Concept-wise Practice

factorisation MCQ Questions for Class 10

factorisation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

207 questions tagged with factorisation.

समीकरण \(x^2+9x+20=0\) के मूल कौन से हैं?

What are the roots of \(x^2+9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. (-4) और (-5)(-4) and (-5)

Step 1

Concept

(x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).

Step 2

Why this answer is correct

The correct answer is A. (-4) और (-5) / (-4) and (-5). (x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).

Step 3

Exam Tip

(x-2+9x+20=(x+4)(x+5)) है। इसलिए मूल (-4) और (-5) हैं।

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समीकरण \(x^2-7x+12=0\) के मूल कौन से हैं?

What are the roots of \(x^2-7x+12=0\)?

Explanation opens after your attempt
Correct Answer

A. (3) और (4)(3) and (4)

Step 1

Concept

(x-2-7x+12=(x-3)(x-4)). Therefore the roots are (3) and (4).

Step 2

Why this answer is correct

The correct answer is A. (3) और (4) / (3) and (4). (x-2-7x+12=(x-3)(x-4)). Therefore the roots are (3) and (4).

Step 3

Exam Tip

(x-2-7x+12=(x-3)(x-4)) है। इसलिए मूल (3) और (4) हैं।

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समीकरण \(x^2-25=0\) के मूल कौन से हैं?

What are the roots of \(x^2-25=0\)?

Explanation opens after your attempt
Correct Answer

A. (5) और (-5)(5) and (-5)

Step 1

Concept

(x-2-25=(x-5)(x+5)). Therefore the roots are (5) and (-5).

Step 2

Why this answer is correct

The correct answer is A. (5) और (-5) / (5) and (-5). (x-2-25=(x-5)(x+5)). Therefore the roots are (5) and (-5).

Step 3

Exam Tip

(x-2-25=(x-5)(x+5)) है। इसलिए मूल (5) और (-5) हैं।

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समीकरण \(2x^2-5x+3=0\) के मूल कौन से हैं?

What are the roots of \(2x^2-5x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. (1) और \(\frac{3}{2}\)(1) and \(\frac{3}{2}\)

Step 1

Concept

(2x-2-5x+3=(2x-3)(x-1)) so the roots are \(\frac{3}{2}\) and (1). Be careful with factors that contain coefficients.

Step 2

Why this answer is correct

The correct answer is A. (1) और \(\frac{3}{2}\) / (1) and \(\frac{3}{2}\). (2x-2-5x+3=(2x-3)(x-1)) so the roots are \(\frac{3}{2}\) and (1). Be careful with factors that contain coefficients.

Step 3

Exam Tip

(2x-2-5x+3=(2x-3)(x-1)) इसलिए मूल \(\frac{3}{2}\) और (1) हैं। गुणांक वाले गुणनखंडों में सावधानी रखें।

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समीकरण \(x^2+2x-8=0\) के मूल कौन से हैं?

What are the roots of \(x^2+2x-8=0\)?

Explanation opens after your attempt
Correct Answer

B. (2) और (-4)(2) and (-4)

Step 1

Concept

(x-2+2x-8=(x+4)(x-2)) so the roots are (-4) and (2). Roots have opposite signs to the factor constants.

Step 2

Why this answer is correct

The correct answer is B. (2) और (-4) / (2) and (-4). (x-2+2x-8=(x+4)(x-2)) so the roots are (-4) and (2). Roots have opposite signs to the factor constants.

Step 3

Exam Tip

(x-2+2x-8=(x+4)(x-2)) इसलिए मूल (-4) और (2) हैं। गुणनखंड के चिन्ह उलटकर मूल मिलते हैं।

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सूत्र या गुणनखंडन से \(x^2-3x+2=0\) के मूल कौन से हैं?

Using formula or factorisation what are the roots of \(x^2-3x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. (1) और (2)(1) and (2)

Step 1

Concept

(x-2-3x+2=(x-1)(x-2)) so the roots are (1) and (2). For small numbers factorisation is faster.

Step 2

Why this answer is correct

The correct answer is A. (1) और (2) / (1) and (2). (x-2-3x+2=(x-1)(x-2)) so the roots are (1) and (2). For small numbers factorisation is faster.

Step 3

Exam Tip

(x-2-3x+2=(x-1)(x-2)) इसलिए मूल (1) और (2) हैं। छोटे अंकों में गुणनखंडन तेज रहता है।

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समीकरण \(3x^2-12x=0\) के मूल कौन से हैं?

What are the roots of \(3x^2-12x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0) और (4)(0) and (4)

Step 1

Concept

(3x-2-12x=3x(x-4)) so the roots are (0) and (4). Take out the common factor first.

Step 2

Why this answer is correct

The correct answer is A. (0) और (4) / (0) and (4). (3x-2-12x=3x(x-4)) so the roots are (0) and (4). Take out the common factor first.

Step 3

Exam Tip

(3x-2-12x=3x(x-4)) इसलिए मूल (0) और (4) हैं। सामान्य गुणनखंड पहले बाहर निकालें।

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निम्न में से कौन सा मान \(x^2-2x=0\) का मूल है?

Which of the following values is a root of \(x^2-2x=0\)?

Explanation opens after your attempt
Correct Answer

C. (2)

Step 1

Concept

(x-2-2x=x(x-2)) so the roots are (0) and (2). Choose the root that appears in the options.

Step 2

Why this answer is correct

The correct answer is C. (2). (x-2-2x=x(x-2)) so the roots are (0) and (2). Choose the root that appears in the options.

Step 3

Exam Tip

(x-2-2x=x(x-2)) इसलिए मूल (0) और (2) हैं। विकल्पों में मौजूद मूल को चुनें।

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समीकरण \(x^2-6x+8=0\) का एक मूल (4) है तो दूसरा मूल क्या है?

If one root of \(x^2-6x+8=0\) is (4) then what is the other root?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

(x-2-6x+8=(x-4)(x-2)) so the other root is (2). Use the given root to find the other factor.

Step 2

Why this answer is correct

The correct answer is B. (2). (x-2-6x+8=(x-4)(x-2)) so the other root is (2). Use the given root to find the other factor.

Step 3

Exam Tip

(x-2-6x+8=(x-4)(x-2)) इसलिए दूसरा मूल (2) है। दिए गए एक मूल से दूसरा गुणनखंड खोजें।

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किस समीकरण के मूल (2) और (5) हैं?

Which equation has roots (2) and (5)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-7x+10=0\)

Step 1

Concept

The equation ((x-2)(x-5)=0) gives \(x^2-7x+10=0\). You can also check the sum and product of roots.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7x+10=0\). The equation ((x-2)(x-5)=0) gives \(x^2-7x+10=0\). You can also check the sum and product of roots.

Step 3

Exam Tip

समीकरण ((x-2)(x-5)=0) से \(x^2-7x+10=0\) मिलता है। मूलों का योग और गुणनफल भी जांच सकते हैं।

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समीकरण \(x^2=x\) के मूल कौन से हैं?

What are the roots of \(x^2=x\)?

Explanation opens after your attempt
Correct Answer

A. (0) और (1)(0) and (1)

Step 1

Concept

Writing \(x^2=x\) as \(x^2-x=0\) gives (x(x-1)=0). So the roots are (0) and (1).

Step 2

Why this answer is correct

The correct answer is A. (0) और (1) / (0) and (1). Writing \(x^2=x\) as \(x^2-x=0\) gives (x(x-1)=0). So the roots are (0) and (1).

Step 3

Exam Tip

\(x^2=x\) को \(x^2-x=0\) लिखने पर (x(x-1)=0) मिलता है। इसलिए मूल (0) और (1) हैं।

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समीकरण \(x^2+5x+6=0\) के मूल कौन से हैं?

What are the roots of \(x^2+5x+6=0\)?

Explanation opens after your attempt
Correct Answer

A. (-2) और (-3)(-2) and (-3)

Step 1

Concept

(x-2+5x+6=(x+2)(x+3)) so the roots are (-2) and (-3). Pay special attention to signs.

Step 2

Why this answer is correct

The correct answer is A. (-2) और (-3) / (-2) and (-3). (x-2+5x+6=(x+2)(x+3)) so the roots are (-2) and (-3). Pay special attention to signs.

Step 3

Exam Tip

(x-2+5x+6=(x+2)(x+3)) इसलिए मूल (-2) और (-3) हैं। चिन्हों पर विशेष ध्यान दें।

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समीकरण \(x^2-4x+3=0\) के मूल कौन से हैं?

What are the roots of \(x^2-4x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. (1) और (3)(1) and (3)

Step 1

Concept

(x-2-4x+3=(x-1)(x-3)) so the roots are (1) and (3). Factorisation is the fastest method for easy questions.

Step 2

Why this answer is correct

The correct answer is A. (1) और (3) / (1) and (3). (x-2-4x+3=(x-1)(x-3)) so the roots are (1) and (3). Factorisation is the fastest method for easy questions.

Step 3

Exam Tip

(x-2-4x+3=(x-1)(x-3)) इसलिए मूल (1) और (3) हैं। आसान प्रश्न में गुणनखंड बनाना सबसे तेज तरीका है।

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समीकरण \(x^2-9=0\) के मूल कौन से हैं?

What are the roots of \(x^2-9=0\)?

Explanation opens after your attempt
Correct Answer

A. (3) और (-3)(3) and (-3)

Step 1

Concept

(x-2-9=(x-3)(x+3)) so the roots are (3) and (-3). In exams quickly identify the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (3) और (-3) / (3) and (-3). (x-2-9=(x-3)(x+3)) so the roots are (3) and (-3). In exams quickly identify the difference of squares.

Step 3

Exam Tip

(x-2-9=(x-3)(x+3)) इसलिए मूल (3) और (-3) हैं। परीक्षा में वर्गों के अंतर को तुरंत पहचानें।

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समीकरण \(x^2-17x+72=0\) के गुणनखंड पहचानने के लिए कौन-सी संख्या जोड़ी उपयोगी है?

Which pair of numbers is useful to identify the factors of \(x^2-17x+72=0\)?

Explanation opens after your attempt
Correct Answer

A. (8) और (9)(8) and (9)

Step 1

Concept

\(8\cdot9=72\) and (8+9=17). Because the middle term is negative, the factors are ((x-8)(x-9)).

Step 2

Why this answer is correct

The correct answer is A. (8) और (9) / (8) and (9). \(8\cdot9=72\) and (8+9=17). Because the middle term is negative, the factors are ((x-8)(x-9)).

Step 3

Exam Tip

\(8\cdot9=72\) और (8+9=17) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-8)(x-9)) बनते हैं।

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समीकरण \(x^2-3x-40=0\) के मूलों का सही युग्म कौन-सा है?

Which pair is the correct roots of \(x^2-3x-40=0\)?

Explanation opens after your attempt
Correct Answer

A. (8,-5)

Step 1

Concept

From ((x-8)(x+5)=0), the roots are (8) and (-5). Check both product and sum.

Step 2

Why this answer is correct

The correct answer is A. (8,-5). From ((x-8)(x+5)=0), the roots are (8) and (-5). Check both product and sum.

Step 3

Exam Tip

((x-8)(x+5)=0) से मूल (8) और (-5) मिलते हैं। गुणनफल और योग दोनों मिलाकर जांचें।

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समीकरण \(x^2-10x=0\) के मूल कौन-से हैं?

What are the roots of \(x^2-10x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0,10)

Step 1

Concept

(x-2-10x=x(x-10)), so the roots are (0) and (10). Taking the common factor is a quick method.

Step 2

Why this answer is correct

The correct answer is A. (0,10). (x-2-10x=x(x-10)), so the roots are (0) and (10). Taking the common factor is a quick method.

Step 3

Exam Tip

(x-2-10x=x(x-10)), इसलिए मूल (0) और (10) हैं। समान गुणनखंड निकालना तेज तरीका है।

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समीकरण \(x^2-13x+42=0\) के गुणनखंड पहचानने के लिए कौन-सी संख्या जोड़ी उपयोगी है?

Which pair of numbers is useful to identify the factors of \(x^2-13x+42=0\)?

Explanation opens after your attempt
Correct Answer

A. (6) और (7)(6) and (7)

Step 1

Concept

\(6\cdot7=42\) and (6+7=13). Because the middle term is negative, the factors are ((x-6)(x-7)).

Step 2

Why this answer is correct

The correct answer is A. (6) और (7) / (6) and (7). \(6\cdot7=42\) and (6+7=13). Because the middle term is negative, the factors are ((x-6)(x-7)).

Step 3

Exam Tip

\(6\cdot7=42\) और (6+7=13) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-6)(x-7)) बनते हैं।

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समीकरण \(x^2+2x-35=0\) के मूलों का सही युग्म कौन-सा है?

Which pair is the correct roots of \(x^2+2x-35=0\)?

Explanation opens after your attempt
Correct Answer

A. (5,-7)

Step 1

Concept

From ((x+7)(x-5)=0), the roots are (-7) and (5). Check both product and sum.

Step 2

Why this answer is correct

The correct answer is A. (5,-7). From ((x+7)(x-5)=0), the roots are (-7) and (5). Check both product and sum.

Step 3

Exam Tip

((x+7)(x-5)=0) से मूल (-7) और (5) मिलते हैं। गुणनफल और योग दोनों मिलाकर जांचें।

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समीकरण \(x^2+9x=0\) के मूल कौन-से हैं?

What are the roots of \(x^2+9x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0,-9)

Step 1

Concept

(x-2+9x=x(x+9)), so the roots are (0) and (-9). Taking the common factor is a quick method.

Step 2

Why this answer is correct

The correct answer is A. (0,-9). (x-2+9x=x(x+9)), so the roots are (0) and (-9). Taking the common factor is a quick method.

Step 3

Exam Tip

(x-2+9x=x(x+9)), इसलिए मूल (0) और (-9) हैं। समान गुणनखंड निकालना जल्दी तरीका है।

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समीकरण \(x^2-11x+30=0\) में मूलों की पहचान के लिए कौन-सी संख्या जोड़ी उपयोगी है?

Which pair of numbers is useful to identify the roots of \(x^2-11x+30=0\)?

Explanation opens after your attempt
Correct Answer

A. (5) और (6)(5) and (6)

Step 1

Concept

\(5\cdot6=30\) and (5+6=11). Because the middle term is negative, the factors are ((x-5)(x-6)).

Step 2

Why this answer is correct

The correct answer is A. (5) और (6) / (5) and (6). \(5\cdot6=30\) and (5+6=11). Because the middle term is negative, the factors are ((x-5)(x-6)).

Step 3

Exam Tip

\(5\cdot6=30\) और (5+6=11) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-5)(x-6)) बनते हैं।

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समीकरण \(x^2-2x-15=0\) के मूलों में से कौन-सा सही युग्म है?

Which pair is the correct roots of \(x^2-2x-15=0\)?

Explanation opens after your attempt
Correct Answer

B. (5,-3)

Step 1

Concept

From ((x-5)(x+3)=0), the roots are (5) and (-3). Match both product and sum in such questions.

Step 2

Why this answer is correct

The correct answer is B. (5,-3). From ((x-5)(x+3)=0), the roots are (5) and (-3). Match both product and sum in such questions.

Step 3

Exam Tip

((x-5)(x+3)=0) से मूल (5) और (-3) मिलते हैं। ऐसे प्रश्नों में गुणनफल और योग दोनों मिलाएं।

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समीकरण \(x^2-8x=0\) के मूल कौन-से हैं?

What are the roots of \(x^2-8x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0,8)

Step 1

Concept

(x-2-8x=x(x-8)), so the roots are (0) and (8). Taking the common factor is an easy method.

Step 2

Why this answer is correct

The correct answer is A. (0,8). (x-2-8x=x(x-8)), so the roots are (0) and (8). Taking the common factor is an easy method.

Step 3

Exam Tip

(x-2-8x=x(x-8)), इसलिए मूल (0) और (8) हैं। समान गुणनखंड बाहर निकालना आसान तरीका है।

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यदि (p(x)=x-2-\sqrt{5}x), तो इसके शून्यक कौन से हैं?

If (p(x)=x-2-\sqrt{5}x), what are its zeroes?

Explanation opens after your attempt
Correct Answer

A. \(0,\sqrt{5}\)

Step 1

Concept

(p(x)=x\(x-\sqrt{5}\)), so the zeroes are (0) and \(\sqrt{5}\). Taking the common factor is a fast method in exams.

Step 2

Why this answer is correct

The correct answer is A. \(0,\sqrt{5}\). (p(x)=x\(x-\sqrt{5}\)), so the zeroes are (0) and \(\sqrt{5}\). Taking the common factor is a fast method in exams.

Step 3

Exam Tip

(p(x)=x\(x-\sqrt{5}\)), इसलिए शून्यक (0) और \(\sqrt{5}\) हैं। परीक्षा में सामान्य गुणनखंड निकालना तेज तरीका है।

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यदि (p(x)=x-2-2\sqrt{2}x+2) है, तो (p(x)) का सही गुणनखंड रूप कौन सा है?

If (p(x)=x-2-2\sqrt{2}x+2), which is the correct factorized form of (p(x))?

Explanation opens after your attempt
Correct Answer

A. (\(x-\sqrt{2}\)2)

Step 1

Concept

(x-2-2\sqrt{2}x+2=\(x-\sqrt{2}\)2). Recognizing a perfect square gives equal irrational zeroes.

Step 2

Why this answer is correct

The correct answer is A. (\(x-\sqrt{2}\)2). (x-2-2\sqrt{2}x+2=\(x-\sqrt{2}\)2). Recognizing a perfect square gives equal irrational zeroes.

Step 3

Exam Tip

(x-2-2\sqrt{2}x+2=\(x-\sqrt{2}\)2) है। पूर्ण वर्ग पहचानने से समान अपरिमेय शून्यक मिलते हैं।

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यदि (p(x)=x-2-11x+30) का ग्राफ खींचा जाए तो (x)-अक्ष पर कौन से बिंदु मिलेंगे?

If the graph of (p(x)=x-2-11x+30) is drawn, which points will lie on the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. ((5,0)) और ((6,0))((5,0)) and ((6,0))

Step 1

Concept

(x-2-11x+30=(x-5)(x-6)). So the graph meets the (x)-axis at (x=5) and (x=6).

Step 2

Why this answer is correct

The correct answer is A. ((5,0)) और ((6,0)) / ((5,0)) and ((6,0)). (x-2-11x+30=(x-5)(x-6)). So the graph meets the (x)-axis at (x=5) and (x=6).

Step 3

Exam Tip

(x-2-11x+30=(x-5)(x-6)) है। इसलिए (x=5) और (x=6) पर ग्राफ (x)-अक्ष से मिलता है।

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द्विघात (p(x)=x-2+2x-15) का ग्राफ (x)-अक्ष को किन (x)-मानों पर काटेगा?

At which (x)-values will the graph of (p(x)=x-2+2x-15) cut the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. (3) और (-5)(3) and (-5)

Step 1

Concept

(x-2+2x-15=(x+5)(x-3)). Zeroes are the (x)-values of (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is A. (3) और (-5) / (3) and (-5). (x-2+2x-15=(x+5)(x-3)). Zeroes are the (x)-values of (x)-axis intersections.

Step 3

Exam Tip

(x-2+2x-15=(x+5)(x-3)) है। शून्यक (x)-अक्ष पर कटान के (x)-मान होते हैं।

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