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Mathematics Quiz - Class 10 Mathematics Easy Level 32 Quiz

Question 1/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किसी द्विघात समीकरण (p(x)=0) का मूल वह संख्या है जिससे (p(x)) का मान क्या हो जाता है?

A root of a quadratic equation (p(x)=0) is a number for which the value of (p(x)) becomes what?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

When a root is substituted, (p(x)=0) becomes true. In exams always check a root by substitution.

Step 2

Why this answer is correct

The correct answer is B. (0). When a root is substituted, (p(x)=0) becomes true. In exams always check a root by substitution.

Step 3

Exam Tip

मूल रखने पर (p(x)=0) बनता है। परीक्षा में मूल की जांच हमेशा प्रतिस्थापन से करें।

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Question 2/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

क्या (x=1) समीकरण \(x^2-3x+2=0\) का मूल है?

Is (x=1) a root of \(x^2-3x+2=0\)?

Explanation opens after your attempt

Correct Answer

A. हाँYes

Step 1

Concept

Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.

Step 2

Why this answer is correct

The correct answer is A. हाँ / Yes. Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.

Step 3

Exam Tip

(x=1) रखने पर (1-3+2=0) मिलता है। इसलिए (1) इसका मूल है।

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Question 3/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

क्या (x=-2) समीकरण \(x^2+3x+2=0\) का मूल है?

Is (x=-2) a root of \(x^2+3x+2=0\)?

Explanation opens after your attempt

Correct Answer

A. हाँYes

Step 1

Concept

Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.

Step 2

Why this answer is correct

The correct answer is A. हाँ / Yes. Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.

Step 3

Exam Tip

(x=-2) रखने पर (4-6+2=0) मिलता है। ऋणात्मक मान रखते समय चिन्हों पर ध्यान दें।

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Question 4/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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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Question 5/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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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Question 6/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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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Question 7/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (0) और (-6) हैं?

Which equation has roots (0) and (-6)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+6x=0\)

Step 1

Concept

With roots (0) and (-6), the equation is (x(x+6)=0). Expanding it gives \(x^2+6x=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+6x=0\). With roots (0) and (-6), the equation is (x(x+6)=0). Expanding it gives \(x^2+6x=0\).

Step 3

Exam Tip

मूल (0) और (-6) होने पर समीकरण (x(x+6)=0) होगा। इसे खोलने पर \(x^2+6x=0\) मिलता है।

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Question 8/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (2) समीकरण \(x^2+qx-10=0\) का मूल है तो (q) का मान क्या है?

If (2) is a root of \(x^2+qx-10=0\), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.

Step 2

Why this answer is correct

The correct answer is B. (3). Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.

Step 3

Exam Tip

(x=2) रखने पर (4+2q-10=0) इसलिए (q=3)। दिए गए मूल को सीधे समीकरण में रखें।

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Question 9/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-5x+2=0\) के मूलों का योग क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(\frac{5}{3}\)

Step 1

Concept

The sum of roots is \(-\frac{b}{a}\). Here (a=3) and (b=-5), so the sum is \(\frac{5}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{5}{3}\). The sum of roots is \(-\frac{b}{a}\). Here (a=3) and (b=-5), so the sum is \(\frac{5}{3}\).

Step 3

Exam Tip

मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=3) और (b=-5) इसलिए योग \(\frac{5}{3}\) है।

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Question 10/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(4x^2+7x-3=0\) के मूलों का गुणनफल क्या है?

What is the product of roots of \(4x^2+7x-3=0\)?

Explanation opens after your attempt

Correct Answer

B. \(-\frac{3}{4}\)

Step 1

Concept

The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).

Step 2

Why this answer is correct

The correct answer is B. \(-\frac{3}{4}\). The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).

Step 3

Exam Tip

मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{c}{a}=\frac{-3}{4}\) है।

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Question 11/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (D>0) है तो द्विघात समीकरण के वास्तविक मूल कैसे होते हैं?

If (D>0), how are the real roots of a quadratic equation?

Explanation opens after your attempt

Correct Answer

B. दो भिन्न वास्तविक मूलTwo distinct real roots

Step 1

Concept

When (D>0), two distinct real roots are obtained. To know the nature of roots, check \(D=b^2-4ac\).

Step 2

Why this answer is correct

The correct answer is B. दो भिन्न वास्तविक मूल / Two distinct real roots. When (D>0), two distinct real roots are obtained. To know the nature of roots, check \(D=b^2-4ac\).

Step 3

Exam Tip

(D>0) होने पर दो भिन्न वास्तविक मूल मिलते हैं। मूलों की प्रकृति जानने के लिए \(D=b^2-4ac\) देखें।

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Question 12/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-2x+5=0\) का डिस्क्रिमिनेंट (D) क्या है?

What is the discriminant (D) of \(x^2-2x+5=0\)?

Explanation opens after your attempt

Correct Answer

C. (-16)

Step 1

Concept

Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.

Step 2

Why this answer is correct

The correct answer is C. (-16). Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.

Step 3

Exam Tip

यहां \(D=b^2-4ac=4-20=-16\) है। इसलिए वास्तविक मूल नहीं होंगे।

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Question 13/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस स्थिति में द्विघात समीकरण के कोई वास्तविक मूल नहीं होते?

In which condition does a quadratic equation have no real roots?

Explanation opens after your attempt

Correct Answer

C. (D<0)

Step 1

Concept

When (D<0), there are no real roots. This is a direct rule for the nature of roots.

Step 2

Why this answer is correct

The correct answer is C. (D<0). When (D<0), there are no real roots. This is a direct rule for the nature of roots.

Step 3

Exam Tip

जब (D<0) होता है तब वास्तविक मूल नहीं होते। यह मूलों की प्रकृति का सीधा नियम है।

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Question 14/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+9=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?

Which statement is correct about the real roots of \(x^2+9=0\)?

Explanation opens after your attempt

Correct Answer

C. कोई वास्तविक मूल नहीं हैIt has no real roots

Step 1

Concept

For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.

Step 2

Why this answer is correct

The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.

Step 3

Exam Tip

किसी वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+9=0\) वास्तविक संख्या से संतुष्ट नहीं होता।

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Question 15/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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

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

Explanation opens after your attempt

Correct Answer

A. (0) और (5)(0) and (5)

Step 1

Concept

(x^-2-5x=x(x-5)). Therefore the roots are (0) and (5).

Step 2

Why this answer is correct

The correct answer is A. (0) और (5) / (0) and (5). (x^-2-5x=x(x-5)). Therefore the roots are (0) and (5).

Step 3

Exam Tip

(x^-2-5x=x(x-5)) है। इसलिए मूल (0) और (5) हैं।

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Question 16/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2=9x\) के मूल कौन से हैं?

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

Explanation opens after your attempt

Correct Answer

A. (0) और (9)(0) and (9)

Step 1

Concept

Write \(x^2=9x\) as \(x^2-9x=0\). Then (x(x-9)=0) gives roots (0) and (9).

Step 2

Why this answer is correct

The correct answer is A. (0) और (9) / (0) and (9). Write \(x^2=9x\) as \(x^2-9x=0\). Then (x(x-9)=0) gives roots (0) and (9).

Step 3

Exam Tip

\(x^2=9x\) को \(x^2-9x=0\) लिखें। फिर (x(x-9)=0) से मूल (0) और (9) मिलते हैं।

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Question 17/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-27=0\) के मूल कौन से हैं?

What are the roots of \(3x^2-27=0\)?

Explanation opens after your attempt

Correct Answer

A. (3) और (-3)(3) and (-3)

Step 1

Concept

From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).

Step 2

Why this answer is correct

The correct answer is A. (3) और (-3) / (3) and (-3). From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).

Step 3

Exam Tip

\(3x^2-27=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है।

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Question 18/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-8x+16=0\) का दोहराया हुआ मूल क्या है?

What is the repeated root of \(x^2-8x+16=0\)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(x^-2-8x+16=(x-4)²). Therefore the repeated root is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). (x^-2-8x+16=(x-4)²). Therefore the repeated root is (4).

Step 3

Exam Tip

(x^-2-8x+16=(x-4)²) है। इसलिए दोहराया हुआ मूल (4) है।

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Question 19/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (-2) और (6) हैं?

Which equation has roots (-2) and (6)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-4x-12=0\)

Step 1

Concept

With roots (-2) and (6), we get ((x+2)(x-6)=0). Expanding it gives \(x^2-4x-12=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-12=0\). With roots (-2) and (6), we get ((x+2)(x-6)=0). Expanding it gives \(x^2-4x-12=0\).

Step 3

Exam Tip

मूल (-2) और (6) होने पर ((x+2)(x-6)=0) होगा। इसे खोलने पर \(x^2-4x-12=0\) मिलता है।

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Question 20/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-9x+18=0\) का एक मूल (3) है तो दूसरा मूल क्या है?

If one root of \(x^2-9x+18=0\) is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(x^-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).

Step 2

Why this answer is correct

The correct answer is B. (6). (x^-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).

Step 3

Exam Tip

(x^-2-9x+18=(x-3)(x-6)) है। इसलिए दूसरा मूल (6) है।

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Question 21/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि दो वास्तविक मूलों का गुणनफल धनात्मक और योग ऋणात्मक है तो दोनों मूल कैसे होंगे?

If the product of two real roots is positive and their sum is negative, how will both roots be?

Explanation opens after your attempt

Correct Answer

B. दोनों ऋणात्मकBoth negative

Step 1

Concept

A positive product means both roots have the same sign. A negative sum means both roots are negative.

Step 2

Why this answer is correct

The correct answer is B. दोनों ऋणात्मक / Both negative. A positive product means both roots have the same sign. A negative sum means both roots are negative.

Step 3

Exam Tip

गुणनफल धनात्मक होने पर दोनों मूलों का चिन्ह समान होता है। योग ऋणात्मक होने से दोनों मूल ऋणात्मक होंगे।

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Question 22/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (x+5) किसी द्विघात बहुपद का गुणनखंड है तो कौन सा मूल निश्चित होगा?

If (x+5) is a factor of a quadratic polynomial, which root is certain?

Explanation opens after your attempt

Correct Answer

B. (-5)

Step 1

Concept

Solving (x+5=0) gives (x=-5). Therefore the certain root is (-5).

Step 2

Why this answer is correct

The correct answer is B. (-5). Solving (x+5=0) gives (x=-5). Therefore the certain root is (-5).

Step 3

Exam Tip

(x+5=0) करने पर (x=-5) मिलता है। इसलिए निश्चित मूल (-5) है।

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Question 23/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (4) समीकरण \(x^2+mx-20=0\) का मूल है तो (m) का मान क्या है?

If (4) is a root of \(x^2+mx-20=0\), what is the value of (m)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Putting (x=4) gives (16+4m-20=0), so (m=1). For a parameter, substitute the root directly.

Step 2

Why this answer is correct

The correct answer is A. (1). Putting (x=4) gives (16+4m-20=0), so (m=1). For a parameter, substitute the root directly.

Step 3

Exam Tip

(x=4) रखने पर (16+4m-20=0) इसलिए (m=1)। पैरामीटर के लिए मूल को सीधे रखें।

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Question 24/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(7x^2=0\) के मूलों के बारे में सही कथन कौन सा है?

Which statement is correct about the roots of \(7x^2=0\)?

Explanation opens after your attempt

Correct Answer

A. (0) दोहराया हुआ मूल है(0) is a repeated root

Step 1

Concept

From \(7x^2=0\), we get \(x^2=0\). Therefore (0) is a repeated root.

Step 2

Why this answer is correct

The correct answer is A. (0) दोहराया हुआ मूल है / (0) is a repeated root. From \(7x^2=0\), we get \(x^2=0\). Therefore (0) is a repeated root.

Step 3

Exam Tip

\(7x^2=0\) से \(x^2=0\) मिलता है। इसलिए (0) दोहराया हुआ मूल है।

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Question 25/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-49=0\) के मूल कौन से हैं?

What are the roots of \(x^2-49=0\)?

Explanation opens after your attempt

Correct Answer

A. (7) और (-7)(7) and (-7)

Step 1

Concept

(x^-2-49=(x-7)(x+7)). Therefore the roots are (7) and (-7).

Step 2

Why this answer is correct

The correct answer is A. (7) और (-7) / (7) and (-7). (x^-2-49=(x-7)(x+7)). Therefore the roots are (7) and (-7).

Step 3

Exam Tip

(x^-2-49=(x-7)(x+7)) है। इसलिए मूल (7) और (-7) हैं।

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Question 26/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

निम्न में से कौन सा मान \(x^2+4x=0\) का मूल है?

Which of the following values is a root of \(x^2+4x=0\)?

Explanation opens after your attempt

Correct Answer

B. (-4)

Step 1

Concept

(x^-2+4x=x(x+4)). Therefore the roots are (0) and (-4).

Step 2

Why this answer is correct

The correct answer is B. (-4). (x^-2+4x=x(x+4)). Therefore the roots are (0) and (-4).

Step 3

Exam Tip

(x^-2+4x=x(x+4)) है। इसलिए मूल (0) और (-4) हैं।

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Question 27/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (5) और (-3) हैं?

Which equation has roots (5) and (-3)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-2x-15=0\)

Step 1

Concept

With roots (5) and (-3), we get ((x-5)(x+3)=0). Expanding it gives \(x^2-2x-15=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-15=0\). With roots (5) and (-3), we get ((x-5)(x+3)=0). Expanding it gives \(x^2-2x-15=0\).

Step 3

Exam Tip

मूल (5) और (-3) होने पर ((x-5)(x+3)=0) होगा। इसे खोलने पर \(x^2-2x-15=0\) मिलता है।

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Question 28/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+11x+30=0\) के मूलों का योग क्या है?

What is the sum of roots of \(x^2+11x+30=0\)?

Explanation opens after your attempt

Correct Answer

B. (-11)

Step 1

Concept

The sum of roots is \(-\frac{b}{a}\). Here the sum is (-11).

Step 2

Why this answer is correct

The correct answer is B. (-11). The sum of roots is \(-\frac{b}{a}\). Here the sum is (-11).

Step 3

Exam Tip

मूलों का योग \(-\frac{b}{a}\) है। यहां योग (-11) होगा।

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Question 29/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(5x^2-2x-8=0\) के मूलों का गुणनफल क्या है?

What is the product of roots of \(5x^2-2x-8=0\)?

Explanation opens after your attempt

Correct Answer

C. \(-\frac{8}{5}\)

Step 1

Concept

The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.

Step 2

Why this answer is correct

The correct answer is C. \(-\frac{8}{5}\). The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.

Step 3

Exam Tip

मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-8}{5}\) सही है।

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Question 30/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (0) समीकरण \(2x^2+bx+c=0\) का मूल है तो (c) का मान कैसा होगा?

If (0) is a root of \(2x^2+bx+c=0\), what must be the value of (c)?

Explanation opens after your attempt

Correct Answer

A. (c=0)

Step 1

Concept

Putting (x=0) must give (c=0). Therefore the constant term is zero for a zero root.

Step 2

Why this answer is correct

The correct answer is A. (c=0). Putting (x=0) must give (c=0). Therefore the constant term is zero for a zero root.

Step 3

Exam Tip

(x=0) रखने पर (c=0) मिलना चाहिए। इसलिए शून्य मूल के लिए अचर पद शून्य होता है।

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Question 31/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (-1) समीकरण \(x^2+rx-12=0\) का मूल है तो (r) का मान क्या है?

If (-1) is a root of \(x^2+rx-12=0\), what is the value of (r)?

Explanation opens after your attempt

Correct Answer

A. (-11)

Step 1

Concept

Putting (x=-1) gives (1-r-12=0), so (r=-11). Check the sign of each term while using a negative root.

Step 2

Why this answer is correct

The correct answer is A. (-11). Putting (x=-1) gives (1-r-12=0), so (r=-11). Check the sign of each term while using a negative root.

Step 3

Exam Tip

(x=-1) रखने पर (1-r-12=0) इसलिए (r=-11)। ऋणात्मक मूल रखते समय प्रत्येक पद का चिन्ह देखें।

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Question 32/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+12x+36=0\) के मूल कौन से हैं?

What are the roots of \(x^2+12x+36=0\)?

Explanation opens after your attempt

Correct Answer

B. (-6) और (-6)(-6) and (-6)

Step 1

Concept

(x^-2+12x+36=(x+6)²). Therefore both roots are (-6).

Step 2

Why this answer is correct

The correct answer is B. (-6) और (-6) / (-6) and (-6). (x^-2+12x+36=(x+6)²). Therefore both roots are (-6).

Step 3

Exam Tip

(x^-2+12x+36=(x+6)²) है। इसलिए दोनों मूल (-6) हैं।

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Question 33/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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

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

Explanation opens after your attempt

Correct Answer

A. (0) और (5)(0) and (5)

Step 1

Concept

(2x^-2-10x=2x(x-5)). Therefore the roots are (0) and (5).

Step 2

Why this answer is correct

The correct answer is A. (0) और (5) / (0) and (5). (2x^-2-10x=2x(x-5)). Therefore the roots are (0) and (5).

Step 3

Exam Tip

(2x^-2-10x=2x(x-5)) है। इसलिए मूल (0) और (5) हैं।

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Question 34/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+14x+49=0\) का मूल कौन सा है?

Which is the root of \(x^2+14x+49=0\)?

Explanation opens after your attempt

Correct Answer

B. (-7) दो बार(-7) twice

Step 1

Concept

(x^-2+14x+49=(x+7)²). Therefore the repeated root is (-7).

Step 2

Why this answer is correct

The correct answer is B. (-7) दो बार / (-7) twice. (x^-2+14x+49=(x+7)²). Therefore the repeated root is (-7).

Step 3

Exam Tip

(x^-2+14x+49=(x+7)²) है। इसलिए दोहराया मूल (-7) है।

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Question 35/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

निम्न में से कौन सा मान \(x^2-64=0\) का मूल नहीं है?

Which of the following values is not a root of \(x^2-64=0\)?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.

Step 2

Why this answer is correct

The correct answer is C. (0). The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.

Step 3

Exam Tip

\(x^2-64=0\) के मूल (8) और (-8) हैं। (0) रखने पर समीकरण सत्य नहीं होता।

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Question 36/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि ((x+1)(x-8)=0) है तो मूल कौन से होंगे?

If ((x+1)(x-8)=0), what are the roots?

Explanation opens after your attempt

Correct Answer

B. (-1) और (8)(-1) and (8)

Step 1

Concept

By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).

Step 2

Why this answer is correct

The correct answer is B. (-1) और (8) / (-1) and (8). By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).

Step 3

Exam Tip

शून्य गुणनफल नियम से (x+1=0) या (x-8=0) होगा। इसलिए मूल (-1) और (8) हैं।

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Question 37/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी समीकरण के मूल (2) और (-5) हैं तो उनका योग क्या है?

If the roots of an equation are (2) and (-5), what is their sum?

Explanation opens after your attempt

Correct Answer

B. (-3)

Step 1

Concept

The sum is (2+(-5)=-3). Do not forget the sign while adding a negative root.

Step 2

Why this answer is correct

The correct answer is B. (-3). The sum is (2+(-5)=-3). Do not forget the sign while adding a negative root.

Step 3

Exam Tip

योग (2+(-5)=-3) है। ऋणात्मक मूल जोड़ते समय चिन्ह न भूलें।

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Question 38/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

जिस मोनिक द्विघात समीकरण के मूलों का योग (-9) और गुणनफल (20) है वह कौन सा है?

Which monic quadratic equation has sum of roots (-9) and product of roots (20)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+9x+20=0\)

Step 1

Concept

\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2+9x+20=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2+9x+20=0) सही है\)।

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Question 39/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (2) समीकरण \(3x^2-8x+n=0\) का मूल है तो (n) का मान क्या है?

If (2) is a root of \(3x^2-8x+n=0\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.

Step 2

Why this answer is correct

The correct answer is B. (4). Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.

Step 3

Exam Tip

(x=2) रखने पर (12-16+n=0) इसलिए (n=4)। ऐसे प्रश्नों में गणना धीरे और सही करें।

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Question 40/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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)). Therefore the roots are (2) and (3).

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)). Therefore the roots are (2) and (3).

Step 3

Exam Tip

(x^-2-5x+6=(x-2)(x-3)) है। इसलिए मूल (2) और (3) हैं।

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Question 41/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (-3) किसी द्विघात बहुपद का मूल है तो कौन सा गुणनखंड निश्चित होगा?

If (-3) is a root of a quadratic polynomial, which factor is certain?

Explanation opens after your attempt

Correct Answer

B. (x+3)

Step 1

Concept

If the root is (r), the factor is (x-r). For (r=-3), the factor is (x+3).

Step 2

Why this answer is correct

The correct answer is B. (x+3). If the root is (r), the factor is (x-r). For (r=-3), the factor is (x+3).

Step 3

Exam Tip

मूल (r) होने पर गुणनखंड (x-r) होता है। (r=-3) के लिए गुणनखंड (x+3) होगा।

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Question 42/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+16=0\) के वास्तविक मूलों की संख्या कितनी है?

How many real roots does \(x^2+16=0\) have?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.

Step 2

Why this answer is correct

The correct answer is C. (0). For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.

Step 3

Exam Tip

वास्तविक संख्या के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+16=0\) का कोई वास्तविक मूल नहीं है।

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Question 43/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-3x-10=0\) के मूल कौन से हैं?

What are the roots of \(x^2-3x-10=0\)?

Explanation opens after your attempt

Correct Answer

A. (5) और (-2)(5) and (-2)

Step 1

Concept

(x^-2-3x-10=(x-5)(x+2)). Therefore the roots are (5) and (-2).

Step 2

Why this answer is correct

The correct answer is A. (5) और (-2) / (5) and (-2). (x^-2-3x-10=(x-5)(x+2)). Therefore the roots are (5) and (-2).

Step 3

Exam Tip

(x^-2-3x-10=(x-5)(x+2)) है। इसलिए मूल (5) और (-2) हैं।

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Question 44/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2=49\) के मूल कौन से हैं?

What are the roots of \(x^2=49\)?

Explanation opens after your attempt

Correct Answer

A. (7) और (-7)(7) and (-7)

Step 1

Concept

From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.

Step 2

Why this answer is correct

The correct answer is A. (7) और (-7) / (7) and (-7). From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.

Step 3

Exam Tip

\(x^2=49\) से \(x=\pm7\) मिलता है। वर्गमूल लेते समय दोनों चिन्ह लें।

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Question 45/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि एक मूल (5) है और मूलों का गुणनफल (35) है तो दूसरा मूल क्या होगा?

If one root is (5) and the product of roots is (35), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 2

Why this answer is correct

The correct answer is B. (7). The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें।

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Question 46/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि मूलों का योग (8) है और एक मूल (3) है तो दूसरा मूल क्या है?

If the sum of roots is (8) and one root is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The other root is (8-3=5). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (5). The other root is (8-3=5). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (8-3=5) है। योग में से दिया हुआ मूल घटाएं।

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Question 47/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी द्विघात समीकरण के मूल (r) और (-r) हैं तो उनके योग का मान क्या होगा?

If the roots of a quadratic equation are (r) and (-r), what is their sum?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

(r+(-r)=0). The sum of opposite roots is always (0).

Step 2

Why this answer is correct

The correct answer is C. (0). (r+(-r)=0). The sum of opposite roots is always (0).

Step 3

Exam Tip

(r+(-r)=0) होता है। विपरीत मूलों का योग हमेशा (0) होता है।

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Question 48/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-10x+3=0\) के मूल कौन से हैं?

What are the roots of \(3x^2-10x+3=0\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(3x^-2-10x+3=(3x-1)(x-3)). Therefore the roots are \(\frac{1}{3}\) and (3).

Step 2

Why this answer is correct

The correct answer is A. (3) और \(\frac{1}{3}\) / (3) and \(\frac{1}{3}\). (3x^-2-10x+3=(3x-1)(x-3)). Therefore the roots are \(\frac{1}{3}\) and (3).

Step 3

Exam Tip

(3x^-2-10x+3=(3x-1)(x-3)) है। इसलिए मूल \(\frac{1}{3}\) और (3) हैं।

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Question 49/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (-4) और (-4) हैं तो समीकरण कौन सा है?

If both roots of a monic quadratic equation are (-4) and (-4), which equation is it?

Explanation opens after your attempt

Correct Answer

A. \(x^2+8x+16=0\)

Step 1

Concept

If both roots are (-4), the equation is ((x+4)²=0). Expanding it gives \(x^2+8x+16=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+8x+16=0\). If both roots are (-4), the equation is ((x+4)²=0). Expanding it gives \(x^2+8x+16=0\).

Step 3

Exam Tip

दोनों मूल (-4) हों तो समीकरण ((x+4)²=0) होगा। इसे खोलने पर \(x^2+8x+16=0\) मिलता है।

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Question 50/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x=\frac{1}{2}\) समीकरण \(4x^2+px-3=0\) का मूल है तो (p) का मान क्या है?

If \(x=\frac{1}{2}\) is a root of \(4x^2+px-3=0\), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Putting \(x=\frac{1}{2}\) gives \(1+\frac{p}{2}-3=0\), so (p=4). When substituting a fractional root, solve each term carefully.

Step 2

Why this answer is correct

The correct answer is B. (4). Putting \(x=\frac{1}{2}\) gives \(1+\frac{p}{2}-3=0\), so (p=4). When substituting a fractional root, solve each term carefully.

Step 3

Exam Tip

\(x=\frac{1}{2}\) रखने पर \(1+\frac{p}{2}-3=0\) इसलिए (p=4)। भिन्न मूल रखते समय हर पद सावधानी से हल करें।

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Class 10 Mathematics Easy Quiz

किसी द्विघात समीकरण (p(x)=0) का मूल वह संख्या है जिससे (p(x)) का मान क्या हो जाता है?

Concept

Why this answer is correct

Exam Tip

क्या (x=1) समीकरण \(x^2-3x+2=0\) का मूल है?

Concept

Why this answer is correct

Exam Tip

क्या (x=-2) समीकरण \(x^2+3x+2=0\) का मूल है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

किस समीकरण के मूल (0) और (-6) हैं?

Concept

Why this answer is correct

Exam Tip

यदि (2) समीकरण \(x^2+qx-10=0\) का मूल है तो (q) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(3x^2-5x+2=0\) के मूलों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(4x^2+7x-3=0\) के मूलों का गुणनफल क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (D>0) है तो द्विघात समीकरण के वास्तविक मूल कैसे होते हैं?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-2x+5=0\) का डिस्क्रिमिनेंट (D) क्या है?

Concept

Why this answer is correct

Exam Tip

किस स्थिति में द्विघात समीकरण के कोई वास्तविक मूल नहीं होते?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+9=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2=9x\) के मूल कौन से हैं?

Concept

Why this answer is correct

Exam Tip

समीकरण \(3x^2-27=0\) के मूल कौन से हैं?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-8x+16=0\) का दोहराया हुआ मूल क्या है?

Concept

Why this answer is correct

Exam Tip

किस समीकरण के मूल (-2) और (6) हैं?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-9x+18=0\) का एक मूल (3) है तो दूसरा मूल क्या है?

Concept

Why this answer is correct