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Mathematics Quiz - Class 10 Mathematics Polynomials Mediu...

Question 1/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद का आलेख (x)-अक्ष को ((-4,0)), ((1,0)) और ((6,0)) पर काटता है। उसके वास्तविक शून्यकों की संख्या कितनी है?

A polynomial graph cuts the (x)-axis at ((-4,0)), ((1,0)) and ((6,0)). How many real zeroes does it have?

Explanation opens after your attempt

Correct Answer

C. तीनThree

Step 1

Concept

There are three distinct (x)-axis intersections, so there are three real zeroes. Tip: count only points with (y=0).

Step 2

Why this answer is correct

The correct answer is C. तीन / Three. There are three distinct (x)-axis intersections, so there are three real zeroes. Tip: count only points with (y=0).

Step 3

Exam Tip

तीन अलग (x)-अक्ष कटान हैं इसलिए तीन वास्तविक शून्यक हैं। टिप: केवल (y=0) वाले बिंदु गिनें।

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Question 2/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी द्विघात बहुपद का परवलय (x)-अक्ष को केवल ((3,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?

If the parabola of a quadratic polynomial only touches the (x)-axis at ((3,0)), what is the number of distinct real zeroes?

Explanation opens after your attempt

Correct Answer

B. एकOne

Step 1

Concept

The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.

Step 2

Why this answer is correct

The correct answer is B. एक / One. The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.

Step 3

Exam Tip

स्पर्श बिंदु केवल एक अलग शून्यक (3) देता है। टिप: दोहराए हुए शून्यक को अलग शून्यक में एक बार गिनें।

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Question 3/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक ग्राफ (x)-अक्ष के ऊपर ही रहता है और उसे कहीं नहीं काटता। उस बहुपद के वास्तविक शून्यक कितने हैं?

A graph stays entirely above the (x)-axis and never cuts it. How many real zeroes does that polynomial have?

Explanation opens after your attempt

Correct Answer

A. शून्यZero

Step 1

Concept

When the graph does not meet the (x)-axis, (p(x)=0) never occurs. Tip: a real zero is seen on the (x)-axis.

Step 2

Why this answer is correct

The correct answer is A. शून्य / Zero. When the graph does not meet the (x)-axis, (p(x)=0) never occurs. Tip: a real zero is seen on the (x)-axis.

Step 3

Exam Tip

जब आलेख (x)-अक्ष से नहीं मिलता तो (p(x)=0) नहीं होता। टिप: वास्तविक शून्यक हमेशा (x)-अक्ष पर दिखता है।

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Question 4/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(a)=0) और (p(b)=0), जहाँ \(a\neq b\), तो आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?

If (p(a)=0) and (p(b)=0), where \(a\neq b\), at which points will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. ((a,0)) और ((b,0))((a,0)) and ((b,0))

Step 1

Concept

The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.

Step 2

Why this answer is correct

The correct answer is C. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0)). The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.

Step 3

Exam Tip

(p(a)=0) का बिंदु ((a,0)) होता है। टिप: (p(x)) ग्राफ में (y)-निर्देशांक होता है।

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Question 5/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद का ग्राफ ((0,-5)), ((2,0)), ((5,0)) और ((7,3)) से गुजरता है। उसके शून्यक कौन से हैं?

A polynomial graph passes through ((0,-5)), ((2,0)), ((5,0)) and ((7,3)). What are its zeroes?

Explanation opens after your attempt

Correct Answer

B. (2) और (5)(2) and (5)

Step 1

Concept

Zeroes are the (x)-values of points where (y=0). Tip: ((0,-5)) is a (y)-intercept, not a zero.

Step 2

Why this answer is correct

The correct answer is B. (2) और (5) / (2) and (5). Zeroes are the (x)-values of points where (y=0). Tip: ((0,-5)) is a (y)-intercept, not a zero.

Step 3

Exam Tip

शून्यक उन बिंदुओं के (x)-मान हैं जहाँ (y=0) है। टिप: ((0,-5)) (y)-अक्ष कटान है, शून्यक नहीं।

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Question 6/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक विद्यार्थी ने (y)-अक्ष कटान ((0,8)) को देखकर (8) को शून्यक माना। सही सुधार क्या है?

A student saw the (y)-axis intercept ((0,8)) and considered (8) as a zero. What is the correct correction?

Explanation opens after your attempt

Correct Answer

C. यह शून्यक नहीं बताता क्योंकि \(y\neq0\) हैIt does not show a zero because \(y\neq0\)

Step 1

Concept

For a zero, the point must lie on the (x)-axis. Tip: check (y=0) when identifying zeroes.

Step 2

Why this answer is correct

The correct answer is C. यह शून्यक नहीं बताता क्योंकि \(y\neq0\) है / It does not show a zero because \(y\neq0\). For a zero, the point must lie on the (x)-axis. Tip: check (y=0) when identifying zeroes.

Step 3

Exam Tip

शून्यक के लिए बिंदु (x)-अक्ष पर होना चाहिए। टिप: शून्यक पहचानते समय (y=0) जांचें।

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Question 7/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

बहुपद (p(x)=(x-4)(x+2)) के आलेख के (x)-अक्ष कटान कौन से होंगे?

What will be the (x)-axis intersections of the graph of (p(x)=(x-4)(x+2))?

Explanation opens after your attempt

Correct Answer

A. ((4,0)) और ((-2,0))((4,0)) and ((-2,0))

Step 1

Concept

Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).

Step 2

Why this answer is correct

The correct answer is A. ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0)). Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).

Step 3

Exam Tip

कारकों को शून्य करने पर (x=4) और (x=-2) मिलते हैं। टिप: शून्यक को ((x,0)) बिंदु में बदलें।

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Question 8/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

रेखा (y=2x-10) (x)-अक्ष को कहाँ काटेगी?

Where will the line (y=2x-10) cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. ((5,0))

Step 1

Concept

On the (x)-axis (y=0), so (2x-10=0) gives (x=5). Tip: put (y=0) to find the zero of a line.

Step 2

Why this answer is correct

The correct answer is B. ((5,0)). On the (x)-axis (y=0), so (2x-10=0) gives (x=5). Tip: put (y=0) to find the zero of a line.

Step 3

Exam Tip

(x)-अक्ष पर (y=0), इसलिए (2x-10=0) से (x=5) है। टिप: रेखा का शून्यक निकालने के लिए (y=0) रखें।

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Question 9/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी परवलय के (x)-अक्ष कटान ((-1,0)) और ((4,0)) हैं, तो शून्यकों का योग क्या है?

If the (x)-axis intersections of a parabola are ((-1,0)) and ((4,0)), what is the sum of zeroes?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The zeroes are (-1) and (4), so their sum is (3). Tip: first read the (x)-values from the points.

Step 2

Why this answer is correct

The correct answer is A. (3). The zeroes are (-1) and (4), so their sum is (3). Tip: first read the (x)-values from the points.

Step 3

Exam Tip

शून्यक (-1) और (4) हैं, इसलिए योग (3) है। टिप: पहले बिंदुओं से (x)-मान पढ़ें।

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Question 10/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x)-अक्ष को ((-6,0)) और ((2,0)) पर काटता है, तो शून्यकों का गुणनफल क्या है?

If a graph cuts the (x)-axis at ((-6,0)) and ((2,0)), what is the product of zeroes?

Explanation opens after your attempt

Correct Answer

C. (-12)

Step 1

Concept

The zeroes are (-6) and (2), so the product is (-12). Tip: do not include the (y)-coordinate in the product.

Step 2

Why this answer is correct

The correct answer is C. (-12). The zeroes are (-6) and (2), so the product is (-12). Tip: do not include the (y)-coordinate in the product.

Step 3

Exam Tip

शून्यक (-6) और (2) हैं, इसलिए गुणनफल (-12) है। टिप: (y)-निर्देशांक को गुणन में शामिल न करें।

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Question 11/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

द्विघात बहुपद का ग्राफ नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?

The graph of a quadratic polynomial opens downward and cuts the (x)-axis at two points. What is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

C. दोTwo

Step 1

Concept

The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is C. दो / Two. The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.

Step 3

Exam Tip

दिशा ऊपर या नीचे होने से संख्या नहीं बदलती, कटान दो हैं। टिप: शून्यकों की संख्या (x)-अक्ष कटान से तय करें।

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Question 12/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(-3)=0), (p(0)=5) और (p(4)=0), तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?

If (p(-3)=0), (p(0)=5) and (p(4)=0), at which points will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. ((-3,0)) और ((4,0))((-3,0)) and ((4,0))

Step 1

Concept

Where (p(x)=0), there is an (x)-axis intersection. Tip: (p(0)=5) does not give a zero.

Step 2

Why this answer is correct

The correct answer is B. ((-3,0)) और ((4,0)) / ((-3,0)) and ((4,0)). Where (p(x)=0), there is an (x)-axis intersection. Tip: (p(0)=5) does not give a zero.

Step 3

Exam Tip

जहाँ (p(x)=0) है वहीं (x)-अक्ष कटान है। टिप: (p(0)=5) शून्यक नहीं देता।

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Question 13/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद का ग्राफ (x)-अक्ष को दो बार काटता है और (y)-अक्ष को एक बार काटता है। वास्तविक शून्यक कितने हैं?

A polynomial graph cuts the (x)-axis twice and the (y)-axis once. How many real zeroes does it have?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.

Step 3

Exam Tip

वास्तविक शून्यक केवल (x)-अक्ष कटान से गिने जाते हैं। टिप: (y)-अक्ष कटान को शून्यक में न जोड़ें।

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Question 14/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि परवलय (x)-अक्ष को नहीं काटता लेकिन (y)-अक्ष को ((0,-2)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?

If a parabola does not cut the (x)-axis but cuts the (y)-axis at ((0,-2)), what is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

A. शून्यZero

Step 1

Concept

A (y)-axis intercept does not give a zero because (p(x)\neq0). Tip: meeting the (x)-axis is necessary for a zero.

Step 2

Why this answer is correct

The correct answer is A. शून्य / Zero. A (y)-axis intercept does not give a zero because (p(x)\neq0). Tip: meeting the (x)-axis is necessary for a zero.

Step 3

Exam Tip

(y)-अक्ष कटान शून्यक नहीं देता, क्योंकि (p(x)=0) नहीं है। टिप: शून्यक के लिए (x)-अक्ष से मिलना जरूरी है।

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Question 15/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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?

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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Question 16/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x=-2) पर (x)-अक्ष को पार करता है और (x=3) पर केवल छूता है, तो अलग वास्तविक शून्यक कौन से हैं?

If a graph crosses the (x)-axis at (x=-2) and only touches it at (x=3), what are the distinct real zeroes?

Explanation opens after your attempt

Correct Answer

C. (-2) और (3)(-2) and (3)

Step 1

Concept

Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.

Step 2

Why this answer is correct

The correct answer is C. (-2) और (3) / (-2) and (3). Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.

Step 3

Exam Tip

पार करना और छूना दोनों (p(x)=0) देते हैं। टिप: अलग शून्यक में दोनों (x)-मान लिखें।

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Question 17/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किस ग्राफ में ठीक एक वास्तविक शून्यक होगा?

Which graph will have exactly one real zero?

Explanation opens after your attempt

Correct Answer

B. जो (x)-अक्ष को एक ही बिंदु पर स्पर्श करेOne that touches the (x)-axis at only one point

Step 1

Concept

One touching point gives one real zero. Tip: zeroes depend on meeting the (x)-axis.

Step 2

Why this answer is correct

The correct answer is B. जो (x)-अक्ष को एक ही बिंदु पर स्पर्श करे / One that touches the (x)-axis at only one point. One touching point gives one real zero. Tip: zeroes depend on meeting the (x)-axis.

Step 3

Exam Tip

एक ही स्पर्श बिंदु एक वास्तविक शून्यक देता है। टिप: शून्यक (x)-अक्ष से मिलने पर निर्भर है।

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Question 18/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-2-16), तो इसके ग्राफ के (x)-अक्ष कटान कौन से हैं?

If (p(x)=x^-2-16), what are the (x)-axis intersections of its graph?

Explanation opens after your attempt

Correct Answer

B. ((4,0)) और ((-4,0))((4,0)) and ((-4,0))

Step 1

Concept

Solving \(x^2-16=0\) gives \(x=\pm4\). Tip: write zeroes as (x)-axis points.

Step 2

Why this answer is correct

The correct answer is B. ((4,0)) और ((-4,0)) / ((4,0)) and ((-4,0)). Solving \(x^2-16=0\) gives \(x=\pm4\). Tip: write zeroes as (x)-axis points.

Step 3

Exam Tip

\(x^2-16=0\) से \(x=\pm4\) मिलता है। टिप: शून्यक को (x)-अक्ष बिंदु में लिखें।

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Question 19/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-2+9), तो इसका ग्राफ (x)-अक्ष को कितनी बार काटेगा?

If (p(x)=x^-2+9), how many times will its graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. शून्य बारZero times

Step 1

Concept

For real (x), \(x^2+9\) is never (0). Tip: \(x^2\) is always (0) or positive.

Step 2

Why this answer is correct

The correct answer is A. शून्य बार / Zero times. For real (x), \(x^2+9\) is never (0). Tip: \(x^2\) is always (0) or positive.

Step 3

Exam Tip

\(x^2+9\) वास्तविक (x) के लिए कभी (0) नहीं होता। टिप: \(x^2\) हमेशा (0) या धनात्मक होता है।

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Question 20/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x+1)²), तो ग्राफ (x)-अक्ष से कैसे मिलेगा?

If (p(x)=(x+1)²), how will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. (x=-1) पर स्पर्श करेगाIt will touch at (x=-1)

Step 1

Concept

((x+1)²=0) gives only (x=-1), and it is a repeated zero. Tip: a squared factor often indicates touching.

Step 2

Why this answer is correct

The correct answer is B. (x=-1) पर स्पर्श करेगा / It will touch at (x=-1). ((x+1)²=0) gives only (x=-1), and it is a repeated zero. Tip: a squared factor often indicates touching.

Step 3

Exam Tip

((x+1)²=0) से केवल (x=-1) मिलता है और यह दोहराया शून्यक है। टिप: वर्ग वाले कारक में स्पर्श की संभावना देखें।

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Question 21/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक परवलय (x)-अक्ष को ((-5,0)) और ((1,0)) पर काटता है। उसके शून्यकों का बड़ा मान क्या है?

A parabola cuts the (x)-axis at ((-5,0)) and ((1,0)). What is the greater zero?

Explanation opens after your attempt

Correct Answer

C. (1)

Step 1

Concept

The zeroes are (-5) and (1), and (1) is greater. Tip: the value to the right on the number line is greater.

Step 2

Why this answer is correct

The correct answer is C. (1). The zeroes are (-5) and (1), and (1) is greater. Tip: the value to the right on the number line is greater.

Step 3

Exam Tip

शून्यक (-5) और (1) हैं, जिनमें (1) बड़ा है। टिप: संख्या रेखा पर दाईं ओर वाला मान बड़ा होता है।

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Question 22/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी ग्राफ के (x)-अक्ष कटान ((m,0)) और ((n,0)) हैं, तो शून्यकों का गुणनफल क्या होगा?

If the (x)-axis intersections of a graph are ((m,0)) and ((n,0)), what is the product of the zeroes?

Explanation opens after your attempt

Correct Answer

B. (mn)

Step 1

Concept

The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.

Step 2

Why this answer is correct

The correct answer is B. (mn). The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.

Step 3

Exam Tip

शून्यक (m) और (n) हैं, इसलिए गुणनफल (mn) है। टिप: कटान बिंदु का पहला निर्देशांक ही शून्यक है।

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Question 23/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद के ग्राफ पर ((2,0)), ((3,4)), ((4,0)) और ((5,-1)) बिंदु हैं। (p(3)) और (p(5)) को शून्यक क्यों नहीं कहा जाएगा?

The points ((2,0)), ((3,4)), ((4,0)) and ((5,-1)) lie on a polynomial graph. Why will (3) and (5) not be called zeroes?

Explanation opens after your attempt

Correct Answer

B. क्योंकि उनके (y)-मान (0) नहीं हैंBecause their (y)-values are not (0)

Step 1

Concept

At (3) and (5), (p(x)) is (4) and (-1). Tip: for a zero, the function value must be exactly (0).

Step 2

Why this answer is correct

The correct answer is B. क्योंकि उनके (y)-मान (0) नहीं हैं / Because their (y)-values are not (0). At (3) and (5), (p(x)) is (4) and (-1). Tip: for a zero, the function value must be exactly (0).

Step 3

Exam Tip

(3) और (5) पर (p(x)) क्रमशः (4) और (-1) है। टिप: शून्यक के लिए फलन मान बिल्कुल (0) होना चाहिए।

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Question 24/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी बहुपद का ग्राफ (x)-अक्ष को चार बार काटता दिखे, तो यह किस प्रकार के बहुपद के लिए संभव हो सकता है?

If a polynomial graph appears to cut the (x)-axis four times, for which type of polynomial can this be possible?

Explanation opens after your attempt

Correct Answer

C. चतुर्थ घात बहुपदFourth degree polynomial

Step 1

Concept

A degree (4) polynomial can have at most (4) real zeroes. Tip: the number of real zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. चतुर्थ घात बहुपद / Fourth degree polynomial. A degree (4) polynomial can have at most (4) real zeroes. Tip: the number of real zeroes cannot exceed the degree.

Step 3

Exam Tip

घात (4) वाला बहुपद अधिकतम (4) वास्तविक शून्यक रख सकता है। टिप: वास्तविक शून्यकों की संख्या घात से अधिक नहीं होती।

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Question 25/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किस स्थिति में रैखिक बहुपद का कोई वास्तविक शून्यक नहीं होगा?

In which situation will a linear polynomial have no real zero?

Explanation opens after your attempt

Correct Answer

B. जब उसका ग्राफ (x)-अक्ष के समांतर और ऊपर होWhen its graph is parallel to and above the (x)-axis

Step 1

Concept

A line parallel to and above the (x)-axis does not meet the (x)-axis. Tip: such a graph behaves like a non-zero constant polynomial.

Step 2

Why this answer is correct

The correct answer is B. जब उसका ग्राफ (x)-अक्ष के समांतर और ऊपर हो / When its graph is parallel to and above the (x)-axis. A line parallel to and above the (x)-axis does not meet the (x)-axis. Tip: such a graph behaves like a non-zero constant polynomial.

Step 3

Exam Tip

(x)-अक्ष के समांतर ऊपर रेखा (x)-अक्ष से नहीं मिलती। टिप: ऐसा ग्राफ अशून्य स्थिर बहुपद जैसा होता है।

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Question 26/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(2)) धनात्मक और (p(5)) ऋणात्मक है, तो ग्राफ के बारे में कौन सा कथन सबसे उचित है?

If (p(2)) is positive and (p(5)) is negative, which statement about the graph is most appropriate?

Explanation opens after your attempt

Correct Answer

A. ग्राफ (x=2) और (x=5) के बीच (x)-अक्ष को पार कर सकता हैThe graph may cross the (x)-axis between (x=2) and (x=5)

Step 1

Concept

A change of sign indicates a meeting with the (x)-axis in between. Tip: polynomial graphs are continuous.

Step 2

Why this answer is correct

The correct answer is A. ग्राफ (x=2) और (x=5) के बीच (x)-अक्ष को पार कर सकता है / The graph may cross the (x)-axis between (x=2) and (x=5). A change of sign indicates a meeting with the (x)-axis in between. Tip: polynomial graphs are continuous.

Step 3

Exam Tip

चिह्न बदलना बीच में (x)-अक्ष से मिलने का संकेत देता है। टिप: बहुपद के ग्राफ सतत होते हैं।

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Question 27/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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?

Explanation opens after your attempt

Correct Answer

C. (2)

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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Question 28/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि द्विघात बहुपद का ग्राफ (x)-अक्ष को ((-2,0)) और ((7,0)) पर काटता है, तो (p(-2)) और (p(7)) के मान क्या होंगे?

If the graph of a quadratic polynomial cuts the (x)-axis at ((-2,0)) and ((7,0)), what will be the values of (p(-2)) and (p(7))?

Explanation opens after your attempt

Correct Answer

A. दोनों (0)Both (0)

Step 1

Concept

At an (x)-axis intersection, (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. दोनों (0) / Both (0). At an (x)-axis intersection, (y=p(x)=0). Tip: read the function value directly from the intersection point.

Step 3

Exam Tip

(x)-अक्ष कटान पर (y=p(x)=0) होता है। टिप: कटान बिंदु से फलन मान सीधे पढ़ें।

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Question 29/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक ग्राफ (x)-अक्ष को (x=-3) और (x=9) पर काटता है। शून्यकों के बीच दूरी कितनी है?

A graph cuts the (x)-axis at (x=-3) and (x=9). What is the distance between the zeroes?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The distance is (9-(-3)=12). Tip: distance is always positive.

Step 2

Why this answer is correct

The correct answer is C. (12). The distance is (9-(-3)=12). Tip: distance is always positive.

Step 3

Exam Tip

दूरी (9-(-3)=12) है। टिप: दूरी हमेशा धनात्मक होती है।

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Question 30/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि शून्यक (-2) और (6) हैं, तो (x)-अक्ष कटान बिंदुओं का मध्यबिंदु कौन सा है?

If the zeroes are (-2) and (6), what is the midpoint of the (x)-axis intersection points?

Explanation opens after your attempt

Correct Answer

A. ((2,0))

Step 1

Concept

The midpoint of ((-2,0)) and ((6,0)) is ((2,0)). Tip: when (y)-values are equal, average the (x)-values.

Step 2

Why this answer is correct

The correct answer is A. ((2,0)). The midpoint of ((-2,0)) and ((6,0)) is ((2,0)). Tip: when (y)-values are equal, average the (x)-values.

Step 3

Exam Tip

बिंदु ((-2,0)) और ((6,0)) का मध्यबिंदु ((2,0)) है। टिप: समान (y)-मान हो तो केवल (x)-मानों का औसत लें।

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Question 31/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी परवलय के (x)-अक्ष कटान ((r,0)) और ((s,0)) हैं। इसके शून्यकों का औसत क्या होगा?

The (x)-axis intersections of a parabola are ((r,0)) and ((s,0)). What is the average of its zeroes?

Explanation opens after your attempt

Correct Answer

C. \(\frac{r+s}{2}\)

Step 1

Concept

The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{r+s}{2}\). The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.

Step 3

Exam Tip

शून्यक (r) और (s) हैं, इसलिए औसत \(\frac{r+s}{2}\) है। टिप: औसत में योग को संख्या से भाग दें।

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Question 32/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x)-अक्ष को ((-4,0)) और ((4,0)) पर काटता है, तो शून्यकों के बारे में सही कथन कौन सा है?

If a graph cuts the (x)-axis at ((-4,0)) and ((4,0)), which statement about the zeroes is correct?

Explanation opens after your attempt

Correct Answer

B. वे परस्पर विपरीत हैंThey are opposites of each other

Step 1

Concept

The zeroes are (-4) and (4), which are opposites. Tip: such zeroes have sum (0).

Step 2

Why this answer is correct

The correct answer is B. वे परस्पर विपरीत हैं / They are opposites of each other. The zeroes are (-4) and (4), which are opposites. Tip: such zeroes have sum (0).

Step 3

Exam Tip

शून्यक (-4) और (4) हैं, जो परस्पर विपरीत हैं। टिप: ऐसे शून्यकों का योग (0) होता है।

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Question 33/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी बहुपद का ग्राफ (x)-अक्ष को ((0,0)), ((2,0)) और ((5,0)) पर काटता है, तो कौन सा कथन सही है?

If a polynomial graph cuts the (x)-axis at ((0,0)), ((2,0)) and ((5,0)), which statement is correct?

Explanation opens after your attempt

Correct Answer

B. (0), (2) और (5) शून्यक हैं(0), (2) and (5) are zeroes

Step 1

Concept

The origin is also on the (x)-axis, so (0) is also a zero. Tip: do not ignore ((0,0)).

Step 2

Why this answer is correct

The correct answer is B. (0), (2) और (5) शून्यक हैं / (0), (2) and (5) are zeroes. The origin is also on the (x)-axis, so (0) is also a zero. Tip: do not ignore ((0,0)).

Step 3

Exam Tip

मूल बिंदु भी (x)-अक्ष पर है, इसलिए (0) भी शून्यक है। टिप: ((0,0)) को नजरअंदाज न करें।

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Question 34/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

रेखा (y=-3x-12) का शून्यक क्या है?

What is the zero of the line (y=-3x-12)?

Explanation opens after your attempt

Correct Answer

B. (-4)

Step 1

Concept

Solving (-3x-12=0) gives (x=-4). Tip: put (y=0) to find the linear zero.

Step 2

Why this answer is correct

The correct answer is B. (-4). Solving (-3x-12=0) gives (x=-4). Tip: put (y=0) to find the linear zero.

Step 3

Exam Tip

(-3x-12=0) से (x=-4) मिलता है। टिप: (y=0) रखकर रैखिक शून्यक निकालें।

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Question 35/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x(x-5)), तो ग्राफ किन (x)-मानों पर (x)-अक्ष को काटेगा?

If (p(x)=x(x-5)), at which (x)-values will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (0) और (5)(0) and (5)

Step 1

Concept

From (x=0) or (x-5=0), we get (x=0,5). Tip: if a product is zero, at least one factor is zero.

Step 2

Why this answer is correct

The correct answer is A. (0) और (5) / (0) and (5). From (x=0) or (x-5=0), we get (x=0,5). Tip: if a product is zero, at least one factor is zero.

Step 3

Exam Tip

(x=0) या (x-5=0) से (x=0,5) मिलते हैं। टिप: गुणनफल शून्य हो तो कम से कम एक कारक शून्य होता है।

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Question 36/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद के लिए (p(1)=0), (p(2)=0), (p(3)=0) है। यदि ये तीनों अलग शून्यक हैं, तो ग्राफ (x)-अक्ष से कितने अलग बिंदुओं पर मिलेगा?

For a polynomial (p(1)=0), (p(2)=0), (p(3)=0). If these are three distinct zeroes, at how many distinct points will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. तीनThree

Step 1

Concept

Three distinct (x)-values give three distinct (x)-axis points. Tip: distinct zeroes make distinct intersection points.

Step 2

Why this answer is correct

The correct answer is C. तीन / Three. Three distinct (x)-values give three distinct (x)-axis points. Tip: distinct zeroes make distinct intersection points.

Step 3

Exam Tip

तीन अलग (x)-मान तीन अलग (x)-अक्ष बिंदु देते हैं। टिप: अलग शून्यक अलग कटान बिंदु बनाते हैं।

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Question 37/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(-2)=0) और (p(2)=0), तो ग्राफ की (y)-अक्ष के सापेक्ष शून्यकों की स्थिति कैसी है?

If (p(-2)=0) and (p(2)=0), how are the zeroes positioned with respect to the (y)-axis?

Explanation opens after your attempt

Correct Answer

C. वे (y)-अक्ष के दोनों ओर समान दूरी पर हैंThey are equally distant on both sides of the (y)-axis

Step 1

Concept

(-2) and (2) are equally distant from the (y)-axis. Tip: opposite zeroes may indicate symmetry in the graph.

Step 2

Why this answer is correct

The correct answer is C. वे (y)-अक्ष के दोनों ओर समान दूरी पर हैं / They are equally distant on both sides of the (y)-axis. (-2) and (2) are equally distant from the (y)-axis. Tip: opposite zeroes may indicate symmetry in the graph.

Step 3

Exam Tip

(-2) और (2) (y)-अक्ष से समान दूरी पर हैं। टिप: विपरीत शून्यक ग्राफ में सममिति का संकेत दे सकते हैं।

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Question 38/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक ग्राफ (x)-अक्ष को (x=1) पर पार करता है और (x=4) पर पार करता है। यदि (x=2) पर (p(x)>0), तो (x=2) शून्यक क्यों नहीं है?

A graph crosses the (x)-axis at (x=1) and (x=4). If (p(x)>0) at (x=2), why is (x=2) not a zero?

Explanation opens after your attempt

Correct Answer

B. क्योंकि (p(2)\neq0) हैBecause (p(2)\neq0)

Step 1

Concept

For a zero, the function value must be (0). Tip: being between zeroes does not guarantee being a zero.

Step 2

Why this answer is correct

The correct answer is B. क्योंकि (p(2)\neq0) है / Because (p(2)\neq0). For a zero, the function value must be (0). Tip: being between zeroes does not guarantee being a zero.

Step 3

Exam Tip

शून्यक के लिए फलन मान (0) होना चाहिए। टिप: बीच में होना शून्यक होने की गारंटी नहीं देता।

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Question 39/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो वास्तविक शून्यकों की संख्या क्या मानी जाएगी?

If the graph of a cubic polynomial cuts the (x)-axis only once, what is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

A. एकOne

Step 1

Concept

There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.

Step 2

Why this answer is correct

The correct answer is A. एक / One. There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.

Step 3

Exam Tip

कटान केवल एक है इसलिए एक वास्तविक शून्यक है। टिप: घन बहुपद में अधिकतम तीन वास्तविक शून्यक हो सकते हैं, जरूरी नहीं कि तीन हों।

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Question 40/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि कोई द्विघात ग्राफ (x)-अक्ष के नीचे रहता है और उसे नहीं छूता, तो कौन सा कथन सही है?

If a quadratic graph stays below the (x)-axis and does not touch it, which statement is correct?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक शून्यक नहीं हैIt has no real zero

Step 1

Concept

The graph does not meet the (x)-axis, so (p(x)=0) does not occur. Tip: staying above or below without meeting gives no intersection.

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक शून्यक नहीं है / It has no real zero. The graph does not meet the (x)-axis, so (p(x)=0) does not occur. Tip: staying above or below without meeting gives no intersection.

Step 3

Exam Tip

ग्राफ (x)-अक्ष से नहीं मिलता इसलिए (p(x)=0) नहीं होता। टिप: ऊपर या नीचे रहना दोनों स्थितियों में कोई कटान नहीं देता।

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Question 41/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (x=7) किसी बहुपद का शून्यक है, तो ग्राफ पर कौन सा बिंदु अवश्य होगा?

If (x=7) is a zero of a polynomial, which point must lie on the graph?

Explanation opens after your attempt

Correct Answer

C. ((7,0))

Step 1

Concept

A zero (7) means (p(7)=0). Tip: place the zero as the first coordinate.

Step 2

Why this answer is correct

The correct answer is C. ((7,0)). A zero (7) means (p(7)=0). Tip: place the zero as the first coordinate.

Step 3

Exam Tip

शून्यक (7) होने का अर्थ (p(7)=0) है। टिप: शून्यक को पहले निर्देशांक में रखें।

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Question 42/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी ग्राफ में (x)-अक्ष कटान ((a,0)), ((b,0)), ((c,0)) हैं। इनमें से कौन सा कथन सही है?

A graph has (x)-axis intersections ((a,0)), ((b,0)), ((c,0)). Which statement is correct?

Explanation opens after your attempt

Correct Answer

B. शून्यक (a,b,c) हैंThe zeroes are (a,b,c)

Step 1

Concept

The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).

Step 2

Why this answer is correct

The correct answer is B. शून्यक (a,b,c) हैं / The zeroes are (a,b,c). The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).

Step 3

Exam Tip

हर कटान बिंदु का पहला निर्देशांक शून्यक है। टिप: ((a,0)) से शून्यक (a) पढ़ें।

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Question 43/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=2(x-3)²), तो ग्राफ (x)-अक्ष को कैसे मिलेगा?

If (p(x)=2(x-3)²), how will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (x=3) पर स्पर्श करेगाIt will touch at (x=3)

Step 1

Concept

((x-3)²=0) gives only (x=3), and the square causes touching. Tip: the outside (2) does not change the zero.

Step 2

Why this answer is correct

The correct answer is A. (x=3) पर स्पर्श करेगा / It will touch at (x=3). ((x-3)²=0) gives only (x=3), and the square causes touching. Tip: the outside (2) does not change the zero.

Step 3

Exam Tip

((x-3)²=0) से केवल (x=3) मिलता है और वर्ग के कारण स्पर्श होता है। टिप: बाहर का (2) शून्यक नहीं बदलता।

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Question 44/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=-x^-2+25), तो ग्राफ के वास्तविक शून्यक कौन से होंगे?

If (p(x)=-x^-2+25), what will be the real zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (5) और (-5)(5) and (-5)

Step 1

Concept

From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).

Step 2

Why this answer is correct

The correct answer is A. (5) और (-5) / (5) and (-5). From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).

Step 3

Exam Tip

\(-x^2+25=0\) से \(x^2=25\), इसलिए \(x=\pm5\) है। टिप: ऋण चिह्न देखकर भी (y=0) रखना न भूलें।

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Question 45/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ पर ((-2,0)) और ((6,0)) शून्यक बिंदु हैं, तो उनके बीच (x)-अक्ष पर कितनी इकाई की दूरी है?

If ((-2,0)) and ((6,0)) are zero points on a graph, how many units apart are they on the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The distance is (6-(-2)=8) units. Tip: distance on the (x)-axis is the absolute difference of (x)-values.

Step 2

Why this answer is correct

The correct answer is C. (8). The distance is (6-(-2)=8) units. Tip: distance on the (x)-axis is the absolute difference of (x)-values.

Step 3

Exam Tip

दूरी (6-(-2)=8) इकाई है। टिप: (x)-अक्ष पर दूरी (x)-मानों के अंतर का परिमाण है।

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Question 46/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(0)=0) और (p(5)=0), तो ग्राफ के बारे में कौन सा कथन सही है?

If (p(0)=0) and (p(5)=0), which statement about the graph is correct?

Explanation opens after your attempt

Correct Answer

A. ग्राफ ((0,0)) और ((5,0)) से गुजरता हैThe graph passes through ((0,0)) and ((5,0))

Step 1

Concept

At both given (x)-values, the function value is (0). Tip: when (p(0)=0), the graph passes through the origin.

Step 2

Why this answer is correct

The correct answer is A. ग्राफ ((0,0)) और ((5,0)) से गुजरता है / The graph passes through ((0,0)) and ((5,0)). At both given (x)-values, the function value is (0). Tip: when (p(0)=0), the graph passes through the origin.

Step 3

Exam Tip

दोनों दिए गए (x)-मानों पर फलन मान (0) है। टिप: (p(0)=0) होने पर ग्राफ मूल बिंदु से गुजरता है।

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Question 47/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)) का ग्राफ (x)-अक्ष को ((2,0)) पर काटता है और ((-1,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यक कितने हैं?

If the graph of (p(x)) cuts the (x)-axis at ((2,0)) and touches it at ((-1,0)), how many distinct real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.

Step 3

Exam Tip

कटान और स्पर्श दोनों से (x)-मान (2) और (-1) शून्यक हैं। टिप: अलग (x)-मानों की गिनती करें।

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Question 48/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक बहुपद का ग्राफ (x)-अक्ष को नहीं काटता, पर (p(1)=4) और (p(3)=9) हैं। सही निष्कर्ष क्या है?

A polynomial graph does not cut the (x)-axis, but (p(1)=4) and (p(3)=9). What is the correct conclusion?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक शून्यक नहीं हैThere is no real zero

Step 1

Concept

The graph does not meet the (x)-axis and the given values are not zero. Tip: do not call a value a zero unless the function value is (0).

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक शून्यक नहीं है / There is no real zero. The graph does not meet the (x)-axis and the given values are not zero. Tip: do not call a value a zero unless the function value is (0).

Step 3

Exam Tip

ग्राफ (x)-अक्ष से नहीं मिलता और दिए गए मान भी शून्य नहीं हैं। टिप: फलन मान (0) न हो तो शून्यक न मानें।

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Question 49/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x)-अक्ष को ((-3,0)), ((2,0)), ((8,0)) पर काटता है, तो सबसे छोटा शून्यक कौन सा है?

If a graph cuts the (x)-axis at ((-3,0)), ((2,0)), ((8,0)), which is the smallest zero?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

The zeroes are (-3), (2), (8), and the smallest is (-3). Tip: a negative number is smaller than a positive number.

Step 2

Why this answer is correct

The correct answer is A. (-3). The zeroes are (-3), (2), (8), and the smallest is (-3). Tip: a negative number is smaller than a positive number.

Step 3

Exam Tip

शून्यक (-3), (2), (8) हैं और सबसे छोटा (-3) है। टिप: ऋणात्मक संख्या धनात्मक से छोटी होती है।

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Question 50/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किसी बहुपद के ग्राफ में (x=4) पर (x)-अक्ष से स्पर्श है और (x=-6) पर कटान है। कौन सा कथन सही है?

In a polynomial graph, there is a touch with the (x)-axis at (x=4) and a crossing at (x=-6). Which statement is correct?

Explanation opens after your attempt

Correct Answer

C. (4) और (-6) दोनों शून्यक हैंBoth (4) and (-6) are zeroes

Step 1

Concept

In both touching and crossing, the graph meets the (x)-axis. Tip: for a zero, meeting the axis is enough, crossing is not necessary.

Step 2

Why this answer is correct

The correct answer is C. (4) और (-6) दोनों शून्यक हैं / Both (4) and (-6) are zeroes. In both touching and crossing, the graph meets the (x)-axis. Tip: for a zero, meeting the axis is enough, crossing is not necessary.

Step 3

Exam Tip

स्पर्श और कटान दोनों स्थितियों में ग्राफ (x)-अक्ष से मिलता है। टिप: शून्यक पहचानते समय मिलना देखें, पार करना जरूरी नहीं।

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Question 51/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी बहुपद के आलेख में (x)-अक्ष से मिलना और (y)-अक्ष से मिलना अलग बातें क्यों हैं?

Why are meeting the (x)-axis and meeting the (y)-axis different for a polynomial graph?

Explanation opens after your attempt

Correct Answer

A. (x)-अक्ष पर (p(x)=0) होता हैOn the (x)-axis (p(x)=0)

Step 1

Concept

A zero is obtained only when the graph lies on the (x)-axis. Tip: always identify (y=0).

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष पर (p(x)=0) होता है / On the (x)-axis (p(x)=0). A zero is obtained only when the graph lies on the (x)-axis. Tip: always identify (y=0).

Step 3

Exam Tip

शून्यक तभी मिलता है जब आलेख (x)-अक्ष पर हो। टिप: (y=0) को हमेशा पहचानें।

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Question 52/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी आलेख के (x)-अक्ष कटान ((-8,0)) और ((3,0)) हैं तो शून्यकों का सही जोड़ा कौन सा है?

If the (x)-axis intersections of a graph are ((-8,0)) and ((3,0)), which is the correct pair of zeroes?

Explanation opens after your attempt

Correct Answer

B. (-8) और (3)(-8) and (3)

Step 1

Concept

The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).

Step 2

Why this answer is correct

The correct answer is B. (-8) और (3) / (-8) and (3). The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).

Step 3

Exam Tip

कटान बिंदुओं के पहले निर्देशांक शून्यक होते हैं। टिप: दूसरे निर्देशांक को (0) देखकर बिंदु चुनें।

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Question 53/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

एक परवलय (x)-अक्ष को (x=-4) और (x=6) पर काटता है। इन शून्यकों के बीच मध्य मान क्या है?

A parabola cuts the (x)-axis at (x=-4) and (x=6). What is the middle value between these zeroes?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The middle value is \(\frac{-4+6}{2}=1\). Tip: the average of two zeroes gives the middle value.

Step 2

Why this answer is correct

The correct answer is A. (1). The middle value is \(\frac{-4+6}{2}=1\). Tip: the average of two zeroes gives the middle value.

Step 3

Exam Tip

मध्य मान \(\frac{-4+6}{2}=1\) है। टिप: दो शून्यकों का औसत उनके बीच का मध्य देता है।

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Question 54/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x+7)(x-1)) है तो आलेख (x)-अक्ष को किन बिंदुओं पर मिलेगा?

If (p(x)=(x+7)(x-1)), at which points will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. ((-7,0)) और ((1,0))((-7,0)) and ((1,0))

Step 1

Concept

Setting the factors equal to zero gives (x=-7) and (x=1). Tip: set each factor separately to (0).

Step 2

Why this answer is correct

The correct answer is C. ((-7,0)) और ((1,0)) / ((-7,0)) and ((1,0)). Setting the factors equal to zero gives (x=-7) and (x=1). Tip: set each factor separately to (0).

Step 3

Exam Tip

कारक शून्य करने पर (x=-7) और (x=1) मिलते हैं। टिप: हर कारक को अलग से (0) रखें।

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Question 55/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद का आलेख ((2,0)) पर स्पर्श करता है और ((5,0)) पर काटता है तो अलग वास्तविक शून्यक कितने हैं?

If a polynomial graph touches at ((2,0)) and crosses at ((5,0)), how many distinct real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.

Step 3

Exam Tip

स्पर्श और कटान दोनों (x)-अक्ष से मिलना दिखाते हैं। टिप: अलग (x)-मान गिनें।

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Question 56/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

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?

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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Question 57/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(0)=-3) है तो आलेख के बारे में कौन सा निष्कर्ष सही है?

If (p(0)=-3), which conclusion about the graph is correct?

Explanation opens after your attempt

Correct Answer

A. आलेख ((0,-3)) से गुजरता हैThe graph passes through ((0,-3))

Step 1

Concept

The value (p(0)=-3) shows a (y)-intercept, not a zero. Tip: (0) is a zero only if (p(0)=0).

Step 2

Why this answer is correct

The correct answer is A. आलेख ((0,-3)) से गुजरता है / The graph passes through ((0,-3)). The value (p(0)=-3) shows a (y)-intercept, not a zero. Tip: (0) is a zero only if (p(0)=0).

Step 3

Exam Tip

(p(0)=-3) (y)-अक्ष कटान बताता है, शून्यक नहीं। टिप: (0) शून्यक तभी होगा जब (p(0)=0) हो।

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Question 58/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

एक द्विघात आलेख (x)-अक्ष को नहीं काटता और उसका शीर्ष (x)-अक्ष के ऊपर है। वास्तविक शून्यकों की संख्या क्या है?

A quadratic graph does not cut the (x)-axis and its vertex is above the (x)-axis. What is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

C. शून्यZero

Step 1

Concept

The graph does not meet the (x)-axis, so there is no real zero. Tip: the vertex position can help judge intersections.

Step 2

Why this answer is correct

The correct answer is C. शून्य / Zero. The graph does not meet the (x)-axis, so there is no real zero. Tip: the vertex position can help judge intersections.

Step 3

Exam Tip

आलेख (x)-अक्ष से नहीं मिलता इसलिए कोई वास्तविक शून्यक नहीं है। टिप: शीर्ष की स्थिति से भी कटान का अंदाजा लग सकता है।

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Question 59/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-2x) है तो ग्राफ (x)-अक्ष को किन (x)-मानों पर काटेगा?

If (p(x)=x^-2-2x), at which (x)-values will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (0) और (2)(0) and (2)

Step 1

Concept

(x^-2-2x=x(x-2)), so the zeroes are (0) and (2). Tip: factor out the common term first.

Step 2

Why this answer is correct

The correct answer is A. (0) और (2) / (0) and (2). (x^-2-2x=x(x-2)), so the zeroes are (0) and (2). Tip: factor out the common term first.

Step 3

Exam Tip

(x^-2-2x=x(x-2)) इसलिए शून्यक (0) और (2) हैं। टिप: पहले सामान्य गुणनखंड निकालें।

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Question 60/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि आलेख (x)-अक्ष को (x=-2), (x=1), (x=5) पर काटता है तो शून्यकों का योग क्या है?

If a graph cuts the (x)-axis at (x=-2), (x=1), (x=5), what is the sum of zeroes?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The sum is (-2+1+5=4). Tip: add only the (x)-values of (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is B. (4). The sum is (-2+1+5=4). Tip: add only the (x)-values of (x)-axis intersections.

Step 3

Exam Tip

योग (-2+1+5=4) है। टिप: केवल (x)-अक्ष कटान के (x)-मान जोड़ें।

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Question 61/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ ((0,4)), ((-3,0)), ((1,7)), ((8,0)) से गुजरता है तो कौन से बिंदु शून्यक दिखाते हैं?

If a graph passes through ((0,4)), ((-3,0)), ((1,7)), ((8,0)), which points show zeroes?

Explanation opens after your attempt

Correct Answer

B. ((-3,0)) और ((8,0))((-3,0)) and ((8,0))

Step 1

Concept

Points showing zeroes have (y=0). Tip: check the second coordinate when choosing points.

Step 2

Why this answer is correct

The correct answer is B. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0)). Points showing zeroes have (y=0). Tip: check the second coordinate when choosing points.

Step 3

Exam Tip

शून्यक दिखाने वाले बिंदुओं में (y=0) होता है। टिप: बिंदु चुनते समय दूसरा निर्देशांक देखें।

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Question 62/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी रैखिक बहुपद का आलेख (y=4x+12) है। इसका शून्यक क्या है?

The graph of a linear polynomial is (y=4x+12). What is its zero?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

Solving (4x+12=0) gives (x=-3). Tip: set (y=0) to find the zero.

Step 2

Why this answer is correct

The correct answer is A. (-3). Solving (4x+12=0) gives (x=-3). Tip: set (y=0) to find the zero.

Step 3

Exam Tip

(4x+12=0) से (x=-3) मिलता है। टिप: शून्यक के लिए (y=0) रखें।

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Question 63/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-6)²) है तो आलेख (x)-अक्ष के साथ क्या करेगा?

If (p(x)=(x-6)²), what will the graph do with the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (x=6) पर स्पर्श करेगाIt will touch at (x=6)

Step 1

Concept

The squared factor gives one repeated zero (6). Tip: a repeated zero often shows touching.

Step 2

Why this answer is correct

The correct answer is A. (x=6) पर स्पर्श करेगा / It will touch at (x=6). The squared factor gives one repeated zero (6). Tip: a repeated zero often shows touching.

Step 3

Exam Tip

वर्ग कारक से एक दोहराया शून्यक (6) मिलता है। टिप: दोहराया शून्यक अक्सर स्पर्श दिखाता है।

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Question 64/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद का आलेख (x)-अक्ष को चार अलग बिंदुओं पर काटता है तो उसका न्यूनतम संभावित घात क्या हो सकता है?

If a polynomial graph cuts the (x)-axis at four distinct points, what can be its minimum possible degree?

Explanation opens after your attempt

Correct Answer

D. (4)

Step 1

Concept

For four distinct real zeroes, the degree must be at least (4). Tip: the number of zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is D. (4). For four distinct real zeroes, the degree must be at least (4). Tip: the number of zeroes cannot exceed the degree.

Step 3

Exam Tip

चार अलग वास्तविक शून्यकों के लिए घात कम से कम (4) होना चाहिए। टिप: शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question 65/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किस स्थिति में (x=0) बहुपद का शून्यक नहीं होगा?

In which situation will (x=0) not be a zero of the polynomial?

Explanation opens after your attempt

Correct Answer

B. आलेख ((0,5)) से गुजरता हैThe graph passes through ((0,5))

Step 1

Concept

At ((0,5)), (p(0)=5), so (0) is not a zero. Tip: (x=0) is a zero only when (y=0) too.

Step 2

Why this answer is correct

The correct answer is B. आलेख ((0,5)) से गुजरता है / The graph passes through ((0,5)). At ((0,5)), (p(0)=5), so (0) is not a zero. Tip: (x=0) is a zero only when (y=0) too.

Step 3

Exam Tip

((0,5)) में (p(0)=5) है इसलिए (0) शून्यक नहीं है। टिप: (x=0) तभी शून्यक है जब (y=0) भी हो।

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Question 66/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-2)) और (p(3)) दोनों (0) हैं, तो ग्राफ पर कौन से बिंदु अवश्य होंगे?

If (p(-2)) and (p(3)) are both (0), which points must be on the graph?

Explanation opens after your attempt

Correct Answer

A. ((-2,0)) और ((3,0))((-2,0)) and ((3,0))

Step 1

Concept

When (p(a)=0), the point is ((a,0)). Tip: place the function value as the second coordinate.

Step 2

Why this answer is correct

The correct answer is A. ((-2,0)) और ((3,0)) / ((-2,0)) and ((3,0)). When (p(a)=0), the point is ((a,0)). Tip: place the function value as the second coordinate.

Step 3

Exam Tip

(p(a)=0) होने पर बिंदु ((a,0)) बनता है। टिप: फलन मान को दूसरे निर्देशांक में रखें।

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Question 67/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2+4x+4) है तो वास्तविक शून्यकों की संख्या कितनी है?

If (p(x)=x^-2+4x+4), how many real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. एक अलगOne distinct

Step 1

Concept

(x^-2+4x+4=(x+2)²), so there is only one distinct zero. Tip: recognize a perfect square.

Step 2

Why this answer is correct

The correct answer is B. एक अलग / One distinct. (x^-2+4x+4=(x+2)²), so there is only one distinct zero. Tip: recognize a perfect square.

Step 3

Exam Tip

(x^-2+4x+4=(x+2)²) इसलिए केवल एक अलग शून्यक है। टिप: पूर्ण वर्ग को पहचानें।

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Question 68/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

ग्राफ (x)-अक्ष को ((-7,0)) और ((2,0)) पर काटता है। शून्यकों का गुणनफल क्या है?

A graph cuts the (x)-axis at ((-7,0)) and ((2,0)). What is the product of zeroes?

Explanation opens after your attempt

Correct Answer

A. (-14)

Step 1

Concept

The zeroes are (-7) and (2), so the product is (-14). Tip: pay attention to signs.

Step 2

Why this answer is correct

The correct answer is A. (-14). The zeroes are (-7) and (2), so the product is (-14). Tip: pay attention to signs.

Step 3

Exam Tip

शून्यक (-7) और (2) हैं इसलिए गुणनफल (-14) है। टिप: चिह्नों का ध्यान रखें।

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Question 69/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी ग्राफ का केवल एक (x)-अक्ष कटान ((-5,0)) है और वह वहाँ पार करता है, तो वास्तविक शून्यक कौन सा है?

If a graph has only one (x)-axis intersection ((-5,0)) and it crosses there, what is the real zero?

Explanation opens after your attempt

Correct Answer

B. (-5)

Step 1

Concept

The (x)-value (-5) of the intersection point is the zero. Tip: do not change the negative sign.

Step 2

Why this answer is correct

The correct answer is B. (-5). The (x)-value (-5) of the intersection point is the zero. Tip: do not change the negative sign.

Step 3

Exam Tip

कटान बिंदु का (x)-मान (-5) शून्यक है। टिप: ऋण चिह्न को न बदलें।

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Question 70/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी आलेख में (x)-अक्ष कटान (x=2) और (x=10) हैं। दोनों शून्यकों के बीच दूरी कितनी है?

A graph has (x)-axis intersections at (x=2) and (x=10). What is the distance between the two zeroes?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

The distance is (10-2=8). Tip: distance is always measured positive.

Step 2

Why this answer is correct

The correct answer is A. (8). The distance is (10-2=8). Tip: distance is always measured positive.

Step 3

Exam Tip

दूरी (10-2=8) है। टिप: दूरी हमेशा धनात्मक मापी जाती है।

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Question 71/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=3(x+4)(x-2)) है तो (3) का शून्यकों पर क्या प्रभाव है?

If (p(x)=3(x+4)(x-2)), what is the effect of (3) on the zeroes?

Explanation opens after your attempt

Correct Answer

B. यह शून्यकों को नहीं बदलताIt does not change the zeroes

Step 1

Concept

A non-zero constant multiplier does not change the zeroes. Tip: find zeroes from the factors.

Step 2

Why this answer is correct

The correct answer is B. यह शून्यकों को नहीं बदलता / It does not change the zeroes. A non-zero constant multiplier does not change the zeroes. Tip: find zeroes from the factors.

Step 3

Exam Tip

अशून्य स्थिर गुणक शून्यकों को नहीं बदलता। टिप: शून्यक कारकों से निकालें।

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Question 72/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि परवलय का शीर्ष ((1,0)) है और वह ऊपर की ओर खुलता है, तो (x)-अक्ष से उसका संबंध क्या होगा?

If the vertex of a parabola is ((1,0)) and it opens upward, what will be its relation with the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. यह (x=1) पर स्पर्श करेगाIt will touch at (x=1)

Step 1

Concept

The vertex is on the (x)-axis, so the parabola touches there. Tip: if the vertex has (y=0), check for touching.

Step 2

Why this answer is correct

The correct answer is A. यह (x=1) पर स्पर्श करेगा / It will touch at (x=1). The vertex is on the (x)-axis, so the parabola touches there. Tip: if the vertex has (y=0), check for touching.

Step 3

Exam Tip

शीर्ष (x)-अक्ष पर है इसलिए परवलय वहाँ स्पर्श करता है। टिप: शीर्ष का (y)-मान (0) हो तो स्पर्श की जाँच करें।

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Question 73/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-1)>0) और (p(4)<0), तो निरंतर बहुपद आलेख के लिए कौन सा कथन उचित है?

If (p(-1)>0) and (p(4)<0), which statement is suitable for a continuous polynomial graph?

Explanation opens after your attempt

Correct Answer

B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता हैThere may be at least one (x)-axis intersection between them

Step 1

Concept

A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.

Step 2

Why this answer is correct

The correct answer is B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them. A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.

Step 3

Exam Tip

चिह्न बदलने से बीच में (p(x)=0) होने का संकेत मिलता है। टिप: बहुपद आलेख टूटता नहीं है।

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Question 74/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

कौन सा कथन सही है जब ग्राफ (x)-अक्ष को ((a,0)) पर छूता है?

Which statement is correct when a graph touches the (x)-axis at ((a,0))?

Explanation opens after your attempt

Correct Answer

C. (a) एक वास्तविक शून्यक है(a) is a real zero

Step 1

Concept

Even on touching, (p(a)=0). Tip: crossing is not necessary for a zero.

Step 2

Why this answer is correct

The correct answer is C. (a) एक वास्तविक शून्यक है / (a) is a real zero. Even on touching, (p(a)=0). Tip: crossing is not necessary for a zero.

Step 3

Exam Tip

छूने पर भी (p(a)=0) होता है। टिप: शून्यक के लिए पार करना जरूरी नहीं है।

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Question 75/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-6x+9) है तो इसका आलेख (x)-अक्ष को किस बिंदु पर स्पर्श करेगा?

If (p(x)=x^-2-6x+9), at which point will its graph touch the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. ((3,0))

Step 1

Concept

(x^-2-6x+9=(x-3)²), so the touching point is ((3,0)). Tip: identify the zero of a perfect square quickly.

Step 2

Why this answer is correct

The correct answer is B. ((3,0)). (x^-2-6x+9=(x-3)²), so the touching point is ((3,0)). Tip: identify the zero of a perfect square quickly.

Step 3

Exam Tip

(x^-2-6x+9=(x-3)²) इसलिए स्पर्श बिंदु ((3,0)) है। टिप: पूर्ण वर्ग का शून्यक तुरंत पहचानें।

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Question 76/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद का आलेख (x)-अक्ष को तीन बार काटता है और एक बार छूता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?

If a polynomial graph crosses the (x)-axis three times and touches it once, what is the number of distinct real zeroes?

Explanation opens after your attempt

Correct Answer

B. चारFour

Step 1

Concept

Each distinct crossing or touching point gives a distinct real zero. Tip: count distinct points.

Step 2

Why this answer is correct

The correct answer is B. चार / Four. Each distinct crossing or touching point gives a distinct real zero. Tip: count distinct points.

Step 3

Exam Tip

हर अलग कटान या स्पर्श बिंदु एक अलग वास्तविक शून्यक देता है। टिप: अलग बिंदुओं को गिनें।

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Question 77/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी ग्राफ में ((4,0)) और ((4,0)) वही स्पर्श बिंदु दो बार लिखा है, तो अलग शून्यक कितने हैं?

If the same touching point ((4,0)) is written twice on a graph, how many distinct zeroes are there?

Explanation opens after your attempt

Correct Answer

A. एकOne

Step 1

Concept

The same (x)-value (4) is repeated, so there is one distinct zero. Tip: do not count repetition for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. एक / One. The same (x)-value (4) is repeated, so there is one distinct zero. Tip: do not count repetition for distinct zeroes.

Step 3

Exam Tip

एक ही (x)-मान (4) दोहराया गया है इसलिए अलग शून्यक एक है। टिप: अलग शून्यक में दोहराव न गिनें।

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Question 78/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-1) है तो कौन सा बिंदु आलेख पर शून्यक नहीं दिखाता?

If (p(x)=x^-2-1), which point does not show a zero on the graph?

Explanation opens after your attempt

Correct Answer

C. ((0,-1))

Step 1

Concept

((0,-1)) has \(y\neq0\), so it does not show a zero. Tip: it is a (y)-axis intercept.

Step 2

Why this answer is correct

The correct answer is C. ((0,-1)). ((0,-1)) has \(y\neq0\), so it does not show a zero. Tip: it is a (y)-axis intercept.

Step 3

Exam Tip

((0,-1)) में \(y\neq0\) है इसलिए यह शून्यक नहीं दिखाता। टिप: यह (y)-अक्ष कटान है।

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Question 79/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी बहुपद के शून्यक (-9) और (-2) हैं। बड़ा शून्यक कौन सा है?

The zeroes of a polynomial are (-9) and (-2). Which zero is greater?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

On the number line, (-2) is to the right of (-9). Tip: the less negative number is greater.

Step 2

Why this answer is correct

The correct answer is B. (-2). On the number line, (-2) is to the right of (-9). Tip: the less negative number is greater.

Step 3

Exam Tip

संख्या रेखा पर (-2), (-9) के दाईं ओर है। टिप: कम ऋणात्मक संख्या बड़ी होती है।

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Question 80/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि आलेख (x)-अक्ष को ((-10,0)) और ((0,0)) पर काटता है तो शून्यकों का गुणनफल क्या होगा?

If a graph cuts the (x)-axis at ((-10,0)) and ((0,0)), what will be the product of zeroes?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

The zeroes are (-10) and (0), so the product is (0). Tip: multiplying by (0) gives (0).

Step 2

Why this answer is correct

The correct answer is C. (0). The zeroes are (-10) and (0), so the product is (0). Tip: multiplying by (0) gives (0).

Step 3

Exam Tip

शून्यक (-10) और (0) हैं इसलिए गुणनफल (0) है। टिप: (0) से गुणा करने पर परिणाम (0) होता है।

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Question 81/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=5) है तो इसके आलेख के बारे में कौन सा कथन सही है?

If (p(x)=5), which statement about its graph is correct?

Explanation opens after your attempt

Correct Answer

C. यह (x)-अक्ष के समांतर है और उसे नहीं काटताIt is parallel to the (x)-axis and does not cut it

Step 1

Concept

(p(x)=5) is never (0). Tip: a non-zero constant polynomial has no real zero.

Step 2

Why this answer is correct

The correct answer is C. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it. (p(x)=5) is never (0). Tip: a non-zero constant polynomial has no real zero.

Step 3

Exam Tip

(p(x)=5) कभी (0) नहीं होता। टिप: अशून्य स्थिर बहुपद का वास्तविक शून्यक नहीं होता।

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Question 82/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=0) शून्य बहुपद है तो उसके आलेख पर कौन सा कथन सही है?

If (p(x)=0) is the zero polynomial, which statement about its graph is correct?

Explanation opens after your attempt

Correct Answer

A. आलेख (x)-अक्ष ही हैThe graph is the (x)-axis itself

Step 1

Concept

For the zero polynomial, (y=0) for every (x). Tip: this is a special case.

Step 2

Why this answer is correct

The correct answer is A. आलेख (x)-अक्ष ही है / The graph is the (x)-axis itself. For the zero polynomial, (y=0) for every (x). Tip: this is a special case.

Step 3

Exam Tip

शून्य बहुपद में हर (x) पर (y=0) होता है। टिप: यह विशेष स्थिति है।

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Question 83/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(2)=0), (p(5)=0) और (p(9)=0), तो ग्राफ पर (x)-अक्ष कटान कितने अलग होंगे?

If (p(2)=0), (p(5)=0) and (p(9)=0), how many distinct (x)-axis intersections will be on the graph?

Explanation opens after your attempt

Correct Answer

C. तीनThree

Step 1

Concept

Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).

Step 2

Why this answer is correct

The correct answer is C. तीन / Three. Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).

Step 3

Exam Tip

तीन अलग (x)-मान तीन अलग (x)-अक्ष बिंदु देते हैं। टिप: (p(a)=0) से ((a,0)) मिलता है।

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Question 84/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि एक परवलय (x)-अक्ष को ((-2,0)) और ((6,0)) पर काटता है तो उसका सममिति अक्ष किस (x)-मान से गुजर सकता है?

If a parabola cuts the (x)-axis at ((-2,0)) and ((6,0)), through which (x)-value can its axis of symmetry pass?

Explanation opens after your attempt

Correct Answer

B. (x=2)

Step 1

Concept

The axis of symmetry passes through the midpoint of zeroes, \(\frac{-2+6}{2}=2\). Tip: the average of two zeroes is useful for a parabola.

Step 2

Why this answer is correct

The correct answer is B. (x=2). The axis of symmetry passes through the midpoint of zeroes, \(\frac{-2+6}{2}=2\). Tip: the average of two zeroes is useful for a parabola.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के मध्य से गुजरता है, \(\frac{-2+6}{2}=2\)। टिप: परवलय में दो शून्यकों का औसत उपयोगी होता है।

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Question 85/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2+2x+5) है तो इसके वास्तविक शून्यकों के बारे में सही कथन कौन सा है?

If (p(x)=x^-2+2x+5), which statement about its real zeroes is correct?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक शून्यक नहीं हैIt has no real zero

Step 1

Concept

It is ((x+1)²+4), which is always positive. Tip: if the value never becomes (0), there is no (x)-axis intersection.

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक शून्यक नहीं है / It has no real zero. It is ((x+1)²+4), which is always positive. Tip: if the value never becomes (0), there is no (x)-axis intersection.

Step 3

Exam Tip

यह ((x+1)²+4) है जो हमेशा धनात्मक है। टिप: यदि मान कभी (0) न बने तो (x)-अक्ष कटान नहीं होगा।

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Question 86/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी आलेख पर (x=3) पर (p(x)=0) और (x=7) पर (p(x)=4) है। कौन सा कथन सही है?

On a graph (p(x)=0) at (x=3) and (p(x)=4) at (x=7). Which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (3) शून्यक है पर (7) नहीं(3) is a zero but (7) is not

Step 1

Concept

(p(3)=0) but (p(7)=4). Tip: a zero needs the function value exactly (0).

Step 2

Why this answer is correct

The correct answer is A. (3) शून्यक है पर (7) नहीं / (3) is a zero but (7) is not. (p(3)=0) but (p(7)=4). Tip: a zero needs the function value exactly (0).

Step 3

Exam Tip

(p(3)=0) है लेकिन (p(7)=4) है। टिप: शून्यक के लिए फलन मान ठीक (0) चाहिए।

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Question 87/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=2x^-2-8) है तो ग्राफ के शून्यक कौन से हैं?

If (p(x)=2x^-2-8), what are the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (2) और (-2)(2) and (-2)

Step 1

Concept

From \(2x^2-8=0\), \(x^2=4\) and \(x=\pm2\). Tip: simplify by the common factor first.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-2) / (2) and (-2). From \(2x^2-8=0\), \(x^2=4\) and \(x=\pm2\). Tip: simplify by the common factor first.

Step 3

Exam Tip

\(2x^2-8=0\) से \(x^2=4\) और \(x=\pm2\) मिलता है। टिप: पहले समान गुणक से सरल करें।

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Question 88/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी आलेख में (x)-अक्ष कटान ((r,0)) है। यदि (r<0) है तो शून्यक के बारे में क्या कहा जा सकता है?

A graph has an (x)-axis intersection ((r,0)). If (r<0), what can be said about the zero?

Explanation opens after your attempt

Correct Answer

B. शून्यक ऋणात्मक हैThe zero is negative

Step 1

Concept

The first coordinate (r) of the intersection is the zero, and (r<0). Tip: the same rule works in symbolic questions.

Step 2

Why this answer is correct

The correct answer is B. शून्यक ऋणात्मक है / The zero is negative. The first coordinate (r) of the intersection is the zero, and (r<0). Tip: the same rule works in symbolic questions.

Step 3

Exam Tip

कटान का पहला निर्देशांक (r) ही शून्यक है और (r<0) है। टिप: प्रतीकात्मक प्रश्न में भी नियम वही रहता है।

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Question 89/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=-(x+3)²) है तो आलेख (x)-अक्ष से कैसे मिलेगा?

If (p(x)=-(x+3)²), how will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (x=-3) पर स्पर्श करेगाIt will touch at (x=-3)

Step 1

Concept

The negative sign does not change the zero, and ((x+3)²=0) gives (x=-3). Tip: an outside multiplier does not change the zero.

Step 2

Why this answer is correct

The correct answer is A. (x=-3) पर स्पर्श करेगा / It will touch at (x=-3). The negative sign does not change the zero, and ((x+3)²=0) gives (x=-3). Tip: an outside multiplier does not change the zero.

Step 3

Exam Tip

ऋण चिह्न शून्यक नहीं बदलता और ((x+3)²=0) से (x=-3) है। टिप: बाहर का गुणक शून्यक नहीं बदलता।

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Question 90/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x)-अक्ष को ((-1,0)), ((2,0)), ((4,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?

If a graph cuts the (x)-axis at ((-1,0)), ((2,0)), ((4,0)), what is the product of zeroes?

Explanation opens after your attempt

Correct Answer

B. (-8)

Step 1

Concept

The product is ((-1)\times2\times4=-8). Tip: multiply all three (x)-values.

Step 2

Why this answer is correct

The correct answer is B. (-8). The product is ((-1)\times2\times4=-8). Tip: multiply all three (x)-values.

Step 3

Exam Tip

गुणनफल ((-1)\times2\times4=-8) है। टिप: तीनों (x)-मानों को गुणा करें।

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Question 91/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी बहुपद का आलेख (x)-अक्ष को ((a,0)) और ((-a,0)) पर काटता है। यदि \(a\neq0\) है तो शून्यकों का योग क्या है?

A polynomial graph cuts the (x)-axis at ((a,0)) and ((-a,0)). If \(a\neq0\), what is the sum of zeroes?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

The zeroes are (a) and (-a), whose sum is (0). Tip: opposite numbers add to (0).

Step 2

Why this answer is correct

The correct answer is C. (0). The zeroes are (a) and (-a), whose sum is (0). Tip: opposite numbers add to (0).

Step 3

Exam Tip

शून्यक (a) और (-a) हैं जिनका योग (0) है। टिप: विपरीत संख्याएँ जोड़ने पर (0) देती हैं।

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Question 92/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद के वास्तविक शून्यक (2), (2) और (-5) लिखे हैं, तो अलग वास्तविक शून्यक कौन से हैं?

If the real zeroes of a polynomial are written as (2), (2) and (-5), what are the distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (-5)(2) and (-5)

Step 1

Concept

The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-5) / (2) and (-5). The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.

Step 3

Exam Tip

दोहराया (2) अलग शून्यक में एक बार गिना जाता है। टिप: अलग शून्यक में समान मान पुनः न लिखें।

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Question 93/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-3-x) है तो ग्राफ (x)-अक्ष को किन (x)-मानों पर मिल सकता है?

If (p(x)=x^-3-x), at which (x)-values can the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (-1), (0), (1)

Step 1

Concept

(x^-3-x=x(x-1)(x+1)), so the zeroes are (-1), (0), (1). Tip: factor out the common term first.

Step 2

Why this answer is correct

The correct answer is A. (-1), (0), (1). (x^-3-x=x(x-1)(x+1)), so the zeroes are (-1), (0), (1). Tip: factor out the common term first.

Step 3

Exam Tip

(x^-3-x=x(x-1)(x+1)) इसलिए शून्यक (-1), (0), (1) हैं। टिप: पहले सामान्य गुणनखंड निकालें।

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Question 94/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि आलेख (x)-अक्ष को केवल (x=11) पर छूता है तो कौन सा कथन सही है?

If a graph only touches the (x)-axis at (x=11), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (11) वास्तविक शून्यक है(11) is a real zero

Step 1

Concept

At a touching point, the function value is also (0). Tip: touching also means meeting the (x)-axis.

Step 2

Why this answer is correct

The correct answer is A. (11) वास्तविक शून्यक है / (11) is a real zero. At a touching point, the function value is also (0). Tip: touching also means meeting the (x)-axis.

Step 3

Exam Tip

स्पर्श बिंदु पर भी फलन मान (0) होता है। टिप: छूना भी (x)-अक्ष से मिलना है।

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Question 95/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-7x+12) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?

If (p(x)=x^-2-7x+12), what are the (x)-axis intersections of the graph?

Explanation opens after your attempt

Correct Answer

A. ((3,0)) और ((4,0))((3,0)) and ((4,0))

Step 1

Concept

(x^-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.

Step 2

Why this answer is correct

The correct answer is A. ((3,0)) और ((4,0)) / ((3,0)) and ((4,0)). (x^-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.

Step 3

Exam Tip

(x^-2-7x+12=(x-3)(x-4)) इसलिए शून्यक (3) और (4) हैं। टिप: गुणनखंड बनाकर कटान बिंदु लिखें।

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Question 96/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी ग्राफ के (x)-अक्ष कटान ((3,0)) और ((12,0)) हैं तो शून्यकों का औसत क्या है?

If the (x)-axis intersections of a graph are ((3,0)) and ((12,0)), what is the average of the zeroes?

Explanation opens after your attempt

Correct Answer

C. (7.5)

Step 1

Concept

The average is \(\frac{3+12}{2}=7.5\). Tip: divide the sum by (2) for the average.

Step 2

Why this answer is correct

The correct answer is C. (7.5). The average is \(\frac{3+12}{2}=7.5\). Tip: divide the sum by (2) for the average.

Step 3

Exam Tip

औसत \(\frac{3+12}{2}=7.5\) है। टिप: औसत में योग को (2) से भाग दें।

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Question 97/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

किसी बहुपद का आलेख (x)-अक्ष को (x=-5) और (x=5) पर काटता है। यह (y)-अक्ष के सापेक्ष कैसा संकेत देता है?

A polynomial graph cuts the (x)-axis at (x=-5) and (x=5). What does this indicate with respect to the (y)-axis?

Explanation opens after your attempt

Correct Answer

B. शून्यक (y)-अक्ष से समान दूरी पर हैंThe zeroes are equally distant from the (y)-axis

Step 1

Concept

(-5) and (5) are equally distant from the (y)-axis. Tip: opposite zeroes show symmetric positions.

Step 2

Why this answer is correct

The correct answer is B. शून्यक (y)-अक्ष से समान दूरी पर हैं / The zeroes are equally distant from the (y)-axis. (-5) and (5) are equally distant from the (y)-axis. Tip: opposite zeroes show symmetric positions.

Step 3

Exam Tip

(-5) और (5) (y)-अक्ष से बराबर दूरी पर हैं। टिप: विपरीत शून्यक सममित स्थिति दिखाते हैं।

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Question 98/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(1)<0), (p(2)=0), (p(3)>0) है तो कौन सा बिंदु (x)-अक्ष पर होगा?

If (p(1)<0), (p(2)=0), (p(3)>0), which point will lie on the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. ((2,0))

Step 1

Concept

Only (p(2)=0), so ((2,0)) lies on the (x)-axis. Tip: inequality values do not show zeroes.

Step 2

Why this answer is correct

The correct answer is B. ((2,0)). Only (p(2)=0), so ((2,0)) lies on the (x)-axis. Tip: inequality values do not show zeroes.

Step 3

Exam Tip

केवल (p(2)=0) है इसलिए ((2,0)) (x)-अक्ष पर होगा। टिप: असमानता वाले मान शून्यक नहीं बताते।

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Question 99/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि आलेख (x)-अक्ष को ((-6,0)), ((-2,0)), ((4,0)) पर काटता है तो सबसे बड़ा शून्यक कौन सा है?

If a graph cuts the (x)-axis at ((-6,0)), ((-2,0)), ((4,0)), which is the greatest zero?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The zeroes are (-6), (-2), (4), and (4) is the greatest. Tip: the value to the right on the number line is greater.

Step 2

Why this answer is correct

The correct answer is C. (4). The zeroes are (-6), (-2), (4), and (4) is the greatest. Tip: the value to the right on the number line is greater.

Step 3

Exam Tip

शून्यक (-6), (-2), (4) हैं और (4) सबसे बड़ा है। टिप: संख्या रेखा पर दाईं ओर का मान बड़ा होता है।

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Question 100/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-1)(x-4)(x+2)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?

If (p(x)=(x-1)(x-4)(x+2)), at how many distinct points will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. तीनThree

Step 1

Concept

The three different factors give three distinct zeroes (1), (4), (-2). Tip: each linear factor gives a possible intersection.

Step 2

Why this answer is correct

The correct answer is C. तीन / Three. The three different factors give three distinct zeroes (1), (4), (-2). Tip: each linear factor gives a possible intersection.

Step 3

Exam Tip

तीन अलग कारक तीन अलग शून्यक (1), (4), (-2) देते हैं। टिप: हर रैखिक कारक एक संभावित कटान देता है।

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Question 101/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद के आलेख पर बिंदु ((-4,0)), ((0,3)), ((2,0)) और ((5,-1)) हैं तो वास्तविक शून्यक कौन से हैं?

If the points ((-4,0)), ((0,3)), ((2,0)) and ((5,-1)) lie on a polynomial graph, which are the real zeroes?

Explanation opens after your attempt

Correct Answer

A. (-4) और (2)(-4) and (2)

Step 1

Concept

Zeroes occur where (y=0). Tip: choose only points lying on the (x)-axis.

Step 2

Why this answer is correct

The correct answer is A. (-4) और (2) / (-4) and (2). Zeroes occur where (y=0). Tip: choose only points lying on the (x)-axis.

Step 3

Exam Tip

जहाँ (y=0) है वहीं शून्यक मिलते हैं। टिप: केवल (x)-अक्ष पर पड़े बिंदु चुनें।

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Question 102/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

एक परवलय (x)-अक्ष को (x=-5) और (x=3) पर काटता है। उसके शून्यकों का औसत क्या है?

A parabola cuts the (x)-axis at (x=-5) and (x=3). What is the average of its zeroes?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

The average is \(\frac{-5+3}{2}=-1\). Tip: the average of two zeroes is linked to the middle of a parabola.

Step 2

Why this answer is correct

The correct answer is A. (-1). The average is \(\frac{-5+3}{2}=-1\). Tip: the average of two zeroes is linked to the middle of a parabola.

Step 3

Exam Tip

औसत \(\frac{-5+3}{2}=-1\) है। टिप: दो शून्यकों का औसत परवलय के मध्य से जुड़ता है।

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Question 103/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x+2)(x-7)) है तो ग्राफ (x)-अक्ष से किन बिंदुओं पर मिलेगा?

If (p(x)=(x+2)(x-7)), at which points will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. ((-2,0)) और ((7,0))((-2,0)) and ((7,0))

Step 1

Concept

Setting the factors to zero gives (x=-2) and (x=7). Tip: convert each zero into the point ((x,0)).

Step 2

Why this answer is correct

The correct answer is B. ((-2,0)) और ((7,0)) / ((-2,0)) and ((7,0)). Setting the factors to zero gives (x=-2) and (x=7). Tip: convert each zero into the point ((x,0)).

Step 3

Exam Tip

कारक शून्य करने पर (x=-2) और (x=7) मिलते हैं। टिप: शून्यक को ((x,0)) बिंदु में बदलें।

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Question 104/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ में (x=1) पर कटान और (x=6) पर स्पर्श है तो अलग वास्तविक शून्यक कितने हैं?

If a graph crosses at (x=1) and touches at (x=6), how many distinct real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.

Step 3

Exam Tip

कटान और स्पर्श दोनों (p(x)=0) बताते हैं। टिप: अलग (x)-मानों को गिनें।

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Question 105/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी बहुपद का ग्राफ (x)-अक्ष को ((-9,0)), ((-1,0)) और ((4,0)) पर काटता है। सबसे बड़ा शून्यक कौन सा है?

A polynomial graph cuts the (x)-axis at ((-9,0)), ((-1,0)) and ((4,0)). Which is the greatest zero?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The zeroes are (-9), (-1), (4) and the greatest is (4). Tip: the value to the right on the number line is greater.

Step 2

Why this answer is correct

The correct answer is C. (4). The zeroes are (-9), (-1), (4) and the greatest is (4). Tip: the value to the right on the number line is greater.

Step 3

Exam Tip

शून्यक (-9), (-1), (4) हैं और सबसे बड़ा (4) है। टिप: संख्या रेखा पर दाईं ओर वाला मान बड़ा होता है।

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Question 106/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(-3)=0), (p(2)=5) और (p(8)=0) है तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?

If (p(-3)=0), (p(2)=5) and (p(8)=0), what will be the (x)-axis intersections of the graph?

Explanation opens after your attempt

Correct Answer

A. ((-3,0)) और ((8,0))((-3,0)) and ((8,0))

Step 1

Concept

An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.

Step 2

Why this answer is correct

The correct answer is A. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0)). An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.

Step 3

Exam Tip

जहाँ (p(x)=0) है वहीं (x)-अक्ष कटान होता है। टिप: (p(2)=5) शून्यक नहीं देता।

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Question 107/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-10x+25) है तो आलेख (x)-अक्ष से कैसे मिलेगा?

If (p(x)=x^-2-10x+25), how will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (x=5) पर स्पर्श करेगाIt will touch at (x=5)

Step 1

Concept

It is ((x-5)²), so it touches only at (x=5). Tip: a perfect square gives a repeated zero.

Step 2

Why this answer is correct

The correct answer is A. (x=5) पर स्पर्श करेगा / It will touch at (x=5). It is ((x-5)²), so it touches only at (x=5). Tip: a perfect square gives a repeated zero.

Step 3

Exam Tip

यह ((x-5)²) है इसलिए केवल (x=5) पर स्पर्श होगा। टिप: पूर्ण वर्ग दोहराया शून्यक देता है।

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Question 108/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2+6x+10) है तो इसके वास्तविक शून्यकों के बारे में कौन सा कथन सही है?

If (p(x)=x^-2+6x+10), which statement about its real zeroes is correct?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक शून्यक नहीं हैIt has no real zero

Step 1

Concept

It is ((x+3)²+1), so it is never (0). Tip: an always positive form gives no (x)-axis intersection.

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक शून्यक नहीं है / It has no real zero. It is ((x+3)²+1), so it is never (0). Tip: an always positive form gives no (x)-axis intersection.

Step 3

Exam Tip

यह ((x+3)²+1) है इसलिए कभी (0) नहीं होता। टिप: हमेशा धनात्मक रूप (x)-अक्ष कटान नहीं देता।

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Question 109/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

एक छात्र ने ((0,-6)) देखकर (-6) को शून्यक लिखा। सही कारण से यह गलत क्यों है?

A student saw ((0,-6)) and wrote (-6) as a zero. Why is this wrong with the correct reason?

Explanation opens after your attempt

Correct Answer

A. क्योंकि यह (y)-अक्ष कटान है और \(y\neq0\)Because it is a (y)-axis intercept and \(y\neq0\)

Step 1

Concept

At ((0,-6)), the function value is not (0). Tip: for a zero the point must lie on the (x)-axis.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि यह (y)-अक्ष कटान है और \(y\neq0\) / Because it is a (y)-axis intercept and \(y\neq0\). At ((0,-6)), the function value is not (0). Tip: for a zero the point must lie on the (x)-axis.

Step 3

Exam Tip

((0,-6)) पर फलन मान (0) नहीं है। टिप: शून्यक के लिए बिंदु (x)-अक्ष पर होना चाहिए।

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Question 110/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ के शून्यक (-4) और (9) हैं तो (x)-अक्ष पर इनके बीच दूरी कितनी है?

If the zeroes of a graph are (-4) and (9), what is the distance between them on the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

The distance is (9-(-4)=13). Tip: distance is always taken as positive.

Step 2

Why this answer is correct

The correct answer is C. (13). The distance is (9-(-4)=13). Tip: distance is always taken as positive.

Step 3

Exam Tip

दूरी (9-(-4)=13) है। टिप: दूरी हमेशा धनात्मक ली जाती है।

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Question 111/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-2,0)) और ((10,0)) पर काटता है तो इन कटान बिंदुओं का मध्यबिंदु क्या है?

If a graph cuts the (x)-axis at ((-2,0)) and ((10,0)), what is the midpoint of these intersection points?

Explanation opens after your attempt

Correct Answer

A. ((4,0))

Step 1

Concept

The (x)-value of the midpoint is \(\frac{-2+10}{2}=4\). Tip: on the (x)-axis both points keep (y=0).

Step 2

Why this answer is correct

The correct answer is A. ((4,0)). The (x)-value of the midpoint is \(\frac{-2+10}{2}=4\). Tip: on the (x)-axis both points keep (y=0).

Step 3

Exam Tip

मध्यबिंदु का (x)-मान \(\frac{-2+10}{2}=4\) है। टिप: (x)-अक्ष पर दोनों बिंदुओं का (y)-मान (0) रहता है।

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Question 112/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी परवलय के (x)-अक्ष कटान ((1,0)) और ((7,0)) हैं। उसका सममिति अक्ष किस (x)-मान से गुजर सकता है?

The (x)-axis intersections of a parabola are ((1,0)) and ((7,0)). Through which (x)-value can its axis of symmetry pass?

Explanation opens after your attempt

Correct Answer

B. (x=4)

Step 1

Concept

The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.

Step 2

Why this answer is correct

The correct answer is B. (x=4). The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के औसत \(x=\frac{1+7}{2}=4\) से गुजरता है। टिप: परवलय में दो शून्यकों का मध्य उपयोगी है।

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Question 113/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=2(x-4)(x+1)) है तो बाहरी गुणक (2) ग्राफ के (x)-अक्ष कटानों को कैसे प्रभावित करता है?

If (p(x)=2(x-4)(x+1)), how does the outside multiplier (2) affect the (x)-axis intersections of the graph?

Explanation opens after your attempt

Correct Answer

B. कटान नहीं बदलतेThe intersections do not change

Step 1

Concept

A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.

Step 2

Why this answer is correct

The correct answer is B. कटान नहीं बदलते / The intersections do not change. A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.

Step 3

Exam Tip

अशून्य स्थिर गुणक शून्यकों को नहीं बदलता। टिप: शून्यक केवल शून्य बनाने वाले कारकों से मिलते हैं।

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Question 114/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-3-4x) है तो ग्राफ (x)-अक्ष को किन (x)-मानों पर मिल सकता है?

If (p(x)=x^-3-4x), at which (x)-values can the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. (-2), (0), (2)

Step 1

Concept

(x^-3-4x=x(x-2)(x+2)), so the zeroes are (-2), (0), (2). Tip: take the common factor first.

Step 2

Why this answer is correct

The correct answer is A. (-2), (0), (2). (x^-3-4x=x(x-2)(x+2)), so the zeroes are (-2), (0), (2). Tip: take the common factor first.

Step 3

Exam Tip

(x^-3-4x=x(x-2)(x+2)) इसलिए शून्यक (-2), (0), (2) हैं। टिप: पहले सामान्य गुणनखंड लें।

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Question 115/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किस स्थिति में (0) बहुपद का वास्तविक शून्यक होगा?

In which situation will (0) be a real zero of a polynomial?

Explanation opens after your attempt

Correct Answer

B. ग्राफ ((0,0)) से गुजरता हैThe graph passes through ((0,0))

Step 1

Concept

(0) is a zero when (p(0)=0). Tip: passing through the origin shows zero as a zero.

Step 2

Why this answer is correct

The correct answer is B. ग्राफ ((0,0)) से गुजरता है / The graph passes through ((0,0)). (0) is a zero when (p(0)=0). Tip: passing through the origin shows zero as a zero.

Step 3

Exam Tip

(0) शून्यक तब है जब (p(0)=0) हो। टिप: मूल बिंदु से गुजरना (0) शून्यक बताता है।

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Question 116/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद का ग्राफ (x)-अक्ष को पाँच अलग बिंदुओं पर काटता है तो बहुपद की न्यूनतम घात क्या हो सकती है?

If a polynomial graph cuts the (x)-axis at five distinct points, what can be the minimum degree of the polynomial?

Explanation opens after your attempt

Correct Answer

D. (5)

Step 1

Concept

For five distinct real zeroes the degree must be at least (5). Tip: the number of zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is D. (5). For five distinct real zeroes the degree must be at least (5). Tip: the number of zeroes cannot exceed the degree.

Step 3

Exam Tip

पाँच अलग वास्तविक शून्यकों के लिए घात कम से कम (5) होनी चाहिए। टिप: शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question 117/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=-2(x+5)²) है तो ग्राफ (x)-अक्ष से कहाँ मिलेगा?

If (p(x)=-2(x+5)²), where will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. (x=-5) परAt (x=-5)

Step 1

Concept

The outside (-2) does not change the zero and ((x+5)²=0) gives (x=-5). Tip: a squared factor can show touching.

Step 2

Why this answer is correct

The correct answer is B. (x=-5) पर / At (x=-5). The outside (-2) does not change the zero and ((x+5)²=0) gives (x=-5). Tip: a squared factor can show touching.

Step 3

Exam Tip

बाहरी (-2) शून्यक नहीं बदलता और ((x+5)²=0) से (x=-5) है। टिप: वर्ग कारक स्पर्श दिखा सकता है।

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Question 118/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी आलेख में ((a,0)) और ((b,0)) कटान बिंदु हैं और (a<b), तो छोटे शून्यक का मान क्या है?

If ((a,0)) and ((b,0)) are intersection points of a graph and (a<b), what is the smaller zero?

Explanation opens after your attempt

Correct Answer

A. (a)

Step 1

Concept

The zeroes are (a) and (b), and (a<b). Tip: even with symbols the first coordinate is the zero.

Step 2

Why this answer is correct

The correct answer is A. (a). The zeroes are (a) and (b), and (a<b). Tip: even with symbols the first coordinate is the zero.

Step 3

Exam Tip

शून्यक (a) और (b) हैं और (a<b) है। टिप: प्रतीकों में भी पहला निर्देशांक शून्यक होता है।

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Question 119/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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?

Explanation opens after your attempt

Correct Answer

A. (-3)

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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Question 120/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((r,0)) पर काटता है और (r>0) है तो शून्यक के बारे में कौन सा कथन सही है?

If a graph cuts the (x)-axis at ((r,0)) and (r>0), which statement about the zero is correct?

Explanation opens after your attempt

Correct Answer

B. शून्यक धनात्मक हैThe zero is positive

Step 1

Concept

The first coordinate of the intersection is (r), and (r>0). Tip: read the zero (r) from ((r,0)).

Step 2

Why this answer is correct

The correct answer is B. शून्यक धनात्मक है / The zero is positive. The first coordinate of the intersection is (r), and (r>0). Tip: read the zero (r) from ((r,0)).

Step 3

Exam Tip

कटान का पहला निर्देशांक (r) है और (r>0) है। टिप: ((r,0)) से शून्यक (r) पढ़ें।

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Question 121/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-3x-10) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?

If (p(x)=x^-2-3x-10), what are the (x)-axis intersections of the graph?

Explanation opens after your attempt

Correct Answer

A. ((5,0)) और ((-2,0))((5,0)) and ((-2,0))

Step 1

Concept

(x^-2-3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.

Step 2

Why this answer is correct

The correct answer is A. ((5,0)) और ((-2,0)) / ((5,0)) and ((-2,0)). (x^-2-3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.

Step 3

Exam Tip

(x^-2-3x-10=(x-5)(x+2)) इसलिए शून्यक (5) और (-2) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।

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Question 122/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किस ग्राफ से ठीक दो अलग वास्तविक शून्यक मिलेंगे?

Which graph will give exactly two distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटेOne that cuts the (x)-axis at two distinct points

Step 1

Concept

Two distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections 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 distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections as zeroes.

Step 3

Exam Tip

दो अलग (x)-अक्ष कटान दो अलग वास्तविक शून्यक देते हैं। टिप: (y)-अक्ष कटान को शून्यक न गिनें।

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Question 123/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ के बिंदु ((3,0)) और ((3,0)) एक ही स्पर्श को दो बार दिखा रहे हैं तो अलग शून्यक कितने हैं?

If the points ((3,0)) and ((3,0)) show the same touch twice on a graph, how many distinct zeroes are there?

Explanation opens after your attempt

Correct Answer

A. एकOne

Step 1

Concept

Both have the same (x)-value (3), so there is one distinct zero. Tip: count a repeated value once for distinct count.

Step 2

Why this answer is correct

The correct answer is A. एक / One. Both have the same (x)-value (3), so there is one distinct zero. Tip: count a repeated value once for distinct count.

Step 3

Exam Tip

दोनों में (x)-मान समान (3) है इसलिए अलग शून्यक एक है। टिप: दोहराए मान को अलग गिनती में एक बार लें।

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Question 124/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x(x+6)) है तो ग्राफ के शून्यक कौन से हैं?

If (p(x)=x(x+6)), what are the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

B. (0) और (-6)(0) and (-6)

Step 1

Concept

From (x=0) or (x+6=0), the zeroes are (0) and (-6). Tip: if a product is zero then one factor is zero.

Step 2

Why this answer is correct

The correct answer is B. (0) और (-6) / (0) and (-6). From (x=0) or (x+6=0), the zeroes are (0) and (-6). Tip: if a product is zero then one factor is zero.

Step 3

Exam Tip

(x=0) या (x+6=0) से शून्यक (0) और (-6) हैं। टिप: गुणनफल शून्य हो तो कोई एक कारक शून्य होता है।

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Question 125/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि परवलय (x)-अक्ष के नीचे रहता है और उसे कहीं नहीं छूता तो (p(x)=0) के वास्तविक हल कितने हैं?

If a parabola stays below the (x)-axis and never touches it, how many real solutions does (p(x)=0) have?

Explanation opens after your attempt

Correct Answer

A. शून्यZero

Step 1

Concept

The graph does not meet the (x)-axis, so there is no real solution. Tip: (p(x)=0) means an (x)-axis intersection on the graph.

Step 2

Why this answer is correct

The correct answer is A. शून्य / Zero. The graph does not meet the (x)-axis, so there is no real solution. Tip: (p(x)=0) means an (x)-axis intersection on the graph.

Step 3

Exam Tip

आलेख (x)-अक्ष से नहीं मिलता इसलिए कोई वास्तविक हल नहीं है। टिप: (p(x)=0) ग्राफ पर (x)-अक्ष कटान है।

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Question 126/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-3,0)), ((0,0)) और ((6,0)) पर काटता है तो शून्यकों का योग क्या है?

If a graph cuts the (x)-axis at ((-3,0)), ((0,0)) and ((6,0)), what is the sum of zeroes?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The sum is (-3+0+6=3). Tip: include the zero (0) from the origin.

Step 2

Why this answer is correct

The correct answer is A. (3). The sum is (-3+0+6=3). Tip: include the zero (0) from the origin.

Step 3

Exam Tip

योग (-3+0+6=3) है। टिप: मूल बिंदु का शून्यक (0) भी जोड़ें।

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Question 127/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-49) है तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?

If (p(x)=x^-2-49), at which points will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. ((7,0)) और ((-7,0))((7,0)) and ((-7,0))

Step 1

Concept

Solving \(x^2-49=0\) gives \(x=\pm7\). Tip: recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((7,0)) और ((-7,0)) / ((7,0)) and ((-7,0)). Solving \(x^2-49=0\) gives \(x=\pm7\). Tip: recognize the difference of squares.

Step 3

Exam Tip

\(x^2-49=0\) से \(x=\pm7\) मिलता है। टिप: वर्गों के अंतर को पहचानें।

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Question 128/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद के वास्तविक शून्यक (5), (5), (-1) हैं तो अलग वास्तविक शून्यक कौन से हैं?

If the real zeroes of a polynomial are (5), (5), (-1), what are the distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. (5) और (-1)(5) and (-1)

Step 1

Concept

The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.

Step 2

Why this answer is correct

The correct answer is A. (5) और (-1) / (5) and (-1). The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.

Step 3

Exam Tip

दोहराया (5) अलग शून्यक में एक बार ही गिना जाता है। टिप: अलग मानों की सूची बनाएं।

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Question 129/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी परवलय का शीर्ष ((-2,0)) है और वह नीचे की ओर खुलता है तो शून्यक के बारे में क्या सही है?

If the vertex of a parabola is ((-2,0)) and it opens downward, what is correct about the zero?

Explanation opens after your attempt

Correct Answer

A. केवल (-2) अलग शून्यक हैOnly (-2) is the distinct zero

Step 1

Concept

The vertex lies on the (x)-axis, so the parabola touches at ((-2,0)). Tip: the opening direction does not change the touching (x)-value.

Step 2

Why this answer is correct

The correct answer is A. केवल (-2) अलग शून्यक है / Only (-2) is the distinct zero. The vertex lies on the (x)-axis, so the parabola touches at ((-2,0)). Tip: the opening direction does not change the touching (x)-value.

Step 3

Exam Tip

शीर्ष (x)-अक्ष पर है इसलिए परवलय ((-2,0)) पर स्पर्श करता है। टिप: खुलने की दिशा स्पर्श बिंदु का (x)-मान नहीं बदलती।

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Question 130/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-12,0)) और ((-4,0)) पर काटता है तो बड़ा शून्यक कौन सा है?

If a graph cuts the (x)-axis at ((-12,0)) and ((-4,0)), which zero is greater?

Explanation opens after your attempt

Correct Answer

B. (-4)

Step 1

Concept

The number (-4) lies to the right of (-12) on the number line. Tip: the less negative number is greater.

Step 2

Why this answer is correct

The correct answer is B. (-4). The number (-4) lies to the right of (-12) on the number line. Tip: the less negative number is greater.

Step 3

Exam Tip

(-4) संख्या रेखा पर (-12) से दाईं ओर है। टिप: कम ऋणात्मक संख्या बड़ी होती है।

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Question 131/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

कौन सा बिंदु (x=9) को शून्यक साबित करता है?

Which point proves that (x=9) is a zero?

Explanation opens after your attempt

Correct Answer

A. ((9,0))

Step 1

Concept

A zero (x=9) means (p(9)=0). Tip: place the zero as the first coordinate.

Step 2

Why this answer is correct

The correct answer is A. ((9,0)). A zero (x=9) means (p(9)=0). Tip: place the zero as the first coordinate.

Step 3

Exam Tip

(x=9) शून्यक होने का अर्थ (p(9)=0) है। टिप: शून्यक को पहले निर्देशांक में रखें।

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Question 132/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ पर ((2,3)) और ((5,0)) हैं तो कौन सा (x)-मान निश्चित शून्यक है?

If ((2,3)) and ((5,0)) lie on a graph, which (x)-value is definitely a zero?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

In ((5,0)), (y=0), so (5) is a zero. Tip: ((2,3)) does not show a zero.

Step 2

Why this answer is correct

The correct answer is C. (5). In ((5,0)), (y=0), so (5) is a zero. Tip: ((2,3)) does not show a zero.

Step 3

Exam Tip

((5,0)) में (y=0) है इसलिए (5) शून्यक है। टिप: ((2,3)) शून्यक नहीं दिखाता।

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Question 133/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2+x-6) है तो वास्तविक शून्यक कौन से हैं?

If (p(x)=x^-2+x-6), what are the real zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (-3)(2) and (-3)

Step 1

Concept

(x^-2+x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-3) / (2) and (-3). (x^-2+x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.

Step 3

Exam Tip

(x^-2+x-6=(x+3)(x-2)) इसलिए शून्यक (-3) और (2) हैं। टिप: गुणनखंडों के चिह्न ध्यान से पढ़ें।

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Question 134/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

एक ग्राफ (x)-अक्ष को ((a,0)), ((0,0)), ((-a,0)) पर काटता है जहाँ \(a\neq0\)। शून्यकों का योग क्या है?

A graph cuts the (x)-axis at ((a,0)), ((0,0)), ((-a,0)) where \(a\neq0\). What is the sum of zeroes?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

The zeroes are (a), (0), (-a), whose sum is (0). Tip: opposite numbers cancel each other.

Step 2

Why this answer is correct

The correct answer is B. (0). The zeroes are (a), (0), (-a), whose sum is (0). Tip: opposite numbers cancel each other.

Step 3

Exam Tip

शून्यक (a), (0), (-a) हैं जिनका योग (0) है। टिप: विपरीत संख्याएँ एक-दूसरे को काट देती हैं।

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Question 135/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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?

Explanation opens after your attempt

Correct Answer

B. (4)

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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Question 136/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी बहुपद का ग्राफ (x)-अक्ष को दो बार काटता है और एक बार उसी बिंदु पर स्पर्श नहीं करता। इसका अर्थ क्या है?

A polynomial graph cuts the (x)-axis twice and does not touch at the same point. What does this mean?

Explanation opens after your attempt

Correct Answer

A. दो अलग वास्तविक शून्यक हैंThere are two distinct real zeroes

Step 1

Concept

Two distinct crossings give two distinct zeroes. Tip: distinct points show distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is A. दो अलग वास्तविक शून्यक हैं / There are two distinct real zeroes. Two distinct crossings give two distinct zeroes. Tip: distinct points show distinct (x)-values.

Step 3

Exam Tip

दो अलग कटान दो अलग शून्यक देते हैं। टिप: अलग बिंदु अलग (x)-मान बताते हैं।

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Question 137/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2+1) है तो इसका ग्राफ (x)-अक्ष को क्यों नहीं काटता?

If (p(x)=x^-2+1), why does its graph not cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. क्योंकि \(x^2+1\) हमेशा धनात्मक हैBecause \(x^2+1\) is always positive

Step 1

Concept

For real (x), \(x^2\geq0\), so \(x^2+1>0\). Tip: if (p(x)) never becomes (0), there is no intersection.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(x^2+1\) हमेशा धनात्मक है / Because \(x^2+1\) is always positive. For real (x), \(x^2\geq0\), so \(x^2+1>0\). Tip: if (p(x)) never becomes (0), there is no intersection.

Step 3

Exam Tip

वास्तविक (x) के लिए \(x^2\geq0\) इसलिए \(x^2+1>0\) है। टिप: (p(x)) कभी (0) न हो तो कटान नहीं होगा।

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Question 138/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-5,0)) और ((5,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?

If a graph cuts the (x)-axis at ((-5,0)) and ((5,0)), what is the product of zeroes?

Explanation opens after your attempt

Correct Answer

C. (-25)

Step 1

Concept

The product is ((-5)\times5=-25). Tip: the product of opposite signs is negative.

Step 2

Why this answer is correct

The correct answer is C. (-25). The product is ((-5)\times5=-25). Tip: the product of opposite signs is negative.

Step 3

Exam Tip

गुणनफल ((-5)\times5=-25) है। टिप: विपरीत चिह्नों का गुणनफल ऋणात्मक होता है।

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Question 139/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=3x-15) है तो ग्राफ का (x)-अक्ष कटान बिंदु कौन सा है?

If (p(x)=3x-15), what is the (x)-axis intersection point of the graph?

Explanation opens after your attempt

Correct Answer

B. ((5,0))

Step 1

Concept

Solving (3x-15=0) gives (x=5). Tip: set (p(x)=0) to find the zero of a linear polynomial.

Step 2

Why this answer is correct

The correct answer is B. ((5,0)). Solving (3x-15=0) gives (x=5). Tip: set (p(x)=0) to find the zero of a linear polynomial.

Step 3

Exam Tip

(3x-15=0) से (x=5) मिलता है। टिप: रैखिक बहुपद में (p(x)=0) रखकर शून्यक निकालें।

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Question 140/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि कोई ग्राफ (x)-अक्ष को ((m,0)) पर छूता है और कहीं और नहीं मिलता तो अलग वास्तविक शून्यकों की संख्या क्या है?

If a graph touches the (x)-axis at ((m,0)) and does not meet it anywhere else, what is the number of distinct real zeroes?

Explanation opens after your attempt

Correct Answer

B. एकOne

Step 1

Concept

One touching point gives one distinct real zero. Tip: touching also means (p(x)=0).

Step 2

Why this answer is correct

The correct answer is B. एक / One. One touching point gives one distinct real zero. Tip: touching also means (p(x)=0).

Step 3

Exam Tip

एक ही स्पर्श बिंदु एक अलग वास्तविक शून्यक देता है। टिप: छूना भी (p(x)=0) है।

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Question 141/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x-2)(x-5)(x-8)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?

If (p(x)=(x-2)(x-5)(x-8)), at how many distinct points will the graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

C. तीनThree

Step 1

Concept

Three distinct linear factors give three distinct zeroes (2), (5), (8). Tip: each distinct factor can give one intersection.

Step 2

Why this answer is correct

The correct answer is C. तीन / Three. Three distinct linear factors give three distinct zeroes (2), (5), (8). Tip: each distinct factor can give one intersection.

Step 3

Exam Tip

तीन अलग रैखिक कारक तीन अलग शून्यक (2), (5), (8) देते हैं। टिप: हर अलग कारक एक कटान दे सकता है।

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Question 142/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ का (y)-अक्ष कटान ((0,0)) है तो कौन सा अतिरिक्त निष्कर्ष सही है?

If the (y)-axis intercept of a graph is ((0,0)), what extra conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (0) भी शून्यक है(0) is also a zero

Step 1

Concept

The point ((0,0)) lies on both the (y)-axis and the (x)-axis. Tip: the origin is common to both axes.

Step 2

Why this answer is correct

The correct answer is A. (0) भी शून्यक है / (0) is also a zero. The point ((0,0)) lies on both the (y)-axis and the (x)-axis. Tip: the origin is common to both axes.

Step 3

Exam Tip

((0,0)) (y)-अक्ष और (x)-अक्ष दोनों पर है। टिप: मूल बिंदु दोनों अक्षों का साझा बिंदु है।

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Question 143/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-12x+36) है तो अलग वास्तविक शून्यक कौन सा है?

If (p(x)=x^-2-12x+36), what is the distinct real zero?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

It is ((x-6)²), so the distinct zero is (6). Tip: identify a repeated zero from a perfect square.

Step 2

Why this answer is correct

The correct answer is A. (6). It is ((x-6)²), so the distinct zero is (6). Tip: identify a repeated zero from a perfect square.

Step 3

Exam Tip

यह ((x-6)²) है इसलिए अलग शून्यक (6) है। टिप: पूर्ण वर्ग देखकर दोहराया शून्यक पहचानें।

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Question 144/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-2,0)), ((3,0)), ((7,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?

If a graph cuts the (x)-axis at ((-2,0)), ((3,0)), ((7,0)), what is the product of zeroes?

Explanation opens after your attempt

Correct Answer

B. (-42)

Step 1

Concept

The product is ((-2)\times3\times7=-42). Tip: multiply the (x)-values of all (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is B. (-42). The product is ((-2)\times3\times7=-42). Tip: multiply the (x)-values of all (x)-axis intersections.

Step 3

Exam Tip

गुणनफल ((-2)\times3\times7=-42) है। टिप: सभी (x)-अक्ष कटान के (x)-मानों को गुणा करें।

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Question 145/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=4) है तो (p(x)=0) के हलों के बारे में क्या सही है?

If (p(x)=4), what is correct about the solutions of (p(x)=0)?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक हल नहीं हैThere is no real solution

Step 1

Concept

(p(x)=4) is never (0), so the graph does not cut the (x)-axis. Tip: a non-zero constant polynomial has no zero.

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक हल नहीं है / There is no real solution. (p(x)=4) is never (0), so the graph does not cut the (x)-axis. Tip: a non-zero constant polynomial has no zero.

Step 3

Exam Tip

(p(x)=4) कभी (0) नहीं होता इसलिए ग्राफ (x)-अक्ष को नहीं काटता। टिप: अशून्य स्थिर बहुपद का शून्यक नहीं होता।

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Question 146/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=0) शून्य बहुपद है तो उसके शून्यकों के बारे में कौन सा कथन सही है?

If (p(x)=0) is the zero polynomial, which statement about its zeroes is correct?

Explanation opens after your attempt

Correct Answer

B. हर वास्तविक (x) शून्यक हैEvery real (x) is a zero

Step 1

Concept

The zero polynomial gives (0) for every (x). Tip: treat it differently from a usual constant polynomial.

Step 2

Why this answer is correct

The correct answer is B. हर वास्तविक (x) शून्यक है / Every real (x) is a zero. The zero polynomial gives (0) for every (x). Tip: treat it differently from a usual constant polynomial.

Step 3

Exam Tip

शून्य बहुपद हर (x) पर (0) देता है। टिप: इसे सामान्य स्थिर बहुपद से अलग समझें।

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Question 147/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((2,0)) और ((14,0)) पर काटता है तो शून्यकों का औसत क्या है?

If a graph cuts the (x)-axis at ((2,0)) and ((14,0)), what is the average of the zeroes?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

The average is \(\frac{2+14}{2}=8\). Tip: use the (x)-coordinates for the average.

Step 2

Why this answer is correct

The correct answer is B. (8). The average is \(\frac{2+14}{2}=8\). Tip: use the (x)-coordinates for the average.

Step 3

Exam Tip

औसत \(\frac{2+14}{2}=8\) है। टिप: औसत में (x)-निर्देशांकों का प्रयोग करें।

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Question 148/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=-(x-1)(x+4)) है तो ग्राफ के वास्तविक शून्यक कौन से हैं?

If (p(x)=-(x-1)(x+4)), what are the real zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1) और (-4)(1) and (-4)

Step 1

Concept

The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).

Step 2

Why this answer is correct

The correct answer is A. (1) और (-4) / (1) and (-4). The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).

Step 3

Exam Tip

बाहरी ऋण चिह्न शून्यकों को नहीं बदलता। टिप: (x-1=0) और (x+4=0) हल करें।

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Question 149/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(-6)=0), (p(0)=0), (p(5)=0) है तो ग्राफ के बारे में सही कथन कौन सा है?

If (p(-6)=0), (p(0)=0), (p(5)=0), which statement about the graph is correct?

Explanation opens after your attempt

Correct Answer

A. ग्राफ ((-6,0)), ((0,0)), ((5,0)) से गुजरेगाThe graph will pass through ((-6,0)), ((0,0)), ((5,0))

Step 1

Concept

Each (p(a)=0) gives the point ((a,0)). Tip: place the function value as the second coordinate.

Step 2

Why this answer is correct

The correct answer is A. ग्राफ ((-6,0)), ((0,0)), ((5,0)) से गुजरेगा / The graph will pass through ((-6,0)), ((0,0)), ((5,0)). Each (p(a)=0) gives the point ((a,0)). Tip: place the function value as the second coordinate.

Step 3

Exam Tip

प्रत्येक (p(a)=0) से बिंदु ((a,0)) मिलता है। टिप: फलन मान को दूसरे निर्देशांक में रखें।

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Question 150/200 Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x+3)(x-1)²) है तो ग्राफ (x)-अक्ष से कितने अलग बिंदुओं पर मिलेगा?

If (p(x)=(x+3)(x-1)²), at how many distinct points will the graph meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

The zeroes are (-3) and (1), so there are two distinct meeting points. Tip: count the repeated zero (1) only once for distinct points.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. The zeroes are (-3) and (1), so there are two distinct meeting points. Tip: count the repeated zero (1) only once for distinct points.

Step 3

Exam Tip

शून्यक (-3) और (1) हैं, इसलिए दो अलग बिंदु मिलेंगे। टिप: दोहराए हुए शून्यक (1) को अलग गिनती में एक बार गिनें।

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Question 151/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(a=\sqrt{20}\) है तो (a) का सरल रूप क्या है?

If \(a=\sqrt{20}\), what is the simplified form of (a)?

Explanation opens after your attempt

Correct Answer

A. \(2\sqrt{5}\)

Step 1

Concept

\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{5}\). \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.

Step 3

Exam Tip

\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\) होता है। जड़ में पूर्ण वर्ग गुणनखंड खोजें।

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Question 152/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा कथन \(3+\sqrt{7}\) के लिए सही है?

Which statement is correct for \(3+\sqrt{7}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.

Step 3

Exam Tip

परिमेय (3) में अपरिमेय \(\sqrt{7}\) जोड़ने पर परिणाम अपरिमेय होता है। परीक्षा में पूर्ण वर्ग न होने वाली जड़ को पहचानें।

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Question 153/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प अनंत आवर्ती दशमलव है?

Which option is a non terminating repeating decimal?

Explanation opens after your attempt

Correct Answer

A. (1.272727...)

Step 1

Concept

The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.

Step 2

Why this answer is correct

The correct answer is A. (1.272727...). The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.

Step 3

Exam Tip

(27) बार बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।

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Question 154/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सी संख्या \(\frac{p}{q}\) रूप में नहीं लिखी जा सकती जहाँ \(q\neq0\)?

Which number cannot be written in the form \(\frac{p}{q}\) where \(q\neq0\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{14}\)

Step 1

Concept

\(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{14}\). \(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.

Step 3

Exam Tip

\(\sqrt{14}\) अपरिमेय है क्योंकि (14) पूर्ण वर्ग नहीं है। बाकी विकल्प परिमेय रूप में लिखे जा सकते हैं।

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Question 155/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(x=\sqrt{11}\) है तो \(x^2+1\) का मान किस प्रकार की संख्या है?

If \(x=\sqrt{11}\), what type of number is \(x^2+1\)?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

Here \(x^2=11\), so \(x^2+1=12\). This is a rational number.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. Here \(x^2=11\), so \(x^2+1=12\). This is a rational number.

Step 3

Exam Tip

\(x^2=11\) इसलिए \(x^2+1=12\) है। यह परिमेय संख्या है।

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Question 156/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{75}-\sqrt{27}\) का सही मान है?

Which option is the correct value of \(\sqrt{75}-\sqrt{27}\)?

Explanation opens after your attempt

Correct Answer

A. \(2\sqrt{3}\)

Step 1

Concept

\(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलेगा।

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Question 157/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प दो अपरिमेय संख्याओं का गुणनफल परिमेय बनने का उदाहरण है?

Which option is an example where the product of two irrational numbers is rational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{12}\times\sqrt{3}\)

Step 1

Concept

\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{12}\times\sqrt{3}\). \(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.

Step 3

Exam Tip

\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\) है। दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता।

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Question 158/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा दशमलव अपरिमेय संख्या दिखाता है?

Which decimal shows an irrational number?

Explanation opens after your attempt

Correct Answer

A. (0.3030030003...)

Step 1

Concept

The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.

Step 2

Why this answer is correct

The correct answer is A. (0.3030030003...). The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.

Step 3

Exam Tip

पहला दशमलव अनंत और अनावर्ती है। अनंत अनावर्ती दशमलव अपरिमेय होता है।

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Question 159/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

\(\sqrt{2}+\sqrt{8}+\sqrt{18}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{2}+\sqrt{8}+\sqrt{18}\)?

Explanation opens after your attempt

Correct Answer

A. \(6\sqrt{2}\)

Step 1

Concept

\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(6\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).

Step 3

Exam Tip

\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। कुल \(6\sqrt{2}\) मिलता है।

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Question 160/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{3}\) और \(\sqrt{12}\) के बीच सही संबंध बताता है?

Which option gives the correct relation between \(\sqrt{3}\) and \(\sqrt{12}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{12}=2\sqrt{3}\)

Step 1

Concept

\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Taking out the perfect square makes comparison easy.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{12}=2\sqrt{3}\). \(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Taking out the perfect square makes comparison easy.

Step 3

Exam Tip

\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\) है। पूर्ण वर्ग बाहर निकालने से तुलना आसान होती है।

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Question 161/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (6) और (7) के बीच की अपरिमेय संख्या है?

Which option is an irrational number between (6) and (7)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{43}\)

Step 1

Concept

Since (36<43<49), \(\sqrt{43}\) lies between (6) and (7). It is also irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{43}\). Since (36<43<49), \(\sqrt{43}\) lies between (6) and (7). It is also irrational.

Step 3

Exam Tip

क्योंकि (36<43<49) इसलिए \(\sqrt{43}\) (6) और (7) के बीच है। यह अपरिमेय भी है।

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Question 162/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(a=2-\sqrt{5}\) और \(b=2+\sqrt{5}\) हैं तो (a+b) किस प्रकार की संख्या है?

If \(a=2-\sqrt{5}\) and \(b=2+\sqrt{5}\), what type of number is (a+b)?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.

Step 3

Exam Tip

योग में \(-\sqrt{5}\) और \(\sqrt{5}\) कट जाते हैं। (a+b=4) परिमेय है।

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Question 163/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{0.25}+\sqrt{0.04}\) का मान है?

Which option is the value of \(\sqrt{0.25}+\sqrt{0.04}\)?

Explanation opens after your attempt

Correct Answer

A. (0.7)

Step 1

Concept

\(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.

Step 2

Why this answer is correct

The correct answer is A. (0.7). \(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.

Step 3

Exam Tip

\(\sqrt{0.25}=0.5\) और \(\sqrt{0.04}=0.2\) है। योग (0.7) है जो परिमेय है।

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Question 164/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

\(\frac{\sqrt{45}}{\sqrt{5}}\) का मान क्या है?

What is the value of \(\frac{\sqrt{45}}{\sqrt{5}}\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). In division of roots simplify the ratio inside.

Step 2

Why this answer is correct

The correct answer is A. (3). \(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). In division of roots simplify the ratio inside.

Step 3

Exam Tip

\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\) है। जड़ों की भाग में अंदर के अनुपात को सरल करें।

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Question 165/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(x=0.\overline{12}\) है तो (x) किस प्रकार की संख्या है?

If \(x=0.\overline{12}\), what type of number is (x)?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

The bar shows that (12) repeats. A repeating decimal is rational.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. The bar shows that (12) repeats. A repeating decimal is rational.

Step 3

Exam Tip

ऊपर की रेखा बताती है कि (12) दोहरता है। आवर्ती दशमलव परिमेय होता है।

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Question 166/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{128}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{128}\)?

Explanation opens after your attempt

Correct Answer

A. \(8\sqrt{2}\)

Step 1

Concept

\(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\). Taking out the greatest perfect square is the better method.

Step 2

Why this answer is correct

The correct answer is A. \(8\sqrt{2}\). \(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\). Taking out the greatest perfect square is the better method.

Step 3

Exam Tip

\(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\) है। सबसे बड़ा पूर्ण वर्ग निकालना बेहतर तरीका है।

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Question 167/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

किस विकल्प में केवल अपरिमेय संख्याएँ हैं?

Which option contains only irrational numbers?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{6}\), \(\sqrt{10}\), \(\sqrt{15}\)

Step 1

Concept

In the first option none is the root of a perfect square. So all are irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{6}\), \(\sqrt{10}\), \(\sqrt{15}\). In the first option none is the root of a perfect square. So all are irrational.

Step 3

Exam Tip

पहले विकल्प में कोई भी संख्या पूर्ण वर्ग की जड़ नहीं है। इसलिए सभी अपरिमेय हैं।

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Question 168/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

किस विकल्प में केवल परिमेय संख्याएँ हैं?

Which option contains only rational numbers?

Explanation opens after your attempt

Correct Answer

A. (0.125), (-4), \(\sqrt{169}\)

Step 1

Concept

(0.125) is terminating and \(\sqrt{169}=13\). All numbers in the first option are rational.

Step 2

Why this answer is correct

The correct answer is A. (0.125), (-4), \(\sqrt{169}\). (0.125) is terminating and \(\sqrt{169}=13\). All numbers in the first option are rational.

Step 3

Exam Tip

(0.125) सांत है और \(\sqrt{169}=13\) है। पहले विकल्प की सभी संख्याएँ परिमेय हैं।

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Question 169/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{3}\) और \(\sqrt{27}\) का गुणनफल बताता है?

Which option gives the product of \(\sqrt{3}\) and \(\sqrt{27}\)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.

Step 2

Why this answer is correct

The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.

Step 3

Exam Tip

\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। गुणन में जड़ों के अंदर के संख्याओं को गुणा करें।

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Question 170/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(y=\sqrt{2}+\sqrt{32}\) है तो (y) का सरल रूप क्या है?

If \(y=\sqrt{2}+\sqrt{32}\), what is the simplified form of (y)?

Explanation opens after your attempt

Correct Answer

A. \(5\sqrt{2}\)

Step 1

Concept

\(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.

Step 2

Why this answer is correct

The correct answer is A. \(5\sqrt{2}\). \(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.

Step 3

Exam Tip

\(\sqrt{32}=4\sqrt{2}\) है इसलिए \(y=5\sqrt{2}\) होगा। समान जड़ वाले पदों को जोड़ें।

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Question 171/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा कथन दो अपरिमेय संख्याओं के योग के बारे में सही है?

Which statement is correct about the sum of two irrational numbers?

Explanation opens after your attempt

Correct Answer

A. योग परिमेय या अपरिमेय दोनों हो सकता हैThe sum can be rational or irrational

Step 1

Concept

(\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.

Step 2

Why this answer is correct

The correct answer is A. योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational. (\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.

Step 3

Exam Tip

(\sqrt{2}+\(-\sqrt{2}\)=0) परिमेय है पर \(\sqrt{2}+\sqrt{3}\) अपरिमेय है। इसलिए एक ही स्थायी नियम नहीं है।

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Question 172/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा कथन दो अपरिमेय संख्याओं के गुणनफल के बारे में सही है?

Which statement is correct about the product of two irrational numbers?

Explanation opens after your attempt

Correct Answer

A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता हैThe product can be rational or irrational

Step 1

Concept

\(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.

Step 2

Why this answer is correct

The correct answer is A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational. \(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.

Step 3

Exam Tip

\(\sqrt{5}\times\sqrt{5}=5\) परिमेय है पर \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) अपरिमेय है। इसलिए स्थिति पर निर्भर करता है।

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Question 173/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (\sqrt{5}\(2+\sqrt{5}\)) का मान है?

Which option is the value of (\sqrt{5}\(2+\sqrt{5}\))?

Explanation opens after your attempt

Correct Answer

A. \(5+2\sqrt{5}\)

Step 1

Concept

Distributing gives \(2\sqrt{5}+5\). Keep rational and irrational parts separate.

Step 2

Why this answer is correct

The correct answer is A. \(5+2\sqrt{5}\). Distributing gives \(2\sqrt{5}+5\). Keep rational and irrational parts separate.

Step 3

Exam Tip

वितरण करने पर \(2\sqrt{5}+5\) मिलता है। पदों को परिमेय और अपरिमेय भाग में अलग रखें।

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Question 174/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (\(\sqrt{7}+1\)\(\sqrt{7}-1\)) का मान है?

Which option is the value of (\(\sqrt{7}+1\)\(\sqrt{7}-1\))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

This is ((a+b)(a-b)=a^-2-b^-2). The value is (7-1=6).

Step 2

Why this answer is correct

The correct answer is A. (6). This is ((a+b)(a-b)=a^-2-b^-2). The value is (7-1=6).

Step 3

Exam Tip

यह ((a+b)(a-b)=a^-2-b^-2) है। मान (7-1=6) मिलेगा।

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Question 175/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (\(2+\sqrt{3}\)²) का सही विस्तार है?

Which option is the correct expansion of (\(2+\sqrt{3}\)²)?

Explanation opens after your attempt

Correct Answer

A. \(7+4\sqrt{3}\)

Step 1

Concept

(\(2+\sqrt{3}\)²=4+4\sqrt{3}+3=7+4\sqrt{3}). Do not forget the middle term in the square formula.

Step 2

Why this answer is correct

The correct answer is A. \(7+4\sqrt{3}\). (\(2+\sqrt{3}\)²=4+4\sqrt{3}+3=7+4\sqrt{3}). Do not forget the middle term in the square formula.

Step 3

Exam Tip

(\(2+\sqrt{3}\)²=4+4\sqrt{3}+3=7+4\sqrt{3}) है। वर्ग सूत्र में बीच का पद न भूलें।

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Question 176/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सी संख्या (3) और (4) के बीच है और अपरिमेय है?

Which number lies between (3) and (4) and is irrational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{13}\)

Step 1

Concept

Since (9<13<16), \(\sqrt{13}\) lies between (3) and (4). (13) is not a perfect square.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{13}\). Since (9<13<16), \(\sqrt{13}\) lies between (3) and (4). (13) is not a perfect square.

Step 3

Exam Tip

क्योंकि (9<13<16) इसलिए \(\sqrt{13}\) (3) और (4) के बीच है। (13) पूर्ण वर्ग नहीं है।

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Question 177/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (0) और (1) के बीच की अपरिमेय संख्या है?

Which option is an irrational number between (0) and (1)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{\sqrt{3}}{3}\)

Step 1

Concept

\(\frac{\sqrt{3}}{3}\) is irrational and lies between (0) and (1). Dividing by a non zero rational keeps irrationality.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\sqrt{3}}{3}\). \(\frac{\sqrt{3}}{3}\) is irrational and lies between (0) and (1). Dividing by a non zero rational keeps irrationality.

Step 3

Exam Tip

\(\frac{\sqrt{3}}{3}\) अपरिमेय है और इसका मान (0) और (1) के बीच है। गैर शून्य परिमेय से भाग देने पर अपरिमेयता रहती है।

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Question 178/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(\sqrt{n}\) परिमेय है और (n) धनात्मक पूर्णांक है तो (n) के बारे में सही कथन क्या है?

If \(\sqrt{n}\) is rational and (n) is a positive integer, what is correct about (n)?

Explanation opens after your attempt

Correct Answer

A. (n) पूर्ण वर्ग है(n) is a perfect square

Step 1

Concept

The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.

Step 2

Why this answer is correct

The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.

Step 3

Exam Tip

धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह सीधा परीक्षा नियम है।

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Question 179/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(2.\overline{45}\) की प्रकृति सही बताता है?

Which option correctly describes the nature of \(2.\overline{45}\)?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

The bar shows repetition of (45). Every repeating decimal is rational.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. The bar shows repetition of (45). Every repeating decimal is rational.

Step 3

Exam Tip

ऊपर की रेखा (45) के आवर्तन को दिखाती है। हर आवर्ती दशमलव परिमेय होता है।

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Question 180/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{162}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{162}\)?

Explanation opens after your attempt

Correct Answer

A. \(9\sqrt{2}\)

Step 1

Concept

\(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\). Take the greatest perfect square inside the root.

Step 2

Why this answer is correct

The correct answer is A. \(9\sqrt{2}\). \(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\). Take the greatest perfect square inside the root.

Step 3

Exam Tip

\(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\) है। जड़ में सबसे बड़ा पूर्ण वर्ग लें।

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Question 181/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(4\sqrt{3}-\sqrt{27}\) का मान है?

Which option is the value of \(4\sqrt{3}-\sqrt{27}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{3}\)

Step 1

Concept

\(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{27}=3\sqrt{3}\) है। इसलिए \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\) होगा।

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Question 182/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{5}+\sqrt{20}-\sqrt{45}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\).

Step 2

Why this answer is correct

The correct answer is A. (0). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\).

Step 3

Exam Tip

\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। इसलिए \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\) है।

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Question 183/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\frac{2}{\sqrt{2}}\) का सरल रूप है?

Which option is the simplified form of \(\frac{2}{\sqrt{2}}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{2}\)

Step 1

Concept

\(\frac{2}{\sqrt{2}}=\sqrt{2}\). Simplify roots in the denominator to identify the nature.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\). \(\frac{2}{\sqrt{2}}=\sqrt{2}\). Simplify roots in the denominator to identify the nature.

Step 3

Exam Tip

\(\frac{2}{\sqrt{2}}=\sqrt{2}\) है। हर में जड़ हो तो सरल करके प्रकृति पहचानें।

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Question 184/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(a=\sqrt{6}+1\) है तो (a-1) किस प्रकार की संख्या है?

If \(a=\sqrt{6}+1\), what type of number is (a-1)?

Explanation opens after your attempt

Correct Answer

A. अपरिमेय संख्याIrrational number

Step 1

Concept

\(a-1=\sqrt{6}\), which is irrational. First simplify the expression.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय संख्या / Irrational number. \(a-1=\sqrt{6}\), which is irrational. First simplify the expression.

Step 3

Exam Tip

\(a-1=\sqrt{6}\) है जो अपरिमेय है। पहले अभिव्यक्ति को सरल करें।

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Question 185/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{2}\) के निकटतम दो पूर्णांकों को सही बताता है?

Which option correctly gives the two nearest integers between which \(\sqrt{2}\) lies?

Explanation opens after your attempt

Correct Answer

A. (1) और (2)(1) and (2)

Step 1

Concept

Since (1<2<4), \(1<\sqrt{2}<2\). Use squares to locate roots.

Step 2

Why this answer is correct

The correct answer is A. (1) और (2) / (1) and (2). Since (1<2<4), \(1<\sqrt{2}<2\). Use squares to locate roots.

Step 3

Exam Tip

क्योंकि (1<2<4) इसलिए \(1<\sqrt{2}<2\)। वर्गों से जड़ की स्थिति पहचानें।

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Question 186/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{50}\) और \(\sqrt{72}\) की तुलना सही करता है?

Which option correctly compares \(\sqrt{50}\) and \(\sqrt{72}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{72}>\sqrt{50}\)

Step 1

Concept

For positive numbers a larger number inside the root gives a larger square root. Since (72>50), \(\sqrt{72}>\sqrt{50}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{72}>\sqrt{50}\). For positive numbers a larger number inside the root gives a larger square root. Since (72>50), \(\sqrt{72}>\sqrt{50}\).

Step 3

Exam Tip

धनात्मक संख्याओं में अंदर की संख्या बड़ी हो तो वर्गमूल भी बड़ा होता है। (72>50) इसलिए \(\sqrt{72}>\sqrt{50}\)।

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Question 187/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{0.81}\) का मान है?

Which option is the value of \(\sqrt{0.81}\)?

Explanation opens after your attempt

Correct Answer

A. (0.9)

Step 1

Concept

Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.

Step 2

Why this answer is correct

The correct answer is A. (0.9). Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.

Step 3

Exam Tip

\(0.9\times0.9=0.81\) इसलिए \(\sqrt{0.81}=0.9\)। यह सांत दशमलव है।

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Question 188/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(u=5+\sqrt{2}\) और \(v=5-\sqrt{2}\) हैं तो (uv) का मान क्या है?

If \(u=5+\sqrt{2}\) and \(v=5-\sqrt{2}\), what is the value of (uv)?

Explanation opens after your attempt

Correct Answer

A. (23)

Step 1

Concept

(\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). In conjugate multiplication the irrational part cancels.

Step 2

Why this answer is correct

The correct answer is A. (23). (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). In conjugate multiplication the irrational part cancels.

Step 3

Exam Tip

(\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23) है। संयुग्मी गुणन में अपरिमेय भाग हट जाता है।

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Question 189/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{24}\times\sqrt{6}\) का मान है?

Which option is the value of \(\sqrt{24}\times\sqrt{6}\)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.

Step 2

Why this answer is correct

The correct answer is A. (12). \(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.

Step 3

Exam Tip

\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\) है। जड़ों के गुणन में अंदर की संख्याएँ गुणा करें।

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Question 190/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt[3]{64}\) की प्रकृति सही बताता है?

Which option correctly describes the nature of \(\sqrt[3]{64}\)?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

\(\sqrt[3]{64}=4\), which is rational. The cube root of a perfect cube is rational.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt[3]{64}=4\), which is rational. The cube root of a perfect cube is rational.

Step 3

Exam Tip

\(\sqrt[3]{64}=4\) है जो परिमेय है। पूर्ण घन की घनमूल परिमेय होती है।

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Question 191/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt[3]{16}\) के लिए सही है?

Which option is correct for \(\sqrt[3]{16}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.

Step 3

Exam Tip

(16) पूर्ण घन नहीं है इसलिए इसकी घनमूल अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

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Question 192/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(2+\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?

If \(2+\sqrt{m}\) is irrational and (m) is a positive integer, which (m) can be correct?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

(18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.

Step 2

Why this answer is correct

The correct answer is A. (18). (18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.

Step 3

Exam Tip

(18) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{18}\) अपरिमेय है। बाकी विकल्पों की जड़ परिमेय है।

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Question 193/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{225}\) और \(\sqrt{226}\) की प्रकृति सही बताता है?

Which option gives the correct nature of \(\sqrt{225}\) and \(\sqrt{226}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{225}\) परिमेय है और \(\sqrt{226}\) अपरिमेय है\(\sqrt{225}\) is rational and \(\sqrt{226}\) is irrational

Step 1

Concept

\(\sqrt{225}=15\), but (226) is not a perfect square. So the first root is rational and the second is irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{225}\) परिमेय है और \(\sqrt{226}\) अपरिमेय है / \(\sqrt{225}\) is rational and \(\sqrt{226}\) is irrational. \(\sqrt{225}=15\), but (226) is not a perfect square. So the first root is rational and the second is irrational.

Step 3

Exam Tip

\(\sqrt{225}=15\) है लेकिन (226) पूर्ण वर्ग नहीं है। इसलिए पहली जड़ परिमेय और दूसरी अपरिमेय है।

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Question 194/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प (0.2020020002...) के बारे में सही है?

Which option is correct about (0.2020020002...)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय संख्या हैIt is an irrational number

Step 1

Concept

It has no fixed repeating block and the decimal is infinite. So it is irrational.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय संख्या है / It is an irrational number. It has no fixed repeating block and the decimal is infinite. So it is irrational.

Step 3

Exam Tip

इसमें कोई निश्चित आवर्ती समूह नहीं है और दशमलव अनंत है। इसलिए यह अपरिमेय है।

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Question 195/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि कोई संख्या सांत या आवर्ती दशमलव है तो वह कैसी संख्या होगी?

If a number has a terminating or repeating decimal, what type of number will it be?

Explanation opens after your attempt

Correct Answer

A. परिमेय संख्याRational number

Step 1

Concept

The decimal expansion of rational numbers is terminating or repeating. This identification is very useful in exams.

Step 2

Why this answer is correct

The correct answer is A. परिमेय संख्या / Rational number. The decimal expansion of rational numbers is terminating or repeating. This identification is very useful in exams.

Step 3

Exam Tip

परिमेय संख्याओं का दशमलव विस्तार सांत या आवर्ती होता है। यह पहचान परीक्षा में बहुत काम आती है।

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Question 196/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(1+\sqrt{3}\) और \(1-\sqrt{3}\) के गुणनफल का मान है?

Which option is the value of the product of \(1+\sqrt{3}\) and \(1-\sqrt{3}\)?

Explanation opens after your attempt

Correct Answer

A. (-2)

Step 1

Concept

(\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2). Multiplying conjugates gives a rational number.

Step 2

Why this answer is correct

The correct answer is A. (-2). (\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2). Multiplying conjugates gives a rational number.

Step 3

Exam Tip

(\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2) है। संयुग्मी जोड़े का गुणन परिमेय देता है।

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Question 197/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{12}+\sqrt{75}-\sqrt{27}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)?

Explanation opens after your attempt

Correct Answer

A. \(4\sqrt{3}\)

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). The result is \(4\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(4\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). The result is \(4\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। परिणाम \(4\sqrt{3}\) है।

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Question 198/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \( \frac{1}{2}+\sqrt{2}\) की प्रकृति सही बताता है?

Which option correctly describes the nature of \( \frac{1}{2}+\sqrt{2}\)?

Explanation opens after your attempt

Correct Answer

A. अपरिमेय संख्याIrrational number

Step 1

Concept

\(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय संख्या / Irrational number. \(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.

Step 3

Exam Tip

\(\frac{1}{2}\) परिमेय है और \(\sqrt{2}\) अपरिमेय है। उनका योग अपरिमेय होता है।

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Question 199/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{300}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{300}\)?

Explanation opens after your attempt

Correct Answer

A. \(10\sqrt{3}\)

Step 1

Concept

\(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\). Take out the greatest perfect square.

Step 2

Why this answer is correct

The correct answer is A. \(10\sqrt{3}\). \(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\). Take out the greatest perfect square.

Step 3

Exam Tip

\(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।

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Question 200/200 Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(x=4+\sqrt{7}\) और \(y=4-\sqrt{7}\) हैं तो (x-y) का सरल रूप क्या है?

If \(x=4+\sqrt{7}\) and \(y=4-\sqrt{7}\), what is the simplified form of (x-y)?

Explanation opens after your attempt

Correct Answer

A. \(2\sqrt{7}\)

Step 1

Concept

On subtracting, the (4) terms cancel and (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}). Watch the signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{7}\). On subtracting, the (4) terms cancel and (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}). Watch the signs carefully.

Step 3

Exam Tip

घटाने पर (4) पद कट जाते हैं और (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}) मिलता है। चिह्नों का ध्यान रखें।

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Class 10 Mathematics - Polynomials Medium Quiz

किसी बहुपद का आलेख (x)-अक्ष को ((-4,0)), ((1,0)) और ((6,0)) पर काटता है। उसके वास्तविक शून्यकों की संख्या कितनी है?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात बहुपद का परवलय (x)-अक्ष को केवल ((3,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?

Concept

Why this answer is correct

Exam Tip

एक ग्राफ (x)-अक्ष के ऊपर ही रहता है और उसे कहीं नहीं काटता। उस बहुपद के वास्तविक शून्यक कितने हैं?

Concept

Why this answer is correct

Exam Tip

यदि (p(a)=0) और (p(b)=0), जहाँ \(a\neq b\), तो आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?

Concept

Why this answer is correct

Exam Tip

किसी बहुपद का ग्राफ ((0,-5)), ((2,0)), ((5,0)) और ((7,3)) से गुजरता है। उसके शून्यक कौन से हैं?

Concept

Why this answer is correct

Exam Tip

एक विद्यार्थी ने (y)-अक्ष कटान ((0,8)) को देखकर (8) को शून्यक माना। सही सुधार क्या है?

Concept

Why this answer is correct

Exam Tip

बहुपद (p(x)=(x-4)(x+2)) के आलेख के (x)-अक्ष कटान कौन से होंगे?

Concept

Why this answer is correct

Exam Tip

रेखा (y=2x-10) (x)-अक्ष को कहाँ काटेगी?

Concept

Why this answer is correct

Exam Tip

यदि किसी परवलय के (x)-अक्ष कटान ((-1,0)) और ((4,0)) हैं, तो शून्यकों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ग्राफ (x)-अक्ष को ((-6,0)) और ((2,0)) पर काटता है, तो शून्यकों का गुणनफल क्या है?

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

यदि (p(-3)=0), (p(0)=5) और (p(4)=0), तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?

Concept

Why this answer is correct

Exam Tip

किसी बहुपद का ग्राफ (x)-अक्ष को दो बार काटता है और (y)-अक्ष को एक बार काटता है। वास्तविक शून्यक कितने हैं?

Concept

Why this answer is correct

Exam Tip

यदि परवलय (x)-अक्ष को नहीं काटता लेकिन (y)-अक्ष को ((0,-2)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?

Concept

Why this answer is correct

Exam Tip

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?

Concept

Why this answer is correct

Exam Tip

यदि ग्राफ (x=-2) पर (x)-अक्ष को पार करता है और (x=3) पर केवल छूता है, तो अलग वास्तविक शून्यक कौन से हैं?

Concept

Why this answer is correct

Exam Tip

किस ग्राफ में ठीक एक वास्तविक शून्यक होगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-16), तो इसके ग्राफ के (x)-अक्ष कटान कौन से हैं?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2+9), तो इसका ग्राफ (x)-अक्ष को कितनी बार काटेगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=(x+1)2), तो ग्राफ (x)-अक्ष से कैसे मिलेगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x^-2-16), तो इसके ग्राफ के (x)-अक्ष कटान कौन से हैं?

यदि (p(x)=x^-2+9), तो इसका ग्राफ (x)-अक्ष को कितनी बार काटेगा?

यदि (p(x)=(x+1)²), तो ग्राफ (x)-अक्ष से कैसे मिलेगा?