Concept-wise Practice

sum MCQ Questions for Class 10

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

Practice Questions

93 questions tagged with sum.

बहुपद \(2x^4+3x^2-5x+7\) में \(x^3\) के गुणांक और (x) के गुणांक का योग क्या है?

In \(2x^4+3x^2-5x+7\), what is the sum of the coefficient of \(x^3\) and the coefficient of (x)?

Explanation opens after your attempt
Correct Answer

A. (-5)

Step 1

Concept

The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).

Step 2

Why this answer is correct

The correct answer is A. (-5). The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).

Step 3

Exam Tip

\(x^3\) का गुणांक (0) और (x) का गुणांक (-5) है। योग (-5) है।

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यदि (p(x)=x-2-2x+3), तो (p(2)+p(-1)) का मान क्या है?

If (p(x)=x-2-2x+3), what is the value of (p(2)+p(-1))?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

(p(2)=3) and (p(-1)=6). Therefore the sum is (9).

Step 2

Why this answer is correct

The correct answer is B. (9). (p(2)=3) and (p(-1)=6). Therefore the sum is (9).

Step 3

Exam Tip

(p(2)=3) और (p(-1)=6) है। इसलिए योग (9) है।

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यदि (p(x)=5x-2-3x+2), तो (p(0)+p(1)) का मान क्या है?

If (p(x)=5x-2-3x+2), what is the value of (p(0)+p(1))?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

(p(0)=2) and (p(1)=4). Therefore the sum is (6).

Step 2

Why this answer is correct

The correct answer is C. (6). (p(0)=2) and (p(1)=4). Therefore the sum is (6).

Step 3

Exam Tip

(p(0)=2) और (p(1)=4) है। इसलिए योग (6) है।

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यदि \(x^2-6x+5=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha+3\) और \(\beta+3\) का योग क्या होगा?

If \(\alpha\) and \(\beta\) are roots of \(x^2-6x+5=0\), what is the sum of \(\alpha+3\) and \(\beta+3\)?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

The old sum of roots is (6). The new sum is (\(\alpha+3\)+\(\beta+3\)=6+6=12).

Step 2

Why this answer is correct

The correct answer is A. (12). The old sum of roots is (6). The new sum is (\(\alpha+3\)+\(\beta+3\)=6+6=12).

Step 3

Exam Tip

पुराने मूलों का योग (6) है। नया योग (\(\alpha+3\)+\(\beta+3\)=6+6=12) होगा।

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यदि \(x^2-5x+4=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha+2\) और \(\beta+2\) का योग क्या होगा?

If \(\alpha\) and \(\beta\) are roots of \(x^2-5x+4=0\), what is the sum of \(\alpha+2\) and \(\beta+2\)?

Explanation opens after your attempt
Correct Answer

A. (9)

Step 1

Concept

The old sum of roots is (5). The new sum is (\(\alpha+2\)+\(\beta+2\)=\alpha+\beta+4=9).

Step 2

Why this answer is correct

The correct answer is A. (9). The old sum of roots is (5). The new sum is (\(\alpha+2\)+\(\beta+2\)=\alpha+\beta+4=9).

Step 3

Exam Tip

पुराने मूलों का योग (5) है। नए योग (\(\alpha+2\)+\(\beta+2\)=\alpha+\beta+4=9) होगा।

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यदि (D=0) और मूलों का योग (14) है तो प्रत्येक मूल क्या होगा?

If (D=0) and the sum of roots is (14), what will each root be?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

When (D=0), both roots are equal. Therefore each root is \(\frac{14}{2}=7\).

Step 2

Why this answer is correct

The correct answer is A. (7). When (D=0), both roots are equal. Therefore each root is \(\frac{14}{2}=7\).

Step 3

Exam Tip

(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{14}{2}=7\) होगा।

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यदि \(4\alpha\) और \(4\beta\) नए मूल हैं तथा \(\alpha+\beta=3\) है तो नए मूलों का योग क्या होगा?

If \(4\alpha\) and \(4\beta\) are new roots and \(\alpha+\beta=3\), what is the sum of the new roots?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

The sum of new roots is (4\alpha+4\beta=4\(\alpha+\beta\)=12). When roots are multiplied by a factor, the sum is also multiplied by that factor.

Step 2

Why this answer is correct

The correct answer is A. (12). The sum of new roots is (4\alpha+4\beta=4\(\alpha+\beta\)=12). When roots are multiplied by a factor, the sum is also multiplied by that factor.

Step 3

Exam Tip

नए मूलों का योग (4\alpha+4\beta=4\(\alpha+\beta\)=12) है। गुणक लगे मूलों में योग भी उसी गुणक से गुणा होता है।

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यदि (D=0) और मूलों का योग (12) है तो प्रत्येक मूल क्या होगा?

If (D=0) and the sum of roots is (12), what will each root be?

Explanation opens after your attempt
Correct Answer

A. (6)

Step 1

Concept

When (D=0), both roots are equal. Therefore each root is \(\frac{12}{2}=6\).

Step 2

Why this answer is correct

The correct answer is A. (6). When (D=0), both roots are equal. Therefore each root is \(\frac{12}{2}=6\).

Step 3

Exam Tip

(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{12}{2}=6\) होगा।

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यदि \(3\alpha\) और \(3\beta\) नए मूल हैं तथा \(\alpha+\beta=4\) है तो नए मूलों का योग क्या होगा?

If \(3\alpha\) and \(3\beta\) are new roots and \(\alpha+\beta=4\), what is the sum of the new roots?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

The sum of new roots is (3\alpha+3\beta=3\(\alpha+\beta\)=12). When roots are multiplied by a factor, the sum is multiplied by the same factor.

Step 2

Why this answer is correct

The correct answer is A. (12). The sum of new roots is (3\alpha+3\beta=3\(\alpha+\beta\)=12). When roots are multiplied by a factor, the sum is multiplied by the same factor.

Step 3

Exam Tip

नए मूलों का योग (3\alpha+3\beta=3\(\alpha+\beta\)=12) है। गुणक लगे मूलों में योग पर भी वही गुणक लगता है।

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यदि (D=0) और मूलों का योग (10) है तो प्रत्येक मूल क्या होगा?

If (D=0) and the sum of roots is (10), what will each root be?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

When (D=0), both roots are equal. Therefore each root is \(\frac{10}{2}=5\).

Step 2

Why this answer is correct

The correct answer is A. (5). When (D=0), both roots are equal. Therefore each root is \(\frac{10}{2}=5\).

Step 3

Exam Tip

(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{10}{2}=5\) होगा।

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यदि \(2\alpha\) और \(2\beta\) मूल हैं तथा \(\alpha+\beta=5\) है तो नए मूलों का योग क्या होगा?

If \(2\alpha\) and \(2\beta\) are roots and \(\alpha+\beta=5\), what is the sum of the new roots?

Explanation opens after your attempt
Correct Answer

A. (10)

Step 1

Concept

The sum of new roots is (2\alpha+2\beta=2\(\alpha+\beta\)=10). When roots are multiplied by a factor, the sum is also multiplied by that factor.

Step 2

Why this answer is correct

The correct answer is A. (10). The sum of new roots is (2\alpha+2\beta=2\(\alpha+\beta\)=10). When roots are multiplied by a factor, the sum is also multiplied by that factor.

Step 3

Exam Tip

नए मूलों का योग (2\alpha+2\beta=2\(\alpha+\beta\)=10) है। गुणक लगे मूलों में योग पर भी वही गुणक लगता है।

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यदि मूलों का योग (12) है और एक मूल (5) है तो दूसरा मूल क्या है?

If the sum of roots is (12) and one root is (5), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

The other root is (12-5=7). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (7). The other root is (12-5=7). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (12-5=7) है। योग में से दिया हुआ मूल घटाएं।

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यदि किसी समीकरण के मूल (4) और (-7) हैं तो उनका योग क्या है?

If the roots of an equation are (4) and (-7), what is their sum?

Explanation opens after your attempt
Correct Answer

B. (-3)

Step 1

Concept

The sum is (4+(-7)=-3). Be careful with the sign while adding a negative number.

Step 2

Why this answer is correct

The correct answer is B. (-3). The sum is (4+(-7)=-3). Be careful with the sign while adding a negative number.

Step 3

Exam Tip

योग (4+(-7)=-3) है। ऋणात्मक संख्या जोड़ते समय चिन्ह का ध्यान रखें।

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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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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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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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यदि मूलों का योग (5) है और एक मूल (2) है तो दूसरा मूल क्या है?

If the sum of roots is (5) and one root is (2) then what is the other root?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

The other root is (5-2=3). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (3). The other root is (5-2=3). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (5-2=3) है। योग में से दिए हुए मूल को घटाएं।

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यदि किसी समीकरण के मूल (1) और (-4) हैं तो उनका योग क्या है?

If the roots of an equation are (1) and (-4) then what is their sum?

Explanation opens after your attempt
Correct Answer

B. (-3)

Step 1

Concept

The sum is (1+(-4)=-3). Be careful with the sign while adding a negative number.

Step 2

Why this answer is correct

The correct answer is B. (-3). The sum is (1+(-4)=-3). Be careful with the sign while adding a negative number.

Step 3

Exam Tip

योग (1+(-4)=-3) है। ऋणात्मक संख्या जोड़ते समय चिन्ह का ध्यान रखें।

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यदि (x=-6) और (x=1) मूल हैं, तो मूलों का योग क्या है?

If (x=-6) and (x=1) are roots, what is the sum of the roots?

Explanation opens after your attempt
Correct Answer

A. (-5)

Step 1

Concept

The sum of roots is (-6+1=-5). For numbers with opposite signs, the sign of the larger magnitude is used.

Step 2

Why this answer is correct

The correct answer is A. (-5). The sum of roots is (-6+1=-5). For numbers with opposite signs, the sign of the larger magnitude is used.

Step 3

Exam Tip

मूलों का योग (-6+1=-5) है। विपरीत चिन्ह वाली संख्याओं में बड़े परिमाण का चिन्ह आता है।

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यदि (x=-5) और (x=2) मूल हैं, तो मूलों का योग क्या है?

If (x=-5) and (x=2) are roots, what is the sum of the roots?

Explanation opens after your attempt
Correct Answer

A. (-3)

Step 1

Concept

The sum of roots is (-5+2=-3). For numbers with opposite signs, the sign of the larger magnitude is used.

Step 2

Why this answer is correct

The correct answer is A. (-3). The sum of roots is (-5+2=-3). For numbers with opposite signs, the sign of the larger magnitude is used.

Step 3

Exam Tip

मूलों का योग (-5+2=-3) है। विपरीत चिन्ह वाली संख्याओं में बड़े परिमाण का चिन्ह आता है।

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यदि (x=2) और (x=-3) किसी द्विघात समीकरण के मूल हैं, तो मूलों का योग क्या है?

If (x=2) and (x=-3) are roots of a quadratic equation, what is the sum of the roots?

Explanation opens after your attempt
Correct Answer

B. (-1)

Step 1

Concept

The sum of roots is (2+(-3)=-1). When adding integers with unlike signs, take the sign of the larger magnitude.

Step 2

Why this answer is correct

The correct answer is B. (-1). The sum of roots is (2+(-3)=-1). When adding integers with unlike signs, take the sign of the larger magnitude.

Step 3

Exam Tip

मूलों का योग (2+(-3)=-1) है। अलग-अलग चिन्ह वाले पूर्णांकों को जोड़ते समय बड़े परिमाण का चिन्ह लें।

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समीकरण \(5x^2+5x+5=0\) में (a+b+c) का मान क्या है?

What is the value of (a+b+c) for \(5x^2+5x+5=0\)?

Explanation opens after your attempt
Correct Answer

C. (15)

Step 1

Concept

Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).

Step 2

Why this answer is correct

The correct answer is C. (15). Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).

Step 3

Exam Tip

यहां (a=5), (b=5), (c=5) हैं। इसलिए (a+b+c=15) है।

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समीकरण \(4x^2+4x+1=0\) में (a+b+c) का मान क्या है?

What is the value of (a+b+c) for \(4x^2+4x+1=0\)?

Explanation opens after your attempt
Correct Answer

C. (9)

Step 1

Concept

Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).

Step 2

Why this answer is correct

The correct answer is C. (9). Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).

Step 3

Exam Tip

यहां (a=4), (b=4), (c=1) हैं। इसलिए (a+b+c=9) है।

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यदि किसी द्विघात बहुपद के शून्यक \(3+\sqrt{5}\) और \(3-\sqrt{5}\) हैं, तो उनके योग का प्रकार क्या है?

If the zeroes of a quadratic polynomial are \(3+\sqrt{5}\) and \(3-\sqrt{5}\), what is the type of their sum?

Explanation opens after your attempt
Correct Answer

B. परिमेय संख्याRational number

Step 1

Concept

The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.

Step 2

Why this answer is correct

The correct answer is B. परिमेय संख्या / Rational number. The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.

Step 3

Exam Tip

योग \(3+\sqrt{5}+3-\sqrt{5}=6\) है, जो परिमेय है। संयुग्मी अपरिमेय संख्याओं का योग अक्सर परिमेय होता है।

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यदि \(\alpha=\sqrt{12}\) और \(\beta=-\sqrt{3}\), तो \(\alpha+\beta\) क्या है?

If \(\alpha=\sqrt{12}\) and \(\beta=-\sqrt{3}\), what is \(\alpha+\beta\)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{3}\)

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\), so \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\). Simplifying radicals is important.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\). Simplifying radicals is important.

Step 3

Exam Tip

\(\sqrt{12}=2\sqrt{3}\), इसलिए \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\)। करणी सरल करना जरूरी है।

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यदि (p(x)=x-2-mx+9) के शून्यक \(3\sqrt{2}\) और \(\frac{3}{\sqrt{2}}\) हैं, तो (m) क्या होगा?

If zeroes of (p(x)=x-2-mx+9) are \(3\sqrt{2}\) and \(\frac{3}{\sqrt{2}}\), what is (m)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9\sqrt{2}}{2}\)

Step 1

Concept

The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{9\sqrt{2}}{2}\). The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).

Step 3

Exam Tip

योग \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\) है। इसलिए \(m=\frac{9\sqrt{2}}{2}\) होगा।

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यदि किसी द्विघात बहुपद के परिमेय गुणांक हैं और शून्यक \(4+\sqrt{11}\) है, तो शून्यकों का योग क्या होगा?

If a quadratic polynomial has rational coefficients and one zero is \(4+\sqrt{11}\), what will be the sum of its zeroes?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).

Step 2

Why this answer is correct

The correct answer is A. (8). The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).

Step 3

Exam Tip

दूसरा शून्यक \(4-\sqrt{11}\) होगा। योग (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8) है।

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कौन सा विकल्प परिमेय और अपरिमेय संख्या का योग दिखाता है?

Which option shows the sum of a rational and an irrational number?

Explanation opens after your attempt
Correct Answer

A. \(4+\sqrt{7}\)

Step 1

Concept

(4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.

Step 2

Why this answer is correct

The correct answer is A. \(4+\sqrt{7}\). (4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.

Step 3

Exam Tip

(4) परिमेय है और \(\sqrt{7}\) अपरिमेय है। उनका योग अपरिमेय होगा।

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यदि ग्राफ (x=-12) और (x=12) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?

If a graph cuts the (x)-axis at (x=-12) and (x=12), what are the product and sum of the zeroes?

Explanation opens after your attempt
Correct Answer

A. गुणनफल (-144), योग (0)Product (-144), sum (0)

Step 1

Concept

The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 2

Why this answer is correct

The correct answer is A. गुणनफल (-144), योग (0) / Product (-144), sum (0). The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 3

Exam Tip

शून्यक (-12) और (12) हैं, इसलिए गुणनफल (-144) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।

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यदि ग्राफ (x=-10) और (x=10) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?

If a graph cuts the (x)-axis at (x=-10) and (x=10), what are the product and sum of the zeroes?

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Correct Answer

A. गुणनफल (-100), योग (0)Product (-100), sum (0)

Step 1

Concept

The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 2

Why this answer is correct

The correct answer is A. गुणनफल (-100), योग (0) / Product (-100), sum (0). The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 3

Exam Tip

शून्यक (-10) और (10) हैं, इसलिए गुणनफल (-100) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।

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