100 results found for "given values zero" in Class 10.
यदि (p(-1)<0), (p(0)<0) और (p(2)=0), तो दिए गए मानों में कौन सा शून्यक निश्चित है?
If (p(-1)<0), (p(0)<0) and (p(2)=0), which zero is definite among the given values?
#definite zero
#function value
#graph
A (-1)
B (0)
C (2)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Only (p(2)=0) directly shows a zero. Tip: positive or negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is C. (2). Only (p(2)=0) directly shows a zero. Tip: positive or negative values are not zeroes.
Step 3
Exam Tip
केवल (p(2)=0) सीधे शून्यक बताता है। टिप: धनात्मक या ऋणात्मक मान शून्यक नहीं होते।
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यदि (p(x)=2x-2 +mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=2x-2 +mx+18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A (3)
B -(3)
C (6)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 3
Exam Tip
गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।
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यदि (p(x)=x-2 +3x-18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 +3x-18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A -(6)
B (6)
C -(3)
D (9)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 3
Exam Tip
शून्यकों का गुणनफल (-18) है। एक शून्यक (3) है, इसलिए दूसरा \(-18\div3=-6\) है।
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यदि (p(x)=x-2 -10x+r) का एक शून्यक (4) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -10x+r) is (4), what is the other zero?
#one-zero-given
#sum-zeroes
#quadratic
A (6)
B (4)
C (10)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 3
Exam Tip
शून्यकों का योग (10) है। एक शून्यक (4) है, इसलिए दूसरा (10-4=6) है।
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कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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यदि किसी ग्राफ पर (p(-5)>0), (p(-2)=0), (p(1)<0), (p(6)=0) है, तो दिए गए मानों में शून्यकों का योग क्या है?
If on a graph (p(-5)>0), (p(-2)=0), (p(1)<0), (p(6)=0), what is the sum of the zeroes among the given values?
#table values
#sum of zeroes
#graph
A (4)
B (-4)
C (7)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-2) and (6), so the sum is (4). Tip: take only the (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (4). The given zeroes are (-2) and (6), so the sum is (4). Tip: take only the (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-2) और (6) हैं, इसलिए योग (4) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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तालिका में (p(-2)=6), (p(1)=0), (p(3)=-4) और (p(5)=0) है। दिए गए मानों से कौन से शून्यक मिलते हैं?
In a table (p(-2)=6), (p(1)=0), (p(3)=-4) and (p(5)=0). Which zeroes are obtained from the given values?
#table values
#zeroes
#graph
A (-2) और (3) / (-2) and (3)
B (1) और (5) / (1) and (5)
C (6) और (-4) / (6) and (-4)
D सभी दिए गए (x)-मान / All given (x)-values
Explanation opens after your attempt
Correct Answer
B. (1) और (5) / (1) and (5)
Step 1
Concept
Zeroes are the (x)-values for which (p(x)=0). Tip: find zero (y)-values in the table.
Step 2
Why this answer is correct
The correct answer is B. (1) और (5) / (1) and (5). Zeroes are the (x)-values for which (p(x)=0). Tip: find zero (y)-values in the table.
Step 3
Exam Tip
शून्यक वही (x)-मान हैं जिन पर (p(x)=0) है। टिप: तालिका में शून्य (y)-मान खोजें।
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यदि (p(3)<0), (p(4)=0), (p(5)<0) है तो ग्राफ (x)-अक्ष से किस दिए गए (x)-मान पर मिलेगा?
If (p(3)<0), (p(4)=0), (p(5)<0), at which given (x)-value will the graph meet the (x)-axis?
#given values zero
A (3)
B (4)
C (5)
D इनमें से कोई नहीं / None of these
Explanation opens after your attempt
Step 1
Concept
Only (p(4)=0), so the graph meets the (x)-axis at (x=4). Tip: negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is B. (4). Only (p(4)=0), so the graph meets the (x)-axis at (x=4). Tip: negative values are not zeroes.
Step 3
Exam Tip
केवल (p(4)=0) है इसलिए (x=4) पर ग्राफ (x)-अक्ष से मिलेगा। टिप: ऋणात्मक मान शून्यक नहीं होते।
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यदि (p(x)=x-2 -2x-2) का एक शून्यक \(1+\sqrt{3}\) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -2x-2) is \(1+\sqrt{3}\), what is the other zero?
#other-zero
#sum-of-zeroes
#conjugate
A \(1-\sqrt{3}\)
B \(-1+\sqrt{3}\)
C \(1+\sqrt{3}\)
D \(-1-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(1-\sqrt{3}\)
Step 1
Concept
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
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यदि (p(x)=x-2 -13x+k) का एक शून्यक (6) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -13x+k) has one zero (6), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
B दूसरा (-7), कटान ((6,0)), ((-7,0)) / Other (-7), intersections ((6,0)), ((-7,0))
C दूसरा (13), कटान ((6,0)), ((13,0)) / Other (13), intersections ((6,0)), ((13,0))
D दूसरा (0), कटान ((6,0)), ((0,0)) / Other (0), intersections ((6,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=5) है और एक शून्यक (-1) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=5) and one zero is (-1), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (11)
B (9)
C (6)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (11). The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (5) है इसलिए दूसरा शून्यक (11) होगा। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -11x+k) का एक शून्यक (4) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -11x+k) has one zero (4), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
B दूसरा (-7), कटान ((4,0)), ((-7,0)) / Other (-7), intersections ((4,0)), ((-7,0))
C दूसरा (11), कटान ((4,0)), ((11,0)) / Other (11), intersections ((4,0)), ((11,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=-2) है और एक शून्यक (5) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=-2) and one zero is (5), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (-9)
B (-7)
C (9)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-9). The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (-2) है, इसलिए दूसरा शून्यक (-9) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य से जोड़ें।
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यदि (p(x)=x-2 -9x+k) का एक शून्यक (4) है तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -9x+k) has one zero (4), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
B दूसरा (-5), कटान ((4,0)), ((-5,0)) / Other (-5), intersections ((4,0)), ((-5,0))
C दूसरा (9), कटान ((4,0)), ((9,0)) / Other (9), intersections ((4,0)), ((9,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (11) है और सममिति अक्ष (x=3) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (11) and axis of symmetry (x=3). What will be the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-8)
D (8)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (3) है इसलिए दूसरा शून्यक (-5) होगा। टिप: \(\frac{a+b}{2}\) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=4) है और एक शून्यक (-2) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=4) and one zero is (-2). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (10)
B (6)
C (8)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (10). The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दोनों शून्यकों का औसत (4) है इसलिए दूसरा शून्यक (10) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य मान से जोड़ें।
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यदि (p(x)=x-2 -7x+k) का एक शून्यक (3) है, तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -7x+k) has one zero (3), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
B दूसरा (-4), कटान ((3,0)), ((-4,0)) / Other (-4), intersections ((3,0)), ((-4,0))
C दूसरा (7), कटान ((3,0)), ((7,0)) / Other (7), intersections ((3,0)), ((7,0))
D दूसरा (0), कटान ((3,0)), ((0,0)) / Other (0), intersections ((3,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (9) है और सममिति अक्ष (x=2) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (9) and axis of symmetry (x=2). What is the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (2) है, इसलिए दूसरा शून्यक (-5) होगा। टिप: \( \frac{a+b}{2} \) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=1) है और एक शून्यक (-5) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=1) and one zero is (-5). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (5)
B (6)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is C. (7). The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (1) होगा इसलिए दूसरा शून्यक (7) है। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -5x+k) का एक शून्यक (2) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होगा?
If (p(x)=x-2 -5x+k) has one zero (2), what will be the other zero and the (x)-axis intersections?
#quadratic
#missing zero
#intercepts
A दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
B दूसरा (-3), कटान ((2,0)), ((-3,0)) / Other (-3), intersections ((2,0)), ((-3,0))
C दूसरा (5), कटान ((2,0)), ((5,0)) / Other (5), intersections ((2,0)), ((5,0))
D दूसरा (0), कटान ((2,0)), ((0,0)) / Other (0), intersections ((2,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (4) है और सममिति अक्ष (x=-1) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (4) and axis of symmetry (x=-1). What will be the other zero?
#axis of symmetry
#missing zero
#parabola
A (-6)
B (-4)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-6). The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (-1) है, इसलिए दूसरा शून्यक (-6) होगा। टिप: औसत को सममिति अक्ष के बराबर रखें।
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घन को वास्तविक दिखाने के लिए अलग अलग सतहों पर अलग मान क्यों दिए जाते हैं?
Why are different values given to different faces of a cube to make it look real?
#cube
#value
#light direction
A सतहों की दिशा और प्रकाश दिखाने के लिए / To show direction of faces and light
B रंग का नाम बदलने के लिए / To change colour name
C रेखा मिटाने के लिए / To erase line
D कागज मोड़ने के लिए / To fold paper
Explanation opens after your attempt
Correct Answer
A. सतहों की दिशा और प्रकाश दिखाने के लिए / To show direction of faces and light
Step 1
Concept
Different values separate the faces of a cube. Exam tip: remember light direction in cube shading.
Step 2
Why this answer is correct
The correct answer is A. सतहों की दिशा और प्रकाश दिखाने के लिए / To show direction of faces and light. Different values separate the faces of a cube. Exam tip: remember light direction in cube shading.
Step 3
Exam Tip
अलग मान घन की सतहों को अलग दिखाते हैं। परीक्षा में cube shading में प्रकाश दिशा याद रखें।
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यदि (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 3
Exam Tip
(-12), (4), (15) पर फलन मान (0) है। टिप: (p(-2)=6) को शून्यक न मानें।
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यदि (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.
Step 3
Exam Tip
(-10), (3), (12) पर फलन मान (0) है। टिप: (p(-1)=4) को शून्यक न मानें।
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यदि (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0) है तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.
Step 3
Exam Tip
(-9), (2), (6) पर फलन मान (0) है। टिप: (p(-4)=2) को शून्यक न मानें।
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यदि (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.
Step 3
Exam Tip
(-7), (1), (4) पर फलन मान (0) है। टिप: (p(-3)=2) को शून्यक न मानें।
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यदि किसी ग्राफ में (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), तो कितने दिए गए (x)-मान शून्यक हैं?
If in a graph (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.
Step 3
Exam Tip
(-4), (2), (5) पर फलन मान (0) है। टिप: (p(0)=3) को शून्यक न मानें।
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तालिका में (p(-4)=-2), (p(-1)=0), (p(3)=0), (p(6)=5) है। दिए गए मानों से शून्यकों का गुणनफल क्या है?
In a table (p(-4)=-2), (p(-1)=0), (p(3)=0), (p(6)=5). What is the product of the zeroes from the given values?
#table product zeroes
A (-3)
B (3)
C (0)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-1) and (3), so the product is (-3). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-3). The zeroes are (-1) and (3), so the product is (-3). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
शून्यक (-1) और (3) हैं इसलिए गुणनफल (-3) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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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
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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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
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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यदि किसी ग्राफ के लिए (p(-3)<0), (p(1)=0), और (p(4)>0) है तो निश्चित शून्यक कौन सा है?
If for a graph (p(-3)<0), (p(1)=0), and (p(4)>0), which zero is certain?
#function-values
#zero-identification
#reasoning
A (1)
B (-3)
C (4)
D (-3) और (4) / (-3) and (4)
Explanation opens after your attempt
Step 1
Concept
Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is A. (1). Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 3
Exam Tip
केवल (p(1)=0) सीधे शून्यक बताता है। धनात्मक या ऋणात्मक मान शून्यक नहीं होते।
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किस स्थिति में बहुपद का (3) शून्यक होगा?
In which situation will (3) be a zero of the polynomial?
#identify given zero
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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कौन सा बहुपद (x=0) को शून्य बनाता है?
Which polynomial makes (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^2+5\)
B \(3x^3-2x\)
C \(x^4+1\)
D \(2x^2-7x+9\)
Explanation opens after your attempt
Correct Answer
B. \(3x^3-2x\)
Step 1
Concept
Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^3-2x\). Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 3
Exam Tip
(x=0) रखने पर \(3x^3-2x=0\) मिलता है। (x=0) को शून्य बनाने के लिए अचर पद (0) होना चाहिए।
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यदि \(x^2+mx+n\) का एक शून्यक (0) है और दूसरा शून्यक (5) है, तो (m+n) क्या होगा?
If one zero of \(x^2+mx+n\) is (0) and the other zero is (5), what is (m+n)?
#polynomials
#zeroes
#constant_term
#hard
A (-5)
B (5)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 3
Exam Tip
योग (5) है इसलिए (m=-5), और गुणनफल (0) है इसलिए (n=0)। अतः (m+n=-5)।
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कौन सा बहुपद (x=0) को शून्य नहीं बनाता?
Which polynomial does not make (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^3-2x\)
B \(5x^2+x\)
C \(x^4\)
D \(x^2+1\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+1\)
Step 1
Concept
On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 2
Why this answer is correct
The correct answer is D. \(x^2+1\). On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 3
Exam Tip
(x=0) रखने पर \(x^2+1=1\), इसलिए (0) इसका शून्य नहीं है। (x=0) पर अचर पद निर्णायक होता है।
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यदि किसी बहुपद का एक शून्यक \(\sqrt{11}\) है और गुणांक परिमेय हैं, तो कौन सा शून्यक भी होना चाहिए?
If one zero of a polynomial is \(\sqrt{11}\) and the coefficients are rational, which zero should also occur?
#conjugate-zeroes
#polynomials
#irrational-roots
A -\(\sqrt{11}\)
B (11)
C \(\frac{1}{\sqrt{11}}\)
D \(1+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. -\(\sqrt{11}\)
Step 1
Concept
The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 2
Why this answer is correct
The correct answer is A. -\(\sqrt{11}\). The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 3
Exam Tip
\(\sqrt{11}=0+\sqrt{11}\) का संयुग्मी \(-\sqrt{11}\) है। परीक्षा में (a=0) वाला संयुग्मी भी पहचानें।
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यदि \(2+\sqrt{3}\) एक बहुपद \(x^2-4x+1\) का शून्यक है, तो दूसरा शून्यक क्या होगा?
If \(2+\sqrt{3}\) is a zero of the polynomial \(x^2-4x+1\), what is the other zero?
#conjugate roots
#polynomials
#irrational zeroes
A \(2-\sqrt{3}\)
B \(-2+\sqrt{3}\)
C \(-2-\sqrt{3}\)
D \(\sqrt{3}-4\)
Explanation opens after your attempt
Correct Answer
A. \(2-\sqrt{3}\)
Step 1
Concept
For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2-\sqrt{3}\). For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 3
Exam Tip
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है।
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यदि (p(x)=x-2 -2kx+5) का एक शून्यक \(\sqrt{5}\) है, तो दूसरा शून्यक और (k) क्या होंगे?
If one zero of (p(x)=x-2 -2kx+5) is \(\sqrt{5}\), what will be the other zero and (k)?
#parameter
#product-of-zeroes
#irrational
A दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\)
B दूसरा \(-\sqrt{5}\), (k=0) / Other \(-\sqrt{5}\), (k=0)
C दूसरा (5), \(k=\frac{5+\sqrt{5}}{2}\) / Other (5), \(k=\frac{5+\sqrt{5}}{2}\)
D दूसरा (1), \(k=\frac{1+\sqrt{5}}{2}\) / Other (1), \(k=\frac{1+\sqrt{5}}{2}\)
Explanation opens after your attempt
Correct Answer
A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\)
Step 1
Concept
The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\). The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 3
Exam Tip
गुणनफल (5) है, इसलिए दूसरा शून्यक \(\frac{5}{\sqrt{5}}=\sqrt{5}\) होगा। योग \(2\sqrt{5}=2k\), अतः \(k=\sqrt{5}\) है।
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किसी परवलय का एक शून्यक (-10) है और दूसरा शून्यक पहले से (18) अधिक है। सममिति अक्ष क्या होगा?
One zero of a parabola is (-10), and the other zero is (18) more than the first. What is the axis of symmetry?
#axis symmetry
#word problem
#zeroes
A (x=-1)
B (x=1)
C (x=8)
D (x=-8)
Explanation opens after your attempt
Step 1
Concept
The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-1). The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (8) है और औसत \(\frac{-10+8}{2}=-1\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
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किसी परवलय का एक शून्यक (-8) है और दूसरा शून्यक पहले से (12) अधिक है। सममिति अक्ष क्या होगा?
One zero of a parabola is (-8), and the other zero is (12) more than the first. What is the axis of symmetry?
#axis symmetry
#word problem
#zeroes
A (x=-2)
B (x=2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-2). The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (4) है और औसत \(\frac{-8+4}{2}=-2\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
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किसी परवलय का सममिति अक्ष (x=2) है और एक शून्यक (-3) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=2) and one zero is (-3). What will be the other zero?
#parabola
#axis of symmetry
#zeroes
A (7)
B (5)
C (3)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (7). The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (2) होगा, इसलिए दूसरा शून्यक (7) है। टिप: परवलय में सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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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
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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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
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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यदि चित्र में सभी मान लगभग समान हों तो विरोध कैसा होगा?
If all values in a picture are almost similar how will the contrast be?
#low contrast
#similar values
#value
A बहुत ऊंचा / Very high
B सिर्फ गर्म / Only warm
C कम / Low
D अधिक चमकीला / More bright
Explanation opens after your attempt
Step 1
Concept
Similar values have little difference so contrast is low. Exam tip: connect close values with low contrast.
Step 2
Why this answer is correct
The correct answer is C. कम / Low. Similar values have little difference so contrast is low. Exam tip: connect close values with low contrast.
Step 3
Exam Tip
समान मानों में अंतर कम होता है इसलिए विरोध कम होता है। परीक्षा में close values को low contrast से जोड़ें।
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यदि समीकरण \(x^2-2mx+3m=0\) के मूल वास्तविक और समान हैं, तो (m) के कौन से मान मिलते हैं?
If \(x^2-2mx+3m=0\) has real and equal roots, which values of (m) are obtained?
#quadratic equations
#two parameter values
#equal roots
A (m=0) या (m=3) / (m=0) or (m=3)
B (m=3) केवल / (m=3) only
C (m=0) केवल / (m=0) only
D (m=-3) या (m=0) / (m=-3) or (m=0)
Explanation opens after your attempt
Correct Answer
A. (m=0) या (m=3) / (m=0) or (m=3)
Step 1
Concept
(D=4m-2 -12m=4m(m-3 )). From (D=0), (m=0) or (m=3).
Step 2
Why this answer is correct
The correct answer is A. (m=0) या (m=3) / (m=0) or (m=3). (D=4m-2 -12m=4m(m-3 )). From (D=0), (m=0) or (m=3).
Step 3
Exam Tip
(D=4m-2 -12m=4m(m-3 )) है। (D=0) से (m=0) या (m=3) मिलता है।
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यदि (x-2 +(m-2 )x+25=0) की जड़ें समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m-2 )x+25=0) has equal roots, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (12) और (-8) / (12) and (-8)
B (10) और (-10) / (10) and (-10)
C (7) और (-3) / (7) and (-3)
D (5) और (-5) / (5) and (-5)
Explanation opens after your attempt
Correct Answer
A. (12) और (-8) / (12) and (-8)
Step 1
Concept
For equal roots, ((m-2 )2 -100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 2
Why this answer is correct
The correct answer is A. (12) और (-8) / (12) and (-8). For equal roots, ((m-2 )2 -100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 3
Exam Tip
समान जड़ों के लिए ((m-2 )2 -100=0) होगा। इसलिए \(m-2=\pm10\), अतः (m=12) या (m=-8)।
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यदि (x-2 +(m+1)x+16=0) की जड़ें समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m+1)x+16=0) has equal roots, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (7) और (-9) / (7) and (-9)
B (8) और (-8) / (8) and (-8)
C (9) और (-7) / (9) and (-7)
D (15) और (-17) / (15) and (-17)
Explanation opens after your attempt
Correct Answer
A. (7) और (-9) / (7) and (-9)
Step 1
Concept
For equal roots, ((m+1)2 -64=0). Thus \(m+1=\pm8\), so (m=7) or (m=-9).
Step 2
Why this answer is correct
The correct answer is A. (7) और (-9) / (7) and (-9). For equal roots, ((m+1)2 -64=0). Thus \(m+1=\pm8\), so (m=7) or (m=-9).
Step 3
Exam Tip
समान जड़ों के लिए ((m+1)2 -64=0) होगा। इसलिए \(m+1=\pm8\), अतः (m=7) या (m=-9)।
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यदि (x-2 +(m-5 )x+9=0) की जड़ें बराबर पर विपरीत चिह्न वाली नहीं हैं और समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m-5 )x+9=0) has equal roots that are not of opposite signs, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (11) और (-1) / (11) and (-1)
B (5) और (-5) / (5) and (-5)
C (8) और (2) / (8) and (2)
D (14) और (-4) / (14) and (-4)
Explanation opens after your attempt
Correct Answer
A. (11) और (-1) / (11) and (-1)
Step 1
Concept
For equal roots, ((m-5 )2 -36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).
Step 2
Why this answer is correct
The correct answer is A. (11) और (-1) / (11) and (-1). For equal roots, ((m-5 )2 -36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).
Step 3
Exam Tip
समान जड़ों के लिए ((m-5 )2 -36=0) होगा। इसलिए \(m-5=\pm6\), अतः (m=11) या (m=-1)।
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(x-2 +2(k-1)x+k+5=0) की जड़ें समान हों, तो (k) के मान कौन-से हैं?
If (x-2 +2(k-1)x+k+5=0) has equal roots, what are the values of (k)?
#quadratic-roots
#equal-roots
#parameter-values
A (4) और (-1) / (4) and (-1)
B (4) और (1) / (4) and (1)
C (-4) और (1) / (-4) and (1)
D (-5) और (4) / (-5) and (4)
Explanation opens after your attempt
Correct Answer
A. (4) और (-1) / (4) and (-1)
Step 1
Concept
For equal roots, put (D=0). This gives \(k^2-3k-4=0\), so (k=4) or (k=-1).
Step 2
Why this answer is correct
The correct answer is A. (4) और (-1) / (4) and (-1). For equal roots, put (D=0). This gives \(k^2-3k-4=0\), so (k=4) or (k=-1).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखें। इससे \(k^2-3k-4=0\) मिलता है, इसलिए (k=4) या (k=-1)।
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तालिका में (p(-5)=0), (p(-1)=2), (p(4)=0), (p(6)=9) है। कौन से (x)-मान शून्यक हैं?
In a table (p(-5)=0), (p(-1)=2), (p(4)=0), (p(6)=9). Which (x)-values are zeroes?
#table values zeroes
A (-1) और (6) / (-1) and (6)
B (2) और (9) / (2) and (9)
C (-5) और (4) / (-5) and (4)
D सभी मान / All values
Explanation opens after your attempt
Correct Answer
C. (-5) और (4) / (-5) and (4)
Step 1
Concept
A zero occurs where (p(x)=0). Tip: find the function value (0) in the table.
Step 2
Why this answer is correct
The correct answer is C. (-5) और (4) / (-5) and (4). A zero occurs where (p(x)=0). Tip: find the function value (0) in the table.
Step 3
Exam Tip
जहाँ (p(x)=0) है वहीं शून्यक मिलता है। टिप: तालिका में (0) वाला फलन मान खोजें।
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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
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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यदि (a=9q+r), तो (r) के कितने संभव मान हो सकते हैं?
If (a=9q+r), how many possible values can (r) have?
#euclids-division-lemma
#possible-values
#remainder
A 8
B 9
C 10
D अनंत / Infinitely many
Explanation opens after your attempt
Step 1
Concept
The remainder must satisfy \(0\le r<9\).
Step 2
Why this answer is correct
The possible values are 0 through 8, so there are 9 values.
Step 3
Exam Tip
The number of possible remainders is equal to the divisor. चरण 1: शेषफल के लिए \(0\le r<9\) होगा। चरण 2: संभव मान 0, 1, 2, 3, 4, 5, 6, 7, 8 हैं, कुल 9 मान। चरण 3: संभव शेषफलों की संख्या हमेशा भाजक के बराबर होती है।
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मरियान का चेहरा और वेशभूषा किन मूल्यों को दिखाने के लिए गढ़े गए?
Marianne's face and dress were designed to show which values?
#marianne
#liberty
#republic
#values
A स्वतंत्रता और गणतंत्र / Liberty and republic
B गुलामी और डर / Slavery and fear
C सामंती विशेषाधिकार / Feudal privileges
D औपनिवेशिक अधीनता / Colonial subordination
Explanation opens after your attempt
Correct Answer
A. स्वतंत्रता और गणतंत्र / Liberty and republic
Step 1
Concept
Marianne was created as a symbol of the French Republic.
Step 2
Why this answer is correct
Her appearance was linked with liberty and republican values.
Step 3
Exam Tip
The form of a symbol shows its message. चरण 1: मरियान को फ्रांसीसी गणराज्य के प्रतीक के रूप में बनाया गया। चरण 2: उसका रूप स्वतंत्रता और गणतांत्रिक मूल्यों से जुड़ा था। चरण 3: प्रतीक का रूप उसके संदेश को दिखाता है।
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यदि (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?
If (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0), what is the distance between the given zeroes?
#function values
#distance
#zeroes
A (11)
B (3)
C (15)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (11). The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-7) और (4) हैं इसलिए दूरी (4-(-7)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?
If (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0), what is the distance between the given zeroes?
#function values
#distance
#zeroes
A (1)
B (11)
C (14)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is B. (11). The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (5) हैं, इसलिए दूरी (5-(-6)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि (p(-8)=0), (p(-2)>0), (p(3)=0) और (p(9)<0) है तो दिए गए शून्यकों का योग क्या है?
If (p(-8)=0), (p(-2)>0), (p(3)=0) and (p(9)<0), what is the sum of the given zeroes?
#function values
#sum of zeroes
#graph
A (-5)
B (5)
C (-11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-5). The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-8) और (3) हैं इसलिए योग (-5) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि (p(-6)=0), (p(-1)>0), (p(4)=0) और (p(7)<0) है, तो दिए गए शून्यकों का गुणनफल क्या है?
If (p(-6)=0), (p(-1)>0), (p(4)=0) and (p(7)<0), what is the product of the given zeroes?
#function values
#product of zeroes
#graph
A (-24)
B (24)
C (-7)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-24). The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (4) हैं, इसलिए गुणनफल (-24) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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एक मोबाइल डेटा योजना में पहले दिन (5) जीबी डेटा मिलता है और हर अगले दिन (3) जीबी अधिक मिलता है। (16)वें दिन कितना डेटा मिलेगा?
In a mobile data plan (5) GB data is given on the first day and (3) GB more each next day. How much data is given on the (16)th day?
#ap
#word-problem
#data
A (47)
B (50)
C (53)
D (56)
Explanation opens after your attempt
Step 1
Concept
The data amounts are \(5,8,11,\ldots\) and \(a_{16}=50\). Exam tip: take the day number as the term number.
Step 2
Why this answer is correct
The correct answer is B. (50). The data amounts are \(5,8,11,\ldots\) and \(a_{16}=50\). Exam tip: take the day number as the term number.
Step 3
Exam Tip
डेटा मात्रा \(5,8,11,\ldots\) है और \(a_{16}=50\)। परीक्षा में दिन संख्या को पद संख्या मानें।
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एक मोबाइल डेटा योजना में पहले दिन (3) जीबी डेटा मिलता है और हर अगले दिन (2) जीबी अधिक मिलता है। (15)वें दिन कितना डेटा मिलेगा?
In a mobile data plan (3) GB data is given on the first day and (2) GB more each next day. How much data is given on the (15)th day?
#ap
#word-problem
#data
A (29) जीबी
B (31) जीबी
C (33) जीबी
D (35) जीबी
Explanation opens after your attempt
Correct Answer
B. (31) जीबी
Step 1
Concept
The data amounts are \(3,5,7,\ldots\) and \(a_{15}=31\). Exam tip: take the day number as the term number.
Step 2
Why this answer is correct
The correct answer is B. (31) जीबी. The data amounts are \(3,5,7,\ldots\) and \(a_{15}=31\). Exam tip: take the day number as the term number.
Step 3
Exam Tip
डेटा मात्रा \(3,5,7,\ldots\) है और \(a_{15}=31\)। परीक्षा में दिन संख्या को पद संख्या मानें।
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एक मोबाइल डेटा योजना में पहले दिन (2) जीबी डेटा मिलता है और हर अगले दिन (3) जीबी अधिक मिलता है। (8) दिनों में कुल कितना डेटा मिलेगा?
In a mobile data plan (2) GB data is given on the first day and (3) GB more each next day. How much total data is given in (8) days?
#ap
#word-problem
#data
A (92) जीबी / (92) GB
B (96) जीबी / (96) GB
C (100) जीबी / (100) GB
D (104) जीबी / (104) GB
Explanation opens after your attempt
Correct Answer
C. (100) जीबी / (100) GB
Step 1
Concept
The data amounts are \(2,5,8,\ldots\). \(S_8=100\) GB.
Step 2
Why this answer is correct
The correct answer is C. (100) जीबी / (100) GB. The data amounts are \(2,5,8,\ldots\). \(S_8=100\) GB.
Step 3
Exam Tip
डेटा मात्रा \(2,5,8,\ldots\) है। \(S_8=100\) जीबी होगा।
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एक मोबाइल डेटा योजना में पहले दिन (1) जीबी डेटा मिलता है और हर अगले दिन (2) जीबी अधिक मिलता है। (10) दिनों में कुल कितना डेटा मिलेगा?
In a mobile data plan (1) GB data is given on the first day and (2) GB more each next day. How much total data is given in (10) days?
#ap
#word-problem
#data
A (90) जीबी
B (95) जीबी
C (100) जीबी
D (105) जीबी
Explanation opens after your attempt
Correct Answer
C. (100) जीबी
Step 1
Concept
The data amounts are \(1,3,5,\ldots\). \(S_{10}=100\) GB.
Step 2
Why this answer is correct
The correct answer is C. (100) जीबी. The data amounts are \(1,3,5,\ldots\). \(S_{10}=100\) GB.
Step 3
Exam Tip
डेटा मात्रा \(1,3,5,\ldots\) है। \(S_{10}=100\) जीबी होगा।
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एक मोबाइल डेटा प्लान में पहले दिन (2) जीबी डेटा मिलता है और हर अगले दिन (1) जीबी अधिक मिलता है। (14)वें दिन कितना डेटा मिलेगा?
In a mobile data plan, (2) GB data is given on the first day and (1) GB more each next day. How much data is given on the (14)th day?
#ap
#word-problem
#data
A (14) जीबी
B (15) जीबी
C (16) जीबी
D (17) जीबी
Explanation opens after your attempt
Correct Answer
B. (15) जीबी
Step 1
Concept
The data amounts are \(2,3,4,\ldots\). (a_{14}=2+13(1)=15).
Step 2
Why this answer is correct
The correct answer is B. (15) जीबी. The data amounts are \(2,3,4,\ldots\). (a_{14}=2+13(1)=15).
Step 3
Exam Tip
डेटा मात्रा \(2,3,4,\ldots\) है। (a_{14}=2+13(1)=15)।
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समांतर श्रेढ़ी \(21,24,27,30,\ldots\) में कौन-सा पद दिए गए चार पदों में नहीं है?
Which term is not among the four given terms of \(21,24,27,30,\ldots\)?
#arithmetic-progression
#given-terms
#class10
A (21)
B (24)
C (30)
D (33)
Explanation opens after your attempt
Step 1
Concept
The four given terms are (21,24,27,30). (33) can be the next term but is not among the four given terms.
Step 2
Why this answer is correct
The correct answer is D. (33). The four given terms are (21,24,27,30). (33) can be the next term but is not among the four given terms.
Step 3
Exam Tip
दिए गए चार पद (21,24,27,30) हैं। (33) अगला पद हो सकता है पर दिए गए चार पदों में नहीं है।
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समांतर श्रेढ़ी \(18,21,24,27,\ldots\) में कौन-सा पद दिया गया नहीं है?
Which term is not given in the arithmetic progression \(18,21,24,27,\ldots\)?
#arithmetic-progression
#given-terms
#class10
A (18)
B (21)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
Step 2
Why this answer is correct
The correct answer is D. (30). The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
Step 3
Exam Tip
लिखे हुए पद (18,21,24,27) हैं। (30) अगला पद हो सकता है पर दिए गए पदों में नहीं है।
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(x-2 -2(a-3)x+a-2 -16=0) की जड़ों का गुणनफल (0) हो, तो (a) के मान क्या हैं?
If the product of roots of (x-2 -2(a-3)x+a-2 -16=0) is (0), what are the values of (a)?
#quadratic-roots
#zero-product
#parameter
A (4) और (-4) / (4) and (-4)
B (3) और (-3) / (3) and (-3)
C (8) और (-8) / (8) and (-8)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
A. (4) और (-4) / (4) and (-4)
Step 1
Concept
The product of roots is \(a^2-16\). Setting it equal to (0) gives \(a^2=16\), so (a=4) or (a=-4).
Step 2
Why this answer is correct
The correct answer is A. (4) और (-4) / (4) and (-4). The product of roots is \(a^2-16\). Setting it equal to (0) gives \(a^2=16\), so (a=4) or (a=-4).
Step 3
Exam Tip
जड़ों का गुणनफल \(a^2-16\) है। इसे (0) रखने पर \(a^2=16\), इसलिए (a=4) या (a=-4)।
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(x-2 -2(a-2)x+a-2 -9=0) की जड़ों का गुणनफल (0) हो, तो (a) के मान क्या हैं?
If the product of the roots of (x-2 -2(a-2)x+a-2 -9=0) is (0), what are the values of (a)?
#quadratic-roots
#zero-product
#parameter
A (0) और (9) / (0) and (9)
B (3) और (-3) / (3) and (-3)
C (2) और (-2) / (2) and (-2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
B. (3) और (-3) / (3) and (-3)
Step 1
Concept
The product of roots is \(a^2-9\). Setting it equal to (0) gives \(a^2=9\), so (a=3) or (a=-3).
Step 2
Why this answer is correct
The correct answer is B. (3) और (-3) / (3) and (-3). The product of roots is \(a^2-9\). Setting it equal to (0) gives \(a^2=9\), so (a=3) or (a=-3).
Step 3
Exam Tip
जड़ों का गुणनफल \(a^2-9\) है। इसे (0) रखने पर \(a^2=9\), इसलिए (a=3) या (a=-3)।
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माया सभ्यता में शून्य के उपयोग का महत्व किस क्षेत्र से सबसे अधिक जुड़ा था?
The importance of the use of zero in Maya civilization was most connected with which field?
#world history
#ancient civilizations
#maya
#zero
A गणना और कैलेंडर / Calculation and calendar
B घुड़सवारी / Horse riding
C लोहे की तलवार / Iron sword
D मुद्रण मशीन / Printing machine
Explanation opens after your attempt
Correct Answer
A. गणना और कैलेंडर / Calculation and calendar
Step 1
Concept
The Maya used zero in calculation and timekeeping. For exams connect the Maya with mathematical achievement.
Step 2
Why this answer is correct
The correct answer is A. गणना और कैलेंडर / Calculation and calendar. The Maya used zero in calculation and timekeeping. For exams connect the Maya with mathematical achievement.
Step 3
Exam Tip
माया गणना और समय मापन में शून्य का उपयोग करते थे। परीक्षा में माया को गणितीय उपलब्धि से जोड़ें।
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किस प्राचीन सभ्यता में शून्य की अवधारणा का उन्नत उपयोग माया कैलेंडर में दिखता है?
In which ancient civilization is an advanced use of zero seen in the Maya calendar?
#world history
#ancient civilizations
#maya zero
A माया / Maya
B रोमन / Roman
C मिस्री / Egyptian
D फोनीशियन / Phoenician
Explanation opens after your attempt
Correct Answer
A. माया / Maya
Step 1
Concept
Maya civilization had an advanced counting and calendar system. Link it with astronomical knowledge in exams.
Step 2
Why this answer is correct
The correct answer is A. माया / Maya. Maya civilization had an advanced counting and calendar system. Link it with astronomical knowledge in exams.
Step 3
Exam Tip
माया सभ्यता में गणना और कैलेंडर प्रणाली उन्नत थी। परीक्षा में इसे खगोल ज्ञान से जोड़ें।
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ब्रह्मगुप्त का शून्य संबंधी नियम किस क्षेत्र की उपलब्धि है?
Brahmagupta's rules related to zero are achievements of which field?
#ancient-history
#brahmagupta
#zero
A गणित / Mathematics
B मूर्तिकला / Sculpture
C राजस्व प्रशासन / Revenue administration
D संगम कविता / Sangam poetry
Explanation opens after your attempt
Correct Answer
A. गणित / Mathematics
Step 1
Concept
Brahmagupta gave important mathematical rules on zero and numbers. For exams, connect zero with a major achievement of Indian mathematics.
Step 2
Why this answer is correct
The correct answer is A. गणित / Mathematics. Brahmagupta gave important mathematical rules on zero and numbers. For exams, connect zero with a major achievement of Indian mathematics.
Step 3
Exam Tip
ब्रह्मगुप्त ने शून्य और संख्याओं पर महत्वपूर्ण गणितीय नियम दिए। परीक्षा में शून्य को भारतीय गणित की प्रमुख उपलब्धि से जोड़ें।
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संख्या रेखा पर (r(x)=4x+6) का शून्यक किस अंतराल में होगा?
In which interval will the zero of (r(x)=4x+6) lie on the number line?
#polynomials
#number-line
#linear-zero
#medium
A (-2) और (-1) / (-2) and (-1)
B (-1) और (0) / (-1) and (0)
C (1) और (2) / (1) and (2)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) / (-2) and (-1)
Step 1
Concept
From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) / (-2) and (-1). From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 3
Exam Tip
(4x+6=0) से \(x=-\frac{3}{2}\), जो (-2) और (-1) के बीच है। परीक्षा में ऋणात्मक भिन्न का अंतराल सावधानी से पहचानें।
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बहुपद (q(x)=3x-7) का शून्यक संख्या रेखा पर किस दो पूर्णांकों के बीच होगा?
Between which two integers will the zero of (q(x)=3x-7) lie on the number line?
#polynomials
#number-line
#zero-location
#medium
A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (-3) और (-2) / (-3) and (-2)
Explanation opens after your attempt
Correct Answer
B. (2) और (3) / (2) and (3)
Step 1
Concept
From (3x-7=0), \(x=\frac{7}{3}\), which lies between (2) and (3). In exams, first find the zero and then locate it.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). From (3x-7=0), \(x=\frac{7}{3}\), which lies between (2) and (3). In exams, first find the zero and then locate it.
Step 3
Exam Tip
(3x-7=0) से \(x=\frac{7}{3}\), जो (2) और (3) के बीच है। परीक्षा में पहले शून्यक निकालें फिर स्थान तय करें।
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संख्या रेखा पर (p(x)=2x+5) का शून्यक किस बिंदु पर होगा?
At which point will the zero of (p(x)=2x+5) lie on the number line?
#polynomials
#number-line
#linear-polynomial-zero
#medium
A (2.5)
B (-2.5)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
From (2x+5=0), we get \(x=-\frac{5}{2}=-2.5\). In exams, find the zero and place it like a real number.
Step 2
Why this answer is correct
The correct answer is B. (-2.5). From (2x+5=0), we get \(x=-\frac{5}{2}=-2.5\). In exams, find the zero and place it like a real number.
Step 3
Exam Tip
(2x+5=0) से \(x=-\frac{5}{2}=-2.5\) मिलता है। परीक्षा में शून्यक निकालकर उसे वास्तविक संख्या की तरह रखें।
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संख्या रेखा पर (u(x)=6x-18) का शून्यक किस बिंदु पर होगा?
At which point will the zero of (u(x)=6x-18) lie on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A (2)
B (3)
C (6)
D (18)
Explanation opens after your attempt
Step 1
Concept
From (6x-18=0), we get (x=3). In exams, find the zero first and then place it correctly on the number line.
Step 2
Why this answer is correct
The correct answer is B. (3). From (6x-18=0), we get (x=3). In exams, find the zero first and then place it correctly on the number line.
Step 3
Exam Tip
(6x-18=0) से (x=3) मिलता है। परीक्षा में शून्यक निकालकर उसे संख्या रेखा पर सही बिंदु पर रखें।
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संख्या रेखा पर (p(x)=x) का शून्यक कौन सा है?
What is the zero of (p(x)=x) on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A \(-1\)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
For (p(x)=x), putting (x=0) gives (p(x)=0). In exams, a zero is the value where the polynomial becomes (0).
Step 2
Why this answer is correct
The correct answer is B. (0). For (p(x)=x), putting (x=0) gives (p(x)=0). In exams, a zero is the value where the polynomial becomes (0).
Step 3
Exam Tip
(p(x)=x) में (x=0) रखने पर (p(x)=0) होता है। परीक्षा में शून्यक वह मान है जहां बहुपद का मान (0) हो।
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यदि बहुपद का शून्यक (-5) है, तो संख्या रेखा पर वह किस दिशा में होगा?
If the zero of a polynomial is (-5), in which direction will it lie on the number line?
#polynomials
#number-line
#zero-direction
#class-10
A (0) के दाईं ओर / To the right of (0)
B (0) के बाईं ओर / To the left of (0)
C ठीक (0) पर / Exactly at (0)
D (5) और (6) के बीच / Between (5) and (6)
Explanation opens after your attempt
Correct Answer
B. (0) के बाईं ओर / To the left of (0)
Step 1
Concept
The zero (-5) is negative, so it lies to the left of (0). In exams, the sign of the zero tells its direction.
Step 2
Why this answer is correct
The correct answer is B. (0) के बाईं ओर / To the left of (0). The zero (-5) is negative, so it lies to the left of (0). In exams, the sign of the zero tells its direction.
Step 3
Exam Tip
शून्यक (-5) ऋणात्मक है इसलिए वह (0) के बाईं ओर होगा। परीक्षा में शून्यक का चिह्न उसकी दिशा बताता है।
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बहुपद (q(x)=x-8) का शून्यक संख्या रेखा पर किस बिंदु पर होगा?
At which point will the zero of the polynomial (q(x)=x-8) lie on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A \(-8\)
B (0)
C (8)
D (1)
Explanation opens after your attempt
Step 1
Concept
From (x-8=0), we get (x=8). In exams, the zero of (x-a) is (a).
Step 2
Why this answer is correct
The correct answer is C. (8). From (x-8=0), we get (x=8). In exams, the zero of (x-a) is (a).
Step 3
Exam Tip
(x-8=0) से (x=8) मिलता है। परीक्षा में (x-a) का शून्यक (a) होता है।
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संख्या रेखा पर (p(x)=x+3) के शून्यक को कहां दर्शाया जाएगा?
Where will the zero of (p(x)=x+3) be represented on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A (3) पर / At (3)
B (-3) पर / At (-3)
C (0) पर / At (0)
D (1) पर / At (1)
Explanation opens after your attempt
Correct Answer
B. (-3) पर / At (-3)
Step 1
Concept
From (x+3=0), we get (x=-3). In exams, find the zero and show it as a point on the number line.
Step 2
Why this answer is correct
The correct answer is B. (-3) पर / At (-3). From (x+3=0), we get (x=-3). In exams, find the zero and show it as a point on the number line.
Step 3
Exam Tip
(x+3=0) से (x=-3) मिलता है। परीक्षा में शून्यक निकालकर उसे संख्या रेखा पर बिंदु की तरह दिखाएं।
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यदि (p(x)=x-3 -2x-2 -13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -2x-2 -13x-10), which of the following is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (5)
B (2)
C -(1)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 2
Why this answer is correct
The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 3
Exam Tip
(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।
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(p(x)=16x-2 -24x+9) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=16x-2 -24x+9)?
#zero
#fraction
#quadratic
A \(\frac{3}{4}\)
B \(-\frac{3}{4}\)
C \(\frac{4}{3}\)
D \(-\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{4}\)
Step 1
Concept
(16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{4}\). (16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 3
Exam Tip
(16x-2 -24x+9=(4x-3)2 ), इसलिए शून्य \(x=\frac{3}{4}\) है। पूर्ण वर्ग पहचानें।
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यदि (x=-3), बहुपद (p(x)=x-2 +kx-18) का शून्य है, तो (k) क्या है?
If (x=-3) is a zero of (p(x)=x-2 +kx-18), what is (k)?
#zero
#parameter
#quadratic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-3)=9-3k-18=0), इसलिए (-3k=9) और (k=-3)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (x=0), (p(x)=7x-3 -2x) का शून्यक है, तो कारण क्या है?
If (x=0) is a zero of (p(x)=7x-3 -2x), what is the reason?
#zero-at-origin
#factor
#polynomial
A हर पद में (x) गुणनखंड है / Every term has factor (x)
B स्थिर पद (7) है / Constant term is (7)
C घात (3) है / Degree is (3)
D गुणांक ऋणात्मक है / A coefficient is negative
Explanation opens after your attempt
Correct Answer
A. हर पद में (x) गुणनखंड है / Every term has factor (x)
Step 1
Concept
(p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 2
Why this answer is correct
The correct answer is A. हर पद में (x) गुणनखंड है / Every term has factor (x). (p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 3
Exam Tip
(p(x)=x\(7x^2-2\)), इसलिए (x=0) पर मान (0) होता है। यदि हर पद में (x) हो, तो (0) शून्यक होता है।
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यदि (p(x)=4x-12), तो इसका शून्यक क्या है?
If (p(x)=4x-12), what is its zero?
#linear-polynomial
#zero
#evaluation
A (3)
B -(3)
C (4)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (4x-12=0), we get (x=3). A zero is the value where the polynomial becomes (0).
Step 2
Why this answer is correct
The correct answer is A. (3). From (4x-12=0), we get (x=3). A zero is the value where the polynomial becomes (0).
Step 3
Exam Tip
(4x-12=0) से (x=3) मिलता है। शून्यक वह मान है जहाँ बहुपद का मान (0) हो।
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यदि (p(x)=ax+b) और \(a\neq0\), तो इसका शून्यक क्या है?
If (p(x)=ax+b) and \(a\neq0\), what is its zero?
#linear-zero
#general-form
#polynomial
A -\(\frac{b}{a}\)
B \(\frac{b}{a}\)
C -\(\frac{a}{b}\)
D \(\frac{a}{b}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{b}{a}\)
Step 1
Concept
Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{b}{a}\). Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 3
Exam Tip
(ax+b=0) रखने पर \(x=-\frac{b}{a}\) मिलता है। रेखीय बहुपद में केवल एक शून्यक होता है।
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कौन-सा कथन सही है: (p(x)=0) जहाँ (p(x)) शून्य बहुपद है?
Which statement is correct for (p(x)=0), where (p(x)) is the zero polynomial?
#zero-polynomial
#degree
#concept
A इसकी घात परिभाषित नहीं होती / Its degree is not defined
B इसकी घात (0) होती है / Its degree is (0)
C इसकी घात (1) होती है / Its degree is (1)
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
A. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is A. इसकी घात परिभाषित नहीं होती / Its degree is not defined. The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
शून्य बहुपद में कोई अशून्य पद नहीं होता, इसलिए उसकी घात परिभाषित नहीं होती। स्थिर अशून्य बहुपद की घात (0) होती है।
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यदि (p(x)=x-3 -4x-2 +x+6), तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -4x-2 +x+6), which of these is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (2)
B (1)
C (-1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 3
Exam Tip
(p(2)=8-16+2+6=0), इसलिए (2) शून्यक है। विकल्पों में छोटे पूर्णांकों को पहले जाँचें।
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(p(x)=9x-2 +12x+4) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=9x-2 +12x+4)?
#zero
#fraction
#quadratic
A \(-\frac{2}{3}\)
B \(\frac{2}{3}\)
C \(-\frac{3}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{2}{3}\)
Step 1
Concept
(9x-2 +12x+4=(3x+2)2 ), so the zero is \(x=-\frac{2}{3}\). Recognize the perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{2}{3}\). (9x-2 +12x+4=(3x+2)2 ), so the zero is \(x=-\frac{2}{3}\). Recognize the perfect square.
Step 3
Exam Tip
(9x-2 +12x+4=(3x+2)2 ), इसलिए शून्य \(x=-\frac{2}{3}\) है। पूर्ण वर्ग पहचानें।
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यदि (x=-2), बहुपद (p(x)=x-2 +kx-8) का शून्य है, तो (k) क्या है?
If (x=-2) is a zero of (p(x)=x-2 +kx-8), what is (k)?
#zero
#parameter
#quadratic
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-2). (p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-2)=4-2k-8=0), इसलिए (-2k=4) और (k=-2)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=kx-2 -5x+6) का एक शून्यक (2) है, तो (k) का मान क्या होगा?
If (2) is a zero of (p(x)=kx-2 -5x+6), what is the value of (k)?
#polynomials
#zero
#value
#hard
A (1)
B (2)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 3
Exam Tip
(p(2)=0) रखने पर (4k-10+6=0) से (k=1) मिलता है। शून्यक के लिए (p\(\alpha\)=0) लगाएं।
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(p(x)=4x-2 -12x+9) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=4x-2 -12x+9)?
#zero
#fraction
#quadratic
A \(\frac{1}{2}\)
B \(\frac{3}{2}\)
C (2)
D (3)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{2}\)
Step 1
Concept
(p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{2}\). (p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.
Step 3
Exam Tip
(p\left\(\frac{3}{2}\right\)=9-18+9=0)। भिन्न मान रखते समय वर्ग और गुणा सही करें।
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यदि (x=3), बहुपद (p(x)=x-2 -kx+12) का शून्य है, तो (k) क्या है?
If (x=3) is a zero of (p(x)=x-2 -kx+12), what is (k)?
#zero
#parameter
#quadratic
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is C. (7). (p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(3)=9-3k+12=0), इसलिए (21=3k) और (k=7)। शून्य की शर्त में बहुपद का मान (0) रखें।
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यदि (p(x)=ax-2 +4x-12) और (x=2) इसका शून्य है, तो (a) क्या होगा?
If (p(x)=ax-2 +4x-12) and (x=2) is its zero, what is (a)?
#zero condition
#parameter
#quadratic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(2)=4a+8-12=0), इसलिए (4a=4) और (a=1)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=cx+d) और \(c\ne0\), तो इसका शून्य क्या होगा?
If (p(x)=cx+d) and \(c\ne0\), what will be its zero?
#linear zero
#general form
#formula
A \(\frac{d}{c}\)
B \(-\frac{d}{c}\)
C (cd)
D (c-d)
Explanation opens after your attempt
Correct Answer
B. \(-\frac{d}{c}\)
Step 1
Concept
From (cx+d=0), we get \(x=-\frac{d}{c}\). Remember the negative sign in the formula.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{d}{c}\). From (cx+d=0), we get \(x=-\frac{d}{c}\). Remember the negative sign in the formula.
Step 3
Exam Tip
(cx+d=0) से \(x=-\frac{d}{c}\) मिलता है। सूत्र में ऋण चिह्न ध्यान रखें।
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(p(x)=4x+20) का शून्य कौन सा है?
Which is the zero of (p(x)=4x+20)?
#linear polynomial
#zero
#solution
A (5)
B (-5)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
From (4x+20=0), we get (x=-5). A zero is the value that makes the polynomial equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-5). From (4x+20=0), we get (x=-5). A zero is the value that makes the polynomial equal to (0).
Step 3
Exam Tip
(4x+20=0) से (x=-5) मिलता है। शून्य वह मान है जिससे बहुपद (0) हो जाए।
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(p(x)=9x-27) का शून्य क्या है?
What is the zero of (p(x)=9x-27)?
#linear zero
#equation
#polynomial
A (2)
B (3)
C (9)
D (27)
Explanation opens after your attempt
Step 1
Concept
From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 2
Why this answer is correct
The correct answer is B. (3). From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 3
Exam Tip
(9x-27=0) से (x=3) मिलता है। रैखिक बहुपद का शून्य समीकरण हल करके निकालें।
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किस मान के लिए \(x^2-6x+m\) में (x=2) शून्य होगा?
For what value of (m) will (x=2) be a zero of \(x^2-6x+m\)?
#zero
#parameter
#quadratic
A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (8). (4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(4-12+m=0), इसलिए (m=8)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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(x=-3) किस बहुपद का शून्य है?
For which polynomial is (x=-3) a zero?
#zero
#linear polynomial
#evaluation
A (p(x)=x+3)
B (p(x)=x-3)
C (p(x)=3x+1)
D (p(x)=x-2 +3)
Explanation opens after your attempt
Correct Answer
A. (p(x)=x+3)
Step 1
Concept
(p(-3)=-3+3=0), so (x=-3) is its zero. To test a zero, substitute the value and check for (0).
Step 2
Why this answer is correct
The correct answer is A. (p(x)=x+3). (p(-3)=-3+3=0), so (x=-3) is its zero. To test a zero, substitute the value and check for (0).
Step 3
Exam Tip
(p(-3)=-3+3=0), इसलिए (x=-3) इसका शून्य है। शून्य जांचने के लिए मान रखकर परिणाम (0) देखें।
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निम्न में से कौन सा कथन शून्य बहुपद के लिए सही है?
Which statement is correct for the zero polynomial?
#zero-polynomial
#degree
#concept
A इसकी घात (0) होती है / Its degree is (0)
B इसकी घात (1) होती है / Its degree is (1)
C इसकी घात परिभाषित नहीं होती / Its degree is not defined
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is C. इसकी घात परिभाषित नहीं होती / Its degree is not defined. The degree of the zero polynomial is not defined. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। गैर-शून्य नियत बहुपद की घात (0) होती है।
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यदि (p(x)=x-2 +px+16) और (4) इसका शून्य है, तो (p) का मान क्या है?
If (4) is a zero of (p(x)=x-2 +px+16), what is the value of (p)?
#zero
#parameter
#quadratic
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). \(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 3
Exam Tip
\(4^2+4p+16=0\) से (32+4p=0) मिलता है। इसलिए (p=-8) है।
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यदि (p(x)=x-2 -9), तो कौन सी संख्या (p(x)) का शून्य नहीं है?
If (p(x)=x-2 -9), which number is not a zero of (p(x))?
#zero-of-polynomial
#quadratic
#checking
A (3)
B (-3)
C (0)
D इनमें से कोई नहीं / None of these
Explanation opens after your attempt
Step 1
Concept
(p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is C. (0). (p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 3
Exam Tip
(p(0)=02 -9=-9) है जो (0) नहीं है। इसलिए (0) शून्य नहीं है।
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यदि (p(x)=kx+12) का शून्य (3) है, तो (k) का मान क्या है?
If (3) is a zero of (p(x)=kx+12), what is the value of (k)?
#linear-polynomial
#zero
#parameter
A (4)
B (-4)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 3
Exam Tip
(p(3)=0) से (3k+12=0) मिलता है। इसलिए (k=-4) है।
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