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algebraic-identities MCQ Questions for Class 10

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

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12 questions tagged with algebraic-identities.

Question 1/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(y \neq 0\), तो (\dfrac{(x+y)3-(x-y)3}{2y}) का सरल रूप क्या है?

If \(y \neq 0\), what is the simplified form of (\dfrac{(x+y)3-(x-y)3}{2y})?

Explanation opens after your attempt
Correct Answer

A. \(,3x^2+y^2,\)

Step 1

Concept

The numerator difference is (6x-2y+2y-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 2

Why this answer is correct

The correct answer is A. \(,3x^2+y^2,\). The numerator difference is (6x-2y+2y-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 3

Exam Tip

ऊपर का अंतर (6x-2y+2y-3=2y\(3x^2+y^2\)) है, इसलिए भाग देने पर \(3x^2+y^2\) मिलता है। परीक्षा में common factor निकालें।

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Question 2/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+1)3-(x-1)3) का सरल रूप क्या है?

What is the simplified form of ((x+1)3-(x-1)3)?

Explanation opens after your attempt
Correct Answer

A. \(,6x^2+2,\)

Step 1

Concept

On expansion, ((x+1)3=x-3+3x-2+3x+1) and ((x-1)3=x-3-3x-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,6x^2+2,\). On expansion, ((x+1)3=x-3+3x-2+3x+1) and ((x-1)3=x-3-3x-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 3

Exam Tip

विस्तार करने पर ((x+1)3=x-3+3x-2+3x+1) और ((x-1)3=x-3-3x-2+3x-1), इसलिए अंतर \(6x^2+2\) है। परीक्षा में cube expansion ध्यान से करें।

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Question 3/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

What is the quotient when (\(8x^3+1\)) is divided by ((2x+1))?

Explanation opens after your attempt
Correct Answer

A. \(,4x^2-2x+1,\)

Step 1

Concept

Because (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,4x^2-2x+1,\). Because (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 3

Exam Tip

क्योंकि (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\))। परीक्षा में sum of cubes की identity याद रखें।

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Question 4/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((3x+2)2-(3x-2)2) का सरल रूप क्या है?

What is the simplified form of ((3x+2)2-(3x-2)2)?

Explanation opens after your attempt
Correct Answer

A. (,24x,)

Step 1

Concept

This is of the form ((A+B)2-(A-B)2=4AB), where (A=3x) and (B=2), so the answer is (24x). In exams, identities save time.

Step 2

Why this answer is correct

The correct answer is A. (,24x,). This is of the form ((A+B)2-(A-B)2=4AB), where (A=3x) and (B=2), so the answer is (24x). In exams, identities save time.

Step 3

Exam Tip

यह ((A+B)2-(A-B)2=4AB) का रूप है, जहां (A=3x) और (B=2), इसलिए उत्तर (24x) है। परीक्षा में identity से समय बचता है।

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Question 5/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-2)\(x^2+2x+4\)) का विस्तार क्या है?

What is the expansion of ((x-2)\(x^2+2x+4\))?

Explanation opens after your attempt
Correct Answer

A. \(,x^3-8,\)

Step 1

Concept

This matches ((a-b)\(a^2+ab+b^2\)=a-3-b-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 2

Why this answer is correct

The correct answer is A. \(,x^3-8,\). This matches ((a-b)\(a^2+ab+b^2\)=a-3-b-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 3

Exam Tip

यह ((a-b)\(a^2+ab+b^2\)=a-3-b-3) का रूप है, इसलिए उत्तर \(x^3-8\) है। परीक्षा में identity पहचानने से विस्तार जल्दी होता है।

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Question 6/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((2m-n)2-(m+n)2) का सरल रूप क्या है?

What is the simplified form of ((2m-n)2-(m+n)2)?

Explanation opens after your attempt
Correct Answer

A. \(,3m^2-6mn,\)

Step 1

Concept

On expansion, ((2m-n)2=4m-2-4mn+n-2) and ((m+n)2=m-2+2mn+n-2), so the difference is \(3m^2-6mn\). In exams, check the signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,3m^2-6mn,\). On expansion, ((2m-n)2=4m-2-4mn+n-2) and ((m+n)2=m-2+2mn+n-2), so the difference is \(3m^2-6mn\). In exams, check the signs carefully.

Step 3

Exam Tip

विस्तार करने पर ((2m-n)2=4m-2-4mn+n-2) और ((m+n)2=m-2+2mn+n-2), इसलिए अंतर \(3m^2-6mn\) है। परीक्षा में चिन्हों की जांच करें।

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Question 7/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(x^3-27\)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-27\)) is divided by ((x-3))?

Explanation opens after your attempt
Correct Answer

A. \(,x^2+3x+9,\)

Step 1

Concept

Because (x-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+3x+9,\). Because (x-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 3

Exam Tip

क्योंकि (x-3-27=(x-3)\(x^2+3x+9\)), इसलिए भागफल \(x^2+3x+9\) है। परीक्षा में घन के अंतर की पहचान करें।

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Question 8/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((m+n)2+(m-n)2) का सरल रूप क्या है?

What is the simplified form of ((m+n)2+(m-n)2)?

Explanation opens after your attempt
Correct Answer

A. \(,2m^2+2n^2,\)

Step 1

Concept

When both expansions are added, (2mn) and (-2mn) cancel, giving \(2m^2+2n^2\). In exams, notice opposite middle terms.

Step 2

Why this answer is correct

The correct answer is A. \(,2m^2+2n^2,\). When both expansions are added, (2mn) and (-2mn) cancel, giving \(2m^2+2n^2\). In exams, notice opposite middle terms.

Step 3

Exam Tip

दोनों विस्तारों को जोड़ने पर (2mn) और (-2mn) कट जाते हैं, इसलिए \(2m^2+2n^2\) मिलता है। परीक्षा में opposite middle terms पर ध्यान दें।

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Question 9/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)) का मान क्या है?

What is the value of (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\))?

Explanation opens after your attempt
Correct Answer

A. (,3,)

Step 1

Concept

This is ((a+b)(a-b)=a-2-b-2), so (5-2=3). In exams, identify a conjugate product.

Step 2

Why this answer is correct

The correct answer is A. (,3,). This is ((a+b)(a-b)=a-2-b-2), so (5-2=3). In exams, identify a conjugate product.

Step 3

Exam Tip

यह ((a+b)(a-b)=a-2-b-2) है, इसलिए (5-2=3)। परीक्षा में conjugate product को पहचानें।

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Question 10/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(x^3-8\)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-8\)) is divided by ((x-2))?

Explanation opens after your attempt
Correct Answer

A. \(,x^2+2x+4,\)

Step 1

Concept

Because (x-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+2x+4,\). Because (x-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 3

Exam Tip

क्योंकि (x-3-8=(x-2)\(x^2+2x+4\)), इसलिए भागफल \(x^2+2x+4\) है। परीक्षा में cubes की identity याद रखें।

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Question 11/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((p+q)2-(p-q)2) का सरल रूप क्या है?

What is the simplified form of ((p+q)2-(p-q)2)?

Explanation opens after your attempt
Correct Answer

A. (,4pq,)

Step 1

Concept

On expansion, ((p+q)2=p-2+2pq+q-2) and ((p-q)2=p-2-2pq+q-2), so the difference is (4pq). In exams, apply standard identities directly.

Step 2

Why this answer is correct

The correct answer is A. (,4pq,). On expansion, ((p+q)2=p-2+2pq+q-2) and ((p-q)2=p-2-2pq+q-2), so the difference is (4pq). In exams, apply standard identities directly.

Step 3

Exam Tip

विस्तार करने पर ((p+q)2=p-2+2pq+q-2) और ((p-q)2=p-2-2pq+q-2), इसलिए अंतर (4pq) है। परीक्षा में standard identities सीधे लगाएं।

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Question 12/12 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(x \neq y\), तो \(\dfrac{x^2-y^2}{x-y}\) का सरल रूप क्या होगा?

If \(x \neq y\), what is the simplified form of \(\dfrac{x^2-y^2}{x-y}\)?

Explanation opens after your attempt
Correct Answer

A. (,x+y,)

Step 1

Concept

Because (x-2-y-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.

Step 2

Why this answer is correct

The correct answer is A. (,x+y,). Because (x-2-y-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.

Step 3

Exam Tip

क्योंकि (x-2-y-2=(x-y)(x+y)), इसलिए सरल रूप (x+y) है। परीक्षा में difference of squares पहचानना बहुत उपयोगी है।

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