर्णांकों के अनुपात में लिखी जाती है। हर बार \(q\neq0\) याद रखें।
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Question 159/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
अपरिमेय संख्या का दशमलव प्रसार कैसा होता है?
What is the decimal expansion of an irrational number like?
#decimal-expansion
#irrational-numbers
#concept
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A अनंत और अनावर्ती / Non terminating and non repeating
B सांत / Terminating
C अनंत और आवर्ती / Non terminating and repeating
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
A. अनंत और अनावर्ती / Non terminating and non repeating
Step 1
Concept
The decimal of an irrational number neither ends nor repeats. This is the easiest identification.
Step 2
Why this answer is correct
The correct answer is A. अनंत और अनावर्ती / Non terminating and non repeating. The decimal of an irrational number neither ends nor repeats. This is the easiest identification.
Step 3
Exam Tip
अपरिमेय संख्या का दशमलव न खत्म होता है और न दोहराता है। यही सबसे आसान पहचान है।
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Question 160/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\pi\) किस प्रकार की संख्या है?
What type of number is \(\pi\)?
#pi
#irrational-numbers
#real-numbers
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A अपरिमेय संख्या / Irrational number
B पूर्णांक / Integer
C पूर्ण संख्या / Whole number
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
The decimal expansion of \(\pi\) is non terminating and non repeating. So it is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. The decimal expansion of \(\pi\) is non terminating and non repeating. So it is irrational.
Step 3
Exam Tip
\(\pi\) का दशमलव अनंत और अनावर्ती है। इसलिए यह अपरिमेय संख्या है।
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Question 161/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
संख्या (0) किस प्रकार की संख्या है?
What type of number is (0)?
#zero
#rational-numbers
#real-numbers
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A परिमेय और वास्तविक / Rational and real
B अपरिमेय / Irrational
C अवास्तविक / Non real
D केवल ऋणात्मक / Negative only
Explanation opens after your attempt
Correct Answer
A. परिमेय और वास्तविक / Rational and real
Step 1
Concept
(0) can be written as \(\frac{0}{1}\) so it is rational. It is also a real number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय और वास्तविक / Rational and real. (0) can be written as \(\frac{0}{1}\) so it is rational. It is also a real number.
Step 3
Exam Tip
\(0=\frac{0}{1}\) लिखा जा सकता है इसलिए यह परिमेय है। यह वास्तविक संख्या भी है।
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Question 162/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(2+\sqrt{3}\) किस प्रकार की संख्या है?
What type of number is \(2+\sqrt{3}\)?
#operation
#irrational-numbers
#addition
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
Adding irrational \(\sqrt{3}\) to rational (2) gives an irrational number. Do not treat such sums as rational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. Adding irrational \(\sqrt{3}\) to rational (2) gives an irrational number. Do not treat such sums as rational.
Step 3
Exam Tip
परिमेय (2) में अपरिमेय \(\sqrt{3}\) जोड़ने पर परिणाम अपरिमेय होता है। परीक्षा में ऐसे योग को परिमेय न मानें।
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Question 163/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{2}+\sqrt{2}\) का सरल रूप क्या है?
What is the simplest form of \(\sqrt{2}+\sqrt{2}\)?
#surds
#simplification
#irrational-numbers
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A \(2\sqrt{2}\)
B \(\sqrt{4}\)
C (4)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
Adding like terms gives \(2\sqrt{2}\). Writing it as \(\sqrt{4}\) is wrong.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). Adding like terms gives \(2\sqrt{2}\). Writing it as \(\sqrt{4}\) is wrong.
Step 3
Exam Tip
समान पदों को जोड़ने पर \(2\sqrt{2}\) मिलता है। इसे \(\sqrt{4}\) लिखना गलत है।
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Question 164/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{18}\) का सही सरल रूप कौन सा है?
Which is the correct simplified form of \(\sqrt{18}\)?
#simplification
#square-root
#surds
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A \(3\sqrt{2}\)
B \(9\sqrt{2}\)
C \(2\sqrt{3}\)
D \(\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Take the perfect square outside the root.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Take the perfect square outside the root.
Step 3
Exam Tip
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\) है। पूर्ण वर्ग को जड़ से बाहर निकालें।
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Question 165/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या वास्तविक संख्या नहीं है?
Which number is not a real number?
#real-numbers
#non-real
#square-root
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A \(\sqrt{-4}\)
B (-5)
C (0.75)
D \(\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{-4}\)
Step 1
Concept
In Class 10 real numbers the square root of a negative number is not real. Note that \(\sqrt{7}\) is real irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{-4}\). In Class 10 real numbers the square root of a negative number is not real. Note that \(\sqrt{7}\) is real irrational.
Step 3
Exam Tip
कक्षा 10 के वास्तविक संख्याओं में ऋणात्मक संख्या की वर्गमूल वास्तविक नहीं मानी जाती। ध्यान दें \(\sqrt{7}\) वास्तविक अपरिमेय है।
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Question 166/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
(1.25) किस प्रकार की संख्या है?
What type of number is (1.25)?
#terminating-decimal
#rational-numbers
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D केवल प्राकृतिक संख्या / Natural number only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
(1.25) is terminating and can be written as \(\frac{5}{4}\). Terminating decimals are rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. (1.25) is terminating and can be written as \(\frac{5}{4}\). Terminating decimals are rational.
Step 3
Exam Tip
(1.25) सांत दशमलव है और इसे \(\frac{5}{4}\) लिखा जा सकता है। सांत दशमलव परिमेय होते हैं।
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Question 167/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा दशमलव परिमेय संख्या दिखाता है?
Which decimal represents a rational number?
#repeating-decimal
#rational-numbers
#decimal
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A (2.454545...)
B (1.010010001...)
C (3.14159265...) बिना आवर्तन / (3.14159265...) without repetition
D (0.1234567891011...)
Explanation opens after your attempt
Correct Answer
A. (2.454545...)
Step 1
Concept
The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (2.454545...). The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(45) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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Question 168/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{64}\) और \(\sqrt{65}\) में कौन सा कथन सही है?
Which statement is correct about \(\sqrt{64}\) and \(\sqrt{65}\)?
#perfect-square
#irrational-root
#comparison
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A \(\sqrt{64}\) परिमेय है और \(\sqrt{65}\) अपरिमेय है / \(\sqrt{64}\) is rational and \(\sqrt{65}\) is irrational
B दोनों परिमेय हैं / Both are rational
C दोनों अपरिमेय हैं / Both are irrational
D \(\sqrt{64}\) अपरिमेय है और \(\sqrt{65}\) परिमेय है / \(\sqrt{64}\) is irrational and \(\sqrt{65}\) is rational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{64}\) परिमेय है और \(\sqrt{65}\) अपरिमेय है / \(\sqrt{64}\) is rational and \(\sqrt{65}\) is irrational
Step 1
Concept
(64) is a perfect square but (65) is not. So their square roots are of different types.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{64}\) परिमेय है और \(\sqrt{65}\) अपरिमेय है / \(\sqrt{64}\) is rational and \(\sqrt{65}\) is irrational. (64) is a perfect square but (65) is not. So their square roots are of different types.
Step 3
Exam Tip
(64) पूर्ण वर्ग है लेकिन (65) नहीं है। इसलिए उनकी वर्गमूल की प्रकृति अलग है।
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Question 169/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि (a) परिमेय है और (b) अपरिमेय है तो (a+b) कब निश्चित रूप से अपरिमेय होगा?
If (a) is rational and (b) is irrational then when is (a+b) definitely irrational?
#addition
#properties
#irrational-numbers
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A जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number
B केवल जब (a=0) हो / Only when (a=0)
C केवल जब (a=1) हो / Only when (a=1)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number
Step 1
Concept
Adding a rational number to an irrational number gives an irrational result. This simple property often appears in MCQs.
Step 2
Why this answer is correct
The correct answer is A. जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number. Adding a rational number to an irrational number gives an irrational result. This simple property often appears in MCQs.
Step 3
Exam Tip
परिमेय में अपरिमेय जोड़ने पर परिणाम अपरिमेय रहता है। यह आसान गुण अक्सर MCQ में आता है।
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Question 170/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{12}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{12}\)?
#surds
#simplification
#square-root
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A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Look for a perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Look for a perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\) है। जड़ के अंदर पूर्ण वर्ग खोजें।
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Question 171/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प केवल वास्तविक संख्याएँ दिखाता है?
Which option shows only real numbers?
#real-numbers
#classification
#square-root
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A (-3), (0), \(\sqrt{2}\)
B \(\sqrt{-1}\), (2), (5)
C \(\sqrt{-9}\), (0), (4)
D \(\sqrt{-16}\), \(\sqrt{3}\), (1)
Explanation opens after your attempt
Correct Answer
A. (-3), (0), \(\sqrt{2}\)
Step 1
Concept
Options with square roots of negatives are not real. (-3), (0), and \(\sqrt{2}\) are all real.
Step 2
Why this answer is correct
The correct answer is A. (-3), (0), \(\sqrt{2}\). Options with square roots of negatives are not real. (-3), (0), and \(\sqrt{2}\) are all real.
Step 3
Exam Tip
ऋणात्मक जड़ वाले विकल्प वास्तविक नहीं हैं। (-3), (0) और \(\sqrt{2}\) सभी वास्तविक हैं।
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Question 172/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(-\sqrt{7}\) किस प्रकार की संख्या है?
What type of number is \(-\sqrt{7}\)?
#negative-irrational
#real-numbers
#classification
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय संख्या / Rational number
C प्राकृतिक संख्या / Natural number
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
\(\sqrt{7}\) is irrational and its negative is also irrational. The negative sign does not stop it from being real.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{7}\) is irrational and its negative is also irrational. The negative sign does not stop it from being real.
Step 3
Exam Tip
\(\sqrt{7}\) अपरिमेय है और उसका ऋण भी अपरिमेय होता है। ऋण चिह्न संख्या को वास्तविक होने से नहीं रोकता।
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Question 173/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(3\sqrt{5}\) किस प्रकार की संख्या है?
What type of number is \(3\sqrt{5}\)?
#multiplication
#irrational-numbers
#properties
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
Multiplying an irrational by a non zero rational gives an irrational result. Here \(3\neq0\).
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. Multiplying an irrational by a non zero rational gives an irrational result. Here \(3\neq0\).
Step 3
Exam Tip
गैर शून्य परिमेय संख्या से अपरिमेय को गुणा करने पर परिणाम अपरिमेय होता है। यहाँ \(3\neq0\) है।
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Question 174/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\frac{\sqrt{2}}{2}\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(\frac{\sqrt{2}}{2}\)?
#division
#irrational-numbers
#classification
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A यह अपरिमेय है / It is irrational
B यह पूर्णांक है / It is an integer
C यह प्राकृतिक संख्या है / It is a natural number
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
Dividing \(\sqrt{2}\) by non zero rational (2) keeps it irrational. Check the nature of the root in such expressions.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. Dividing \(\sqrt{2}\) by non zero rational (2) keeps it irrational. Check the nature of the root in such expressions.
Step 3
Exam Tip
\(\sqrt{2}\) को गैर शून्य परिमेय (2) से भाग देने पर संख्या अपरिमेय रहती है। ऐसी अभिव्यक्तियों में जड़ की प्रकृति देखें।
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Question 175/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
दो अपरिमेय संख्याओं का योग हमेशा कैसा होता है?
What is the sum of two irrational numbers always?
#irrational-numbers
#addition
#properties
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A हमेशा निश्चित नहीं / Not always fixed
B हमेशा परिमेय / Always rational
C हमेशा अपरिमेय / Always irrational
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
A. हमेशा निश्चित नहीं / Not always fixed
Step 1
Concept
(\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no fixed always rule.
Step 2
Why this answer is correct
The correct answer is A. हमेशा निश्चित नहीं / Not always fixed. (\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no fixed always rule.
Step 3
Exam Tip
(\sqrt{2}+\(-\sqrt{2}\)=0) परिमेय है लेकिन \(\sqrt{2}+\sqrt{3}\) अपरिमेय है। इसलिए हमेशा एक जैसा नियम नहीं है।
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Question 176/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
दो अपरिमेय संख्याओं का गुणनफल हमेशा कैसा होता है?
What is the product of two irrational numbers always?
#irrational-numbers
#multiplication
#properties
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A हमेशा निश्चित नहीं / Not always fixed
B हमेशा अपरिमेय / Always irrational
C हमेशा ऋणात्मक / Always negative
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
A. हमेशा निश्चित नहीं / Not always fixed
Step 1
Concept
\(\sqrt{2}\times\sqrt{2}=2\) is rational but \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) is irrational. So it is not always one type.
Step 2
Why this answer is correct
The correct answer is A. हमेशा निश्चित नहीं / Not always fixed. \(\sqrt{2}\times\sqrt{2}=2\) is rational but \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) is irrational. So it is not always one type.
Step 3
Exam Tip
\(\sqrt{2}\times\sqrt{2}=2\) परिमेय है लेकिन \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) अपरिमेय है। इसलिए हमेशा एक जैसा नहीं होता।
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Question 177/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(0.\overline{7}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{7}\)?
#repeating-decimal
#rational-number
#decimal
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 3
Exam Tip
\(0.\overline{7}\) आवर्ती दशमलव है। हर आवर्ती दशमलव परिमेय होता है।
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Question 178/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या प्राकृतिक संख्या भी है और परिमेय संख्या भी है?
Which number is both a natural number and a rational number?
#natural-numbers
#rational-numbers
#sets
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A (9)
B \(\sqrt{10}\)
C (-2.5)
D \(\pi\)
Explanation opens after your attempt
Step 1
Concept
(9) is a counting number and \(9=\frac{9}{1}\). So it is both natural and rational.
Step 2
Why this answer is correct
The correct answer is A. (9). (9) is a counting number and \(9=\frac{9}{1}\). So it is both natural and rational.
Step 3
Exam Tip
(9) गिनती की संख्या है और \(9=\frac{9}{1}\) भी है। इसलिए यह प्राकृतिक और परिमेय दोनों है।
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Question 179/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{2}\) और \(\sqrt{8}\) के बारे में सही संबंध क्या है?
What is the correct relation between \(\sqrt{2}\) and \(\sqrt{8}\)?
#surds
#simplification
#irrational-numbers
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A \(\sqrt{8}=2\sqrt{2}\)
B \(\sqrt{8}=4\sqrt{2}\)
C \(\sqrt{8}=\sqrt{2}\)
D \(\sqrt{8}=8\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{8}=2\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Take the square factor outside.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{8}=2\sqrt{2}\). \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Take the square factor outside.
Step 3
Exam Tip
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\) है। वर्ग गुणनखंड को बाहर निकालें।
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Question 180/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(x=\sqrt{3}\) है तो \(x^2\) किस प्रकार की संख्या है?
If \(x=\sqrt{3}\), what type of number is \(x^2\)?
#square
#irrational-numbers
#rational-result
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
(\(\sqrt{3}\)2 =3) which is rational. The square of an irrational number can sometimes be rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. (\(\sqrt{3}\)2 =3) which is rational. The square of an irrational number can sometimes be rational.
Step 3
Exam Tip
(\(\sqrt{3}\)2 =3) है जो परिमेय है। अपरिमेय संख्या का वर्ग कभी-कभी परिमेय हो सकता है।
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Question 181/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या \(\frac{p}{q}\) रूप में नहीं लिखी जा सकती जहाँ (p) और (q) पूर्णांक हैं तथा \(q\neq0\)?
Which number cannot be written in the form \(\frac{p}{q}\) where (p) and (q) are integers and \(q\neq0\)?
#p-by-q-form
#irrational-numbers
#definition
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A \(\sqrt{6}\)
B (-4)
C (2.75)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{6}\)
Step 1
Concept
\(\sqrt{6}\) is irrational so it cannot be written as \(\frac{p}{q}\). The other numbers are rational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{6}\). \(\sqrt{6}\) is irrational so it cannot be written as \(\frac{p}{q}\). The other numbers are rational.
Step 3
Exam Tip
\(\sqrt{6}\) अपरिमेय है इसलिए इसे \(\frac{p}{q}\) रूप में नहीं लिख सकते। बाकी संख्याएँ परिमेय हैं।
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Question 182/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
सांत दशमलव का सही उदाहरण कौन सा है?
Which is a correct example of a terminating decimal?
#terminating-decimal
#rational-numbers
#example
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A (4.125)
B (0.666...)
C \(\pi\)
D (1.010010001...)
Explanation opens after your attempt
Correct Answer
A. (4.125)
Step 1
Concept
(4.125) ends after a finite number of digits. A terminating decimal is always rational.
Step 2
Why this answer is correct
The correct answer is A. (4.125). (4.125) ends after a finite number of digits. A terminating decimal is always rational.
Step 3
Exam Tip
(4.125) कुछ अंकों के बाद समाप्त हो जाता है। सांत दशमलव हमेशा परिमेय होता है।
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Question 183/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{20}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplest form of \(\sqrt{20}+\sqrt{45}\)?
#surds
#addition
#simplification
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A \(5\sqrt{5}\)
B \(\sqrt{65}\)
C \(13\sqrt{5}\)
D \(25\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{5}\). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। जोड़ने पर \(5\sqrt{5}\) मिलता है।
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Question 184/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प संख्या रेखा पर दर्शाया जा सकता है?
Which option can be represented on the number line?
#number-line
#real-numbers
#concept
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A हर वास्तविक संख्या / Every real number
B केवल प्राकृतिक संख्या / Only natural numbers
C केवल धनात्मक पूर्णांक / Only positive integers
D केवल सांत दशमलव / Only terminating decimals
Explanation opens after your attempt
Correct Answer
A. हर वास्तविक संख्या / Every real number
Step 1
Concept
All real numbers can be represented on the number line. This includes both rational and irrational numbers.
Step 2
Why this answer is correct
The correct answer is A. हर वास्तविक संख्या / Every real number. All real numbers can be represented on the number line. This includes both rational and irrational numbers.
Step 3
Exam Tip
संख्या रेखा पर सभी वास्तविक संख्याएँ दर्शाई जा सकती हैं। इसमें परिमेय और अपरिमेय दोनों आते हैं।
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Question 185/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{27}\) का सरल रूप कौन सा है?
Which is the simplified form of \(\sqrt{27}\)?
#square-root
#surds
#simplification
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A \(3\sqrt{3}\)
B \(9\sqrt{3}\)
C \(\sqrt{9}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\). Take out the greatest perfect square factor.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\). Take out the greatest perfect square factor.
Step 3
Exam Tip
\(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\) है। सबसे बड़े पूर्ण वर्ग गुणनखंड को निकालें।
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Question 186/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि किसी संख्या का दशमलव प्रसार अनंत लेकिन आवर्ती है तो वह कैसी संख्या है?
If the decimal expansion of a number is non terminating but repeating then what type of number is it?
#decimal-expansion
#repeating
#rational-numbers
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
A non terminating repeating decimal is rational. Do not call it irrational just because it is non terminating.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. A non terminating repeating decimal is rational. Do not call it irrational just because it is non terminating.
Step 3
Exam Tip
अनंत आवर्ती दशमलव परिमेय होता है। अनंत देखकर तुरंत अपरिमेय न मानें।
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Question 187/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{2}+\sqrt{8}\) का सही सरल रूप क्या है?
What is the correct simplified form of \(\sqrt{2}+\sqrt{8}\)?
#surds
#addition
#like-terms
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A \(3\sqrt{2}\)
B \(\sqrt{10}\)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) इसलिए योग \(3\sqrt{2}\) है। पहले सरल करें फिर समान पद जोड़ें।
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Question 188/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\frac{1}{7}\) का दशमलव प्रसार कैसा है?
What is the decimal expansion of \(\frac{1}{7}\) like?
#rational-decimal
#repeating
#division
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A अनंत और आवर्ती / Non terminating and repeating
B सांत / Terminating
C अनंत और अनावर्ती / Non terminating and non repeating
D अवास्तविक / Non real
Explanation opens after your attempt
Correct Answer
A. अनंत और आवर्ती / Non terminating and repeating
Step 1
Concept
\(\frac{1}{7}\) is rational and its decimal is repeating. Rational numbers give terminating or repeating decimals.
Step 2
Why this answer is correct
The correct answer is A. अनंत और आवर्ती / Non terminating and repeating. \(\frac{1}{7}\) is rational and its decimal is repeating. Rational numbers give terminating or repeating decimals.
Step 3
Exam Tip
\(\frac{1}{7}\) परिमेय है और इसका दशमलव आवर्ती होता है। परिमेय संख्याएँ सांत या आवर्ती दशमलव देती हैं।
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Question 189/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प परिमेय और अपरिमेय संख्या का योग दिखाता है?
Which option shows the sum of a rational and an irrational number?
#sum
#rational-irrational
#classification
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A \(4+\sqrt{7}\)
B \(\sqrt{2}+\sqrt{3}\)
C \(\frac{1}{2}+\frac{3}{4}\)
D (5+9)
Explanation opens after your attempt
Correct Answer
A. \(4+\sqrt{7}\)
Step 1
Concept
(4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.
Step 2
Why this answer is correct
The correct answer is A. \(4+\sqrt{7}\). (4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.
Step 3
Exam Tip
(4) परिमेय है और \(\sqrt{7}\) अपरिमेय है। उनका योग अपरिमेय होगा।
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Question 190/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प हमेशा सत्य है?
Which option is always true?
#real-numbers
#irrational-numbers
#true-statement
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A प्रत्येक अपरिमेय संख्या वास्तविक होती है / Every irrational number is real
B प्रत्येक वास्तविक संख्या अपरिमेय होती है / Every real number is irrational
C प्रत्येक परिमेय संख्या अपरिमेय होती है / Every rational number is irrational
D प्रत्येक पूर्णांक अपरिमेय होता है / Every integer is irrational
Explanation opens after your attempt
Correct Answer
A. प्रत्येक अपरिमेय संख्या वास्तविक होती है / Every irrational number is real
Step 1
Concept
Irrational numbers are a part of real numbers. But all real numbers are not irrational.
Step 2
Why this answer is correct
The correct answer is A. प्रत्येक अपरिमेय संख्या वास्तविक होती है / Every irrational number is real. Irrational numbers are a part of real numbers. But all real numbers are not irrational.
Step 3
Exam Tip
अपरिमेय संख्याएँ वास्तविक संख्याओं का भाग हैं। लेकिन सभी वास्तविक संख्याएँ अपरिमेय नहीं होतीं।
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Question 191/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{0.04}\) का मान किस प्रकार की संख्या है?
What type of number is the value of \(\sqrt{0.04}\)?
#decimal-square-root
#rational-numbers
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(\sqrt{0.04}=0.2\) which is a terminating decimal. So it is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt{0.04}=0.2\) which is a terminating decimal. So it is rational.
Step 3
Exam Tip
\(\sqrt{0.04}=0.2\) है जो सांत दशमलव है। इसलिए यह परिमेय है।
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Question 192/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
किस संख्या का वर्ग (2) होता है और वह अपरिमेय है?
Which number has square (2) and is irrational?
#square
#irrational-number
#sqrt2
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A \(\sqrt{2}\)
B (2)
C \(\frac{1}{2}\)
D (4)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\)
Step 1
Concept
(\(\sqrt{2}\)2 =2) and \(\sqrt{2}\) is irrational. This is an important basic example.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}\). (\(\sqrt{2}\)2 =2) and \(\sqrt{2}\) is irrational. This is an important basic example.
Step 3
Exam Tip
(\(\sqrt{2}\)2 =2) और \(\sqrt{2}\) अपरिमेय है। यह एक महत्वपूर्ण मूल उदाहरण है।
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Question 193/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(7-\sqrt{2}\) किस प्रकार की संख्या है?
What type of number is \(7-\sqrt{2}\)?
#subtraction
#irrational-numbers
#properties
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
Subtracting irrational \(\sqrt{2}\) from rational (7) gives an irrational number. Changing the sign does not change this property.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. Subtracting irrational \(\sqrt{2}\) from rational (7) gives an irrational number. Changing the sign does not change this property.
Step 3
Exam Tip
परिमेय (7) से अपरिमेय \(\sqrt{2}\) घटाने पर परिणाम अपरिमेय होता है। संकेत बदलने से गुण नहीं बदलता।
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Question 194/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा निष्कर्ष सही है यदि संख्या \(\sqrt{n}\) में (n) पूर्ण वर्ग नहीं है?
Which conclusion is correct if (n) is not a perfect square in the number \(\sqrt{n}\)?
#perfect-square
#irrational-root
#exam-rule
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A \(\sqrt{n}\) अपरिमेय होगी / \(\sqrt{n}\) will be irrational
B \(\sqrt{n}\) हमेशा पूर्णांक होगी / \(\sqrt{n}\) will always be an integer
C \(\sqrt{n}\) हमेशा शून्य होगी / \(\sqrt{n}\) will always be zero
D \(\sqrt{n}\) वास्तविक नहीं होगी / \(\sqrt{n}\) will not be real
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{n}\) अपरिमेय होगी / \(\sqrt{n}\) will be irrational
Step 1
Concept
If positive integer (n) is not a perfect square then \(\sqrt{n}\) is irrational. This is an easy exam rule.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{n}\) अपरिमेय होगी / \(\sqrt{n}\) will be irrational. If positive integer (n) is not a perfect square then \(\sqrt{n}\) is irrational. This is an easy exam rule.
Step 3
Exam Tip
धनात्मक पूर्णांक (n) पूर्ण वर्ग न हो तो \(\sqrt{n}\) अपरिमेय होती है। यह आसान परीक्षा नियम है।
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Question 195/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सी संख्या \(\sqrt{50}\) का सही सरल रूप है?
Which number is the correct simplified form of \(\sqrt{50}\)?
#surds
#simplification
#irrational-numbers
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A \(5\sqrt{2}\)
B \(10\sqrt{5}\)
C \(2\sqrt{5}\)
D \(\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Find the greatest perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}\). \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Find the greatest perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\) है। जड़ के अंदर सबसे बड़ा पूर्ण वर्ग खोजें।
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Question 196/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प परिमेय संख्या और अपरिमेय संख्या के गुणनफल का उदाहरण है जो अपरिमेय है?
Which option is an example of the product of a rational and an irrational number that is irrational?
#rational-irrational-product
#properties
#mcq
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A \(5\times\sqrt{3}\)
B \(0\times\sqrt{3}\)
C \(4\times2\)
D \(\sqrt{3}\times\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(5\times\sqrt{3}\)
Step 1
Concept
(5) is a non zero rational number so \(5\sqrt{3}\) is irrational. Remember multiplication by (0) gives (0).
Step 2
Why this answer is correct
The correct answer is A. \(5\times\sqrt{3}\). (5) is a non zero rational number so \(5\sqrt{3}\) is irrational. Remember multiplication by (0) gives (0).
Step 3
Exam Tip
(5) गैर शून्य परिमेय है इसलिए \(5\sqrt{3}\) अपरिमेय है। ध्यान रखें (0) से गुणा करने पर परिणाम (0) होता है।
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Question 197/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(x=2+\sqrt{5}\) है तो (x-2) किस प्रकार की संख्या है?
If \(x=2+\sqrt{5}\), what type of number is (x-2)?
#irrational-numbers
#expression
#simplification
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(x-2=\sqrt{5}\), which is irrational. In such questions simplify the expression first.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(x-2=\sqrt{5}\), which is irrational. In such questions simplify the expression first.
Step 3
Exam Tip
\(x-2=\sqrt{5}\) है जो अपरिमेय है। ऐसे प्रश्नों में पहले अभिव्यक्ति को सरल करें।
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Question 198/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा दशमलव अनंत और अनावर्ती है?
Which decimal is non terminating and non repeating?
#decimal-expansion
#non-repeating
#irrational
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A (0.2020020002...)
B (0.2222...)
C (0.75)
D (1.5000)
Explanation opens after your attempt
Correct Answer
A. (0.2020020002...)
Step 1
Concept
(0.2020020002...) has no fixed repetition. A non terminating and non repeating decimal is irrational.
Step 2
Why this answer is correct
The correct answer is A. (0.2020020002...). (0.2020020002...) has no fixed repetition. A non terminating and non repeating decimal is irrational.
Step 3
Exam Tip
(0.2020020002...) में कोई स्थायी दोहराव नहीं है। अनंत और अनावर्ती दशमलव अपरिमेय होता है।
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Question 199/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{98}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{98}\)?
#square-root
#surds
#simplification
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A \(7\sqrt{2}\)
B \(14\sqrt{2}\)
C \(2\sqrt{7}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Take the perfect square (49) outside the root.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). \(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Take the perfect square (49) outside the root.
Step 3
Exam Tip
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\) है। पूर्ण वर्ग (49) को जड़ से बाहर निकालें।
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Question 200/200
Easy Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा कथन सही है यदि कोई दशमलव सांत है?
Which statement is correct if a decimal is terminating?
#terminating-decimal
#rational-numbers
#real-numbers
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A वह परिमेय संख्या होती है / It is a rational number
B वह हमेशा अपरिमेय होती है / It is always irrational
C वह वास्तविक संख्या नहीं होती / It is not a real number
D वह हमेशा प्राकृतिक संख्या होती है / It is always a natural number
Explanation opens after your attempt
Correct Answer
A. वह परिमेय संख्या होती है / It is a rational number
Step 1
Concept
A terminating decimal can be written in \(\frac{p}{q}\) form. So it is rational and real.
Step 2
Why this answer is correct
The correct answer is A. वह परिमेय संख्या होती है / It is a rational number. A terminating decimal can be written in \(\frac{p}{q}\) form. So it is rational and real.
Step 3
Exam Tip
सांत दशमलव को \(\frac{p}{q}\) रूप में लिखा जा सकता है। इसलिए वह परिमेय और वास्तविक होता है।
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