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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+3y+4z)² ) में (xz) वाला पद क्या होगा?

What will be the (xz)-term in ( (2x+3y+4z)² )?

Explanation opens after your attempt

Correct Answer

A. (16xz)

Step 1

Concept

Twice the product of (2x) and (4z) is (16xz). Exam tip: check twice the product of each pair.

Step 2

Why this answer is correct

The correct answer is A. (16xz). Twice the product of (2x) and (4z) is (16xz). Exam tip: check twice the product of each pair.

Step 3

Exam Tip

(2x) और (4z) का दोगुना गुणनफल (16xz) है। परीक्षा में हर जोड़ी का दोगुना पद देखें।

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Question 2/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3a-2b+c)² ) में (bc) वाला पद कौन सा है?

Which is the (bc)-term in ( (3a-2b+c)² )?

Explanation opens after your attempt

Correct Answer

C. (-2bc)

Step 1

Concept

Twice the product of (-2b) and (c) is (2\cdot(-2b)\cdot c=-4bc). Match both sign and coefficient carefully.

Step 2

Why this answer is correct

The correct answer is C. (-2bc). Twice the product of (-2b) and (c) is (2\cdot(-2b)\cdot c=-4bc). Match both sign and coefficient carefully.

Step 3

Exam Tip

(-2b) और (c) का दोगुना गुणनफल (-4bc) नहीं बल्कि (2\cdot(-2b)\cdot c=-4bc) है। सही विकल्प में चिन्ह और गुणांक मिलाएँ।

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Question 3/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+2)²-(x-3)² ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (10x-5)

Step 1

Concept

Use (A^-2-B^-2=(A+B)(A-B)). Here (A+B=2x-1) and (A-B=5), so the result is (10x-5).

Step 2

Why this answer is correct

The correct answer is B. (10x-5). Use (A^-2-B^-2=(A+B)(A-B)). Here (A+B=2x-1) and (A-B=5), so the result is (10x-5).

Step 3

Exam Tip

इसे (A^-2-B^-2=(A+B)(A-B)) से करें। (A+B=2x-1) और (A-B=5), इसलिए (10x-5) है।

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Question 4/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x-1)²-(2x+5)² ) का सरल रूप क्या होगा?

What will be the simplified form of ( (2x-1)²-(2x+5)² )?

Explanation opens after your attempt

Correct Answer

C. (-24x-24)

Step 1

Concept

Apply (A^-2-B^-2=(A+B)(A-B)). Here (A-B=-6) and (A+B=4x+4), so it is (-24x-24).

Step 2

Why this answer is correct

The correct answer is C. (-24x-24). Apply (A^-2-B^-2=(A+B)(A-B)). Here (A-B=-6) and (A+B=4x+4), so it is (-24x-24).

Step 3

Exam Tip

(A^-2-B^-2=(A+B)(A-B)) लगाएँ। यहाँ (A-B=-6) और (A+B=4x+4), इसलिए (-24x-24) है।

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Question 5/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( x^2+10x+25-4y^2 \) का गुणनखंड रूप क्या है?

What is the factor form of \( x^2+10x+25-4y^2 \)?

Explanation opens after your attempt

Correct Answer

A. ( (x+5+2y)(x+5-2y) )

Step 1

Concept

First identify (x^-2+10x+25=(x+5)²). Then apply difference of squares to ( (x+5)²-(2y)² ).

Step 2

Why this answer is correct

The correct answer is A. ( (x+5+2y)(x+5-2y) ). First identify (x^-2+10x+25=(x+5)²). Then apply difference of squares to ( (x+5)²-(2y)² ).

Step 3

Exam Tip

पहले (x^-2+10x+25=(x+5)²) पहचानें। फिर ( (x+5)²-(2y)² ) पर अंतर के वर्ग लगाएँ।

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Question 6/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 9p^2-12pq+4q^2-16 \) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \( 9p^2-12pq+4q^2-16 \)?

Explanation opens after your attempt

Correct Answer

B. ( (3p-2q+4)(3p-2q-4) )

Step 1

Concept

First (9p^-2-12pq+4q^-2=(3p-2q)²). Then factor ( (3p-2q)²-4² ).

Step 2

Why this answer is correct

The correct answer is B. ( (3p-2q+4)(3p-2q-4) ). First (9p^-2-12pq+4q^-2=(3p-2q)²). Then factor ( (3p-2q)²-4² ).

Step 3

Exam Tip

पहले (9p^-2-12pq+4q^-2=(3p-2q)²) है। फिर ( (3p-2q)²-4² ) का गुणनखंड करें।

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Question 7/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b+c)²-(a-b-c)² ) का सरल रूप क्या है?

What is the simplified form of ( (a+b+c)²-(a-b-c)² )?

Explanation opens after your attempt

Correct Answer

A. (4a(b+c))

Step 1

Concept

Treat it as ( (a+(b+c))²-(a-(b+c))² ). The identity gives (4a(b+c)).

Step 2

Why this answer is correct

The correct answer is A. (4a(b+c)). Treat it as ( (a+(b+c))²-(a-(b+c))² ). The identity gives (4a(b+c)).

Step 3

Exam Tip

इसे ( (a+(b+c))²-(a-(b+c))² ) मानें। पहचान से (4a(b+c)) मिलता है।

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Question 8/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+y)²+(2x-y)²-8x^-2 ) का सरल रूप क्या है?

What is the simplified form of ( (2x+y)²+(2x-y)²-8x^-2 )?

Explanation opens after your attempt

Correct Answer

B. \(2y^2\)

Step 1

Concept

The sum is first \(8x^2+2y^2\). Subtracting \(8x^2\) leaves \(2y^2\).

Step 2

Why this answer is correct

The correct answer is B. \(2y^2\). The sum is first \(8x^2+2y^2\). Subtracting \(8x^2\) leaves \(2y^2\).

Step 3

Exam Tip

पहले योग \(8x^2+2y^2\) होता है। \(8x^2\) घटाने पर \(2y^2\) बचता है।

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Question 9/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3m+n)²-(3m-n)²=48mn ) हो तो \(n\neq0\) के लिए (m) का मान क्या है?

If ( (3m+n)²-(3m-n)²=48mn ), what is (m) for \(n\neq0\)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

By identity the left side is \(4\cdot3m\cdot n=12mn\). (12mn=48mn) gives no valid nonzero fixed (m); the given equality is not generally true.

Step 2

Why this answer is correct

The correct answer is C. (4). By identity the left side is \(4\cdot3m\cdot n=12mn\). (12mn=48mn) gives no valid nonzero fixed (m); the given equality is not generally true.

Step 3

Exam Tip

पहचान से बायाँ पक्ष \(4\cdot3m\cdot n=12mn\) है। (12mn=48mn) से (m) नहीं बल्कि (mn) कटने पर कथन केवल (12=48) देगा, इसलिए कोई निश्चित (m) नहीं है।

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Question 10/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+4)(x-6)+(x-4)(x+6) ) का सरल रूप क्या है?

What is the simplified form of ( (x+4)(x-6)+(x-4)(x+6) )?

Explanation opens after your attempt

Correct Answer

A. \(2x^2-48\)

Step 1

Concept

The two products are \(x^2-2x-24\) and \(x^2+2x-24\). Adding gives \(2x^2-48\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-48\). The two products are \(x^2-2x-24\) and \(x^2+2x-24\). Adding gives \(2x^2-48\).

Step 3

Exam Tip

दोनों गुणनफल \(x^2-2x-24\) और \(x^2+2x-24\) हैं। जोड़ने पर \(2x^2-48\) मिलता है।

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Question 11/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+4)(x-6)-(x-4)(x+6) ) का सरल रूप क्या है?

What is the simplified form of ( (x+4)(x-6)-(x-4)(x+6) )?

Explanation opens after your attempt

Correct Answer

B. (-4x)

Step 1

Concept

The first product is \(x^2-2x-24\) and the second is \(x^2+2x-24\). Their difference is (-4x).

Step 2

Why this answer is correct

The correct answer is B. (-4x). The first product is \(x^2-2x-24\) and the second is \(x^2+2x-24\). Their difference is (-4x).

Step 3

Exam Tip

पहला गुणनफल \(x^2-2x-24\) और दूसरा \(x^2+2x-24\) है। अंतर (-4x) है।

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Question 12/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x-2)(x+5)(x-7) ) में \(x^2\) का गुणांक क्या होगा?

What will be the coefficient of \(x^2\) in ( (x-2)(x+5)(x-7) )?

Explanation opens after your attempt

Correct Answer

A. (-4)

Step 1

Concept

In three linear factors, the coefficient of \(x^2\) is the sum of constants. Here (-2+5-7=-4).

Step 2

Why this answer is correct

The correct answer is A. (-4). In three linear factors, the coefficient of \(x^2\) is the sum of constants. Here (-2+5-7=-4).

Step 3

Exam Tip

तीन रैखिक गुणनखंडों में \(x^2\) का गुणांक स्थिर संख्याओं का योग होता है। यहाँ (-2+5-7=-4) है।

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Question 13/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+1)(x-3)(x+8) ) में स्थिर पद क्या है?

What is the constant term in ( (x+1)(x-3)(x+8) )?

Explanation opens after your attempt

Correct Answer

B. (-24)

Step 1

Concept

The constant term is (1\cdot(-3)\cdot8=-24). Exam tip: multiply only the constants for constant term.

Step 2

Why this answer is correct

The correct answer is B. (-24). The constant term is (1\cdot(-3)\cdot8=-24). Exam tip: multiply only the constants for constant term.

Step 3

Exam Tip

स्थिर पद (1\cdot(-3)\cdot8=-24) है। परीक्षा में स्थिर पद के लिए केवल संख्याओं का गुणन करें।

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Question 14/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+3)(2x-5)(2x+1) ) में \(x^2\) का गुणांक क्या होगा?

What will be the coefficient of \(x^2\) in ( (2x+3)(2x-5)(2x+1) )?

Explanation opens after your attempt

Correct Answer

B. (-4)

Step 1

Concept

For \(x^2\) terms, choose two (2x) factors and one constant. The total coefficient is (4(3-5+1)=-4).

Step 2

Why this answer is correct

The correct answer is B. (-4). For \(x^2\) terms, choose two (2x) factors and one constant. The total coefficient is (4(3-5+1)=-4).

Step 3

Exam Tip

\(x^2\) पदों के लिए दो (2x) और एक स्थिर पद चुनते हैं। कुल गुणांक (4(3-5+1)=-4) है।

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Question 15/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2a-b)²-\(4a^2+b^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (2a-b)²-\(4a^2+b^2\) )?

Explanation opens after your attempt

Correct Answer

B. (-4ab)

Step 1

Concept

( (2a-b)²=4a^-2-4ab+b^-2 ). Subtracting \(4a^2+b^2\) leaves (-4ab).

Step 2

Why this answer is correct

The correct answer is B. (-4ab). ( (2a-b)²=4a^-2-4ab+b^-2 ). Subtracting \(4a^2+b^2\) leaves (-4ab).

Step 3

Exam Tip

( (2a-b)²=4a^-2-4ab+b^-2 ) है। \(4a^2+b^2\) घटाने पर (-4ab) बचता है।

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Question 16/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+y)²+(x-y)²-\(2x^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (x+y)²+(x-y)²-\(2x^2\) )?

Explanation opens after your attempt

Correct Answer

A. \(2y^2\)

Step 1

Concept

The sum is first \(2x^2+2y^2\). Subtracting \(2x^2\) leaves \(2y^2\).

Step 2

Why this answer is correct

The correct answer is A. \(2y^2\). The sum is first \(2x^2+2y^2\). Subtracting \(2x^2\) leaves \(2y^2\).

Step 3

Exam Tip

पहले योग \(2x^2+2y^2\) है। \(2x^2\) घटाने पर \(2y^2\) बचता है।

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Question 17/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b)²+(a-b)²=50 ) और (a=3) हो तो \(b^2\) कितना है?

If ( (a+b)²+(a-b)²=50 ) and (a=3), what is \(b^2\)?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

By identity \(2a^2+2b^2=50\). With (a=3), \(18+2b^2=50\), so \(b^2=16\).

Step 2

Why this answer is correct

The correct answer is B. (16). By identity \(2a^2+2b^2=50\). With (a=3), \(18+2b^2=50\), so \(b^2=16\).

Step 3

Exam Tip

पहचान से \(2a^2+2b^2=50\) है। (a=3) रखने पर \(18+2b^2=50\), इसलिए \(b^2=16\) है।

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Question 18/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (p+q)²-(p-q)²=36 ) और (p=3) हो तो (q) क्या है?

If ( (p+q)²-(p-q)²=36 ) and (p=3), what is (q)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

By identity (4pq=36). With (p=3), (12q=36), so (q=3).

Step 2

Why this answer is correct

The correct answer is B. (3). By identity (4pq=36). With (p=3), (12q=36), so (q=3).

Step 3

Exam Tip

पहचान से (4pq=36) है। (p=3) रखने पर (12q=36), इसलिए (q=3) है।

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Question 19/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 1004^2-996^2 \) का मान क्या है?

What is the value of \( 1004^2-996^2 \)?

Explanation opens after your attempt

Correct Answer

A. (16000)

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), \(2000\cdot8=16000\). Exam tip: do not calculate both large squares separately.

Step 2

Why this answer is correct

The correct answer is A. (16000). Using (a^-2-b^-2=(a+b)(a-b)), \(2000\cdot8=16000\). Exam tip: do not calculate both large squares separately.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(2000\cdot8=16000\) है। परीक्षा में बड़े वर्ग अलग-अलग न निकालें।

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Question 20/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 503^2+497^2 \) को पहचान से निकालने पर मान क्या होगा?

Using identity, what is the value of \( 503^2+497^2 \)?

Explanation opens after your attempt

Correct Answer

A. (500018)

Step 1

Concept

Treat it as ( (500+3)²+(500-3)² ). It gives \(2\cdot500^2+2\cdot3^2=500018\).

Step 2

Why this answer is correct

The correct answer is A. (500018). Treat it as ( (500+3)²+(500-3)² ). It gives \(2\cdot500^2+2\cdot3^2=500018\).

Step 3

Exam Tip

इसे ( (500+3)²+(500-3)² ) मानें। \(2\cdot500^2+2\cdot3^2=500018\) मिलता है।

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Question 21/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 203^2-197^2 \) का मान क्या है?

What is the value of \( 203^2-197^2 \)?

Explanation opens after your attempt

Correct Answer

A. (2400)

Step 1

Concept

By difference of squares, ( (203+197)(203-197)=400\cdot6=2400 ). Exam tip: directly find sum and difference.

Step 2

Why this answer is correct

The correct answer is A. (2400). By difference of squares, ( (203+197)(203-197)=400\cdot6=2400 ). Exam tip: directly find sum and difference.

Step 3

Exam Tip

अंतर के वर्ग से ( (203+197)(203-197)=400\cdot6=2400 ) है। परीक्षा में योग और अंतर सीधे निकालें।

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Question 22/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( \(x^2+1\)²-x^-4 ) का सरल गुणनखंड रूप क्या है?

What is the simplified factor form of ( \(x^2+1\)²-x^-4 )?

Explanation opens after your attempt

Correct Answer

A. \(2x^2+1\)

Step 1

Concept

Difference of squares gives ( \(x^2+1+x^2\)\(x^2+1-x^2\)=2x^-2+1 ). Exam tip: simplify at the end.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+1\). Difference of squares gives ( \(x^2+1+x^2\)\(x^2+1-x^2\)=2x^-2+1 ). Exam tip: simplify at the end.

Step 3

Exam Tip

अंतर के वर्ग से ( \(x^2+1+x^2\)\(x^2+1-x^2\)=2x^-2+1 ) मिलता है। परीक्षा में अंत में सरल करें।

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Question 23/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

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

Explanation opens after your attempt

Correct Answer

B. \(-16x^2\)

Step 1

Concept

Use (A^-2-B^-2=(A+B)(A-B)). Here \(A+B=2x^2\) and (A-B=-8), so it is \(-16x^2\).

Step 2

Why this answer is correct

The correct answer is B. \(-16x^2\). Use (A^-2-B^-2=(A+B)(A-B)). Here \(A+B=2x^2\) and (A-B=-8), so it is \(-16x^2\).

Step 3

Exam Tip

(A^-2-B^-2=(A+B)(A-B)) लगाएँ। \(A+B=2x^2\) और (A-B=-8), इसलिए \(-16x^2\) है।

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Question 24/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+1)(x+2)(x+3) ) के पूर्ण प्रसार में स्थिर पद क्या है?

What is the constant term in the full expansion of ( (x+1)(x+2)(x+3) )?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The constant term is \(1\cdot2\cdot3=6\). Exam tip: multiply only constants for the constant term.

Step 2

Why this answer is correct

The correct answer is C. (6). The constant term is \(1\cdot2\cdot3=6\). Exam tip: multiply only constants for the constant term.

Step 3

Exam Tip

स्थिर पद \(1\cdot2\cdot3=6\) है। परीक्षा में स्थिर पद के लिए केवल स्थिर संख्याएँ गुणा करें।

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Question 25/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+1)(2x-3)(2x+5) ) में स्थिर पद क्या होगा?

What will be the constant term in ( (2x+1)(2x-3)(2x+5) )?

Explanation opens after your attempt

Correct Answer

B. (-15)

Step 1

Concept

The constant term is (1\cdot(-3)\cdot5=-15). Exam tip: multiply constants with signs.

Step 2

Why this answer is correct

The correct answer is B. (-15). The constant term is (1\cdot(-3)\cdot5=-15). Exam tip: multiply constants with signs.

Step 3

Exam Tip

स्थिर पद (1\cdot(-3)\cdot5=-15) है। परीक्षा में चिन्ह के साथ संख्याएँ गुणा करें।

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Question 26/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+2b)²+(a-2b)²-\(2a^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (a+2b)²+(a-2b)²-\(2a^2\) )?

Explanation opens after your attempt

Correct Answer

B. \(8b^2\)

Step 1

Concept

The sum is first \(2a^2+8b^2\). Subtracting \(2a^2\) leaves \(8b^2\).

Step 2

Why this answer is correct

The correct answer is B. \(8b^2\). The sum is first \(2a^2+8b^2\). Subtracting \(2a^2\) leaves \(8b^2\).

Step 3

Exam Tip

पहले योग \(2a^2+8b^2\) है। \(2a^2\) घटाने पर \(8b^2\) बचता है।

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Question 27/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (4x+y)²-(4x-y)² ) को (32xy) के बराबर क्यों लिखा जा सकता है?

Why can ( (4x+y)²-(4x-y)² ) be written equal to (32xy)?

Explanation opens after your attempt

Correct Answer

A. क्योंकि (4uv) में (u=4x) और (v=y) हैBecause in (4uv), (u=4x) and (v=y)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). With (u=4x) and (v=y), it gives (16xy), so (32xy) is not correct.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि (4uv) में (u=4x) और (v=y) है / Because in (4uv), (u=4x) and (v=y). ( (u+v)²-(u-v)²=4uv ). With (u=4x) and (v=y), it gives (16xy), so (32xy) is not correct.

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। (u=4x) और (v=y) रखने पर (16xy) मिलता है, इसलिए (32xy) सही नहीं है।

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Question 28/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+2)²+(x+5)²-2(x+2)(x+5) ) का मान क्या है?

What is the value of ( (x+2)²+(x+5)²-2(x+2)(x+5) )?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

This is (A^-2+B^-2-2AB=(A-B)²). (A-B=(x+2)-(x+5)=-3), so the value is (9).

Step 2

Why this answer is correct

The correct answer is A. (9). This is (A^-2+B^-2-2AB=(A-B)²). (A-B=(x+2)-(x+5)=-3), so the value is (9).

Step 3

Exam Tip

यह (A^-2+B^-2-2AB=(A-B)²) है। (A-B=(x+2)-(x+5)=-3), इसलिए मान (9) है।

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Question 29/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+7)²+(2x-1)²-2(2x+7)(2x-1) ) का मान क्या है?

What is the value of ( (2x+7)²+(2x-1)²-2(2x+7)(2x-1) )?

Explanation opens after your attempt

Correct Answer

C. (64)

Step 1

Concept

This is ( (A-B)² ). (A-B=(2x+7)-(2x-1)=8), so the value is (64).

Step 2

Why this answer is correct

The correct answer is C. (64). This is ( (A-B)² ). (A-B=(2x+7)-(2x-1)=8), so the value is (64).

Step 3

Exam Tip

यह ( (A-B)² ) है। (A-B=(2x+7)-(2x-1)=8), इसलिए मान (64) है।

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Question 30/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b+c)²-\(a^2+b^2+c^2+2ab\) ) का सरल रूप क्या है?

What is the simplified form of ( (a+b+c)²-\(a^2+b^2+c^2+2ab\) )?

Explanation opens after your attempt

Correct Answer

A. (2bc+2ca)

Step 1

Concept

In the three-term square, (2ab+2bc+2ca) appear. After subtracting the given (2ab), (2bc+2ca) remains.

Step 2

Why this answer is correct

The correct answer is A. (2bc+2ca). In the three-term square, (2ab+2bc+2ca) appear. After subtracting the given (2ab), (2bc+2ca) remains.

Step 3

Exam Tip

तीन पदों के वर्ग में (2ab+2bc+2ca) आते हैं। दिए गए (2ab) को घटाने पर (2bc+2ca) बचता है।

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Question 31/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+2y+z)²-\(x^2+4y^2+z^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (x+2y+z)²-\(x^2+4y^2+z^2\) )?

Explanation opens after your attempt

Correct Answer

A. (4xy+2xz+4yz)

Step 1

Concept

After subtracting square terms, only twice the pair products remain. They are (4xy), (2xz), and (4yz).

Step 2

Why this answer is correct

The correct answer is A. (4xy+2xz+4yz). After subtracting square terms, only twice the pair products remain. They are (4xy), (2xz), and (4yz).

Step 3

Exam Tip

वर्ग पद घटाने पर केवल जोड़ीदार दोगुने पद बचते हैं। ये (4xy), (2xz) और (4yz) हैं।

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Question 32/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3x-2y+z)² ) में (xy) और (yz) पदों का योग क्या है?

What is the sum of the (xy)-term and (yz)-term in ( (3x-2y+z)² )?

Explanation opens after your attempt

Correct Answer

A. ( -12xy-4yz )

Step 1

Concept

The (xy)-term is (2\cdot3x\cdot(-2y)=-12xy) and the (yz)-term is (2\cdot(-2y)\cdot z=-4yz). Their sum is (-12xy-4yz).

Step 2

Why this answer is correct

The correct answer is A. ( -12xy-4yz ). The (xy)-term is (2\cdot3x\cdot(-2y)=-12xy) and the (yz)-term is (2\cdot(-2y)\cdot z=-4yz). Their sum is (-12xy-4yz).

Step 3

Exam Tip

(xy) पद (2\cdot3x\cdot(-2y)=-12xy) और (yz) पद (2\cdot(-2y)\cdot z=-4yz) है। दोनों का योग (-12xy-4yz) है।

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Question 33/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+4)(x-1)(x-6) ) में (x) का गुणांक क्या होगा?

What will be the coefficient of (x) in ( (x+4)(x-1)(x-6) )?

Explanation opens after your attempt

Correct Answer

A. ( -26 )

Step 1

Concept

The coefficient of (x) is the sum of pairwise products of constants. (4(-1)+4(-6)+(-1)(-6)=-22), so check options carefully.

Step 2

Why this answer is correct

The correct answer is A. ( -26 ). The coefficient of (x) is the sum of pairwise products of constants. (4(-1)+4(-6)+(-1)(-6)=-22), so check options carefully.

Step 3

Exam Tip

(x) का गुणांक स्थिर पदों के दो-दो गुणनफल का योग है। (4(-1)+4(-6)+(-1)(-6)=-22) नहीं, सही जोड़ (-4-24+6=-22) है।

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Question 34/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+3)(x-4)(x+2) ) में (x) का गुणांक क्या है?

What is the coefficient of (x) in ( (x+3)(x-4)(x+2) )?

Explanation opens after your attempt

Correct Answer

B. ( -10 )

Step 1

Concept

The coefficient of (x) is the sum of pairwise products of constants. (3(-4)+3(2)+(-4)(2)=-14), so be careful with options.

Step 2

Why this answer is correct

The correct answer is B. ( -10 ). The coefficient of (x) is the sum of pairwise products of constants. (3(-4)+3(2)+(-4)(2)=-14), so be careful with options.

Step 3

Exam Tip

(x) का गुणांक स्थिर पदों के दो-दो गुणनफल का योग है। (3(-4)+3(2)+(-4)(2)=-14) है, इसलिए दिए विकल्पों में सावधानी चाहिए।

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Question 35/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+1)(2x+3)(2x-5) ) में (x) का गुणांक क्या है?

What is the coefficient of (x) in ( (2x+1)(2x+3)(2x-5) )?

Explanation opens after your attempt

Correct Answer

A. ( -22 )

Step 1

Concept

For (x), choose one (2x) and two constants. The coefficient is (2(1\cdot3+1\cdot(-5)+3\cdot(-5))=-34).

Step 2

Why this answer is correct

The correct answer is A. ( -22 ). For (x), choose one (2x) and two constants. The coefficient is (2(1\cdot3+1\cdot(-5)+3\cdot(-5))=-34).

Step 3

Exam Tip

(x) के लिए एक (2x) और दो स्थिर पद चुनते हैं। गुणांक (2(1\cdot3+1\cdot(-5)+3\cdot(-5))=-34) है।

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Question 36/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x-2)(x+2)\(x^2+4\) ) का सरल रूप क्या होगा?

What will be the simplified form of ( (x-2)(x+2)\(x^2+4\) )?

Explanation opens after your attempt

Correct Answer

B. \(x^4-16\)

Step 1

Concept

First ( (x-2)(x+2)=x^-2-4 ). Then ( \(x^2-4\)\(x^2+4\)=x^-4-16 ).

Step 2

Why this answer is correct

The correct answer is B. \(x^4-16\). First ( (x-2)(x+2)=x^-2-4 ). Then ( \(x^2-4\)\(x^2+4\)=x^-4-16 ).

Step 3

Exam Tip

पहले ( (x-2)(x+2)=x^-2-4 ) है। फिर ( \(x^2-4\)\(x^2+4\)=x^-4-16 ) मिलेगा।

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Question 37/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+3)²-(2x-3)² ) को (24x) के बराबर क्यों माना जाता है?

Why is ( (2x+3)²-(2x-3)² ) considered equal to (24x)?

Explanation opens after your attempt

Correct Answer

A. क्योंकि (4uv) में (u=2x) और (v=3) हैBecause in (4uv), (u=2x) and (v=3)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). Here \(4\cdot2x\cdot3=24x\).

Step 2

Why this answer is correct

The correct answer is A. क्योंकि (4uv) में (u=2x) और (v=3) है / Because in (4uv), (u=2x) and (v=3). ( (u+v)²-(u-v)²=4uv ). Here \(4\cdot2x\cdot3=24x\).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। यहाँ \(4\cdot2x\cdot3=24x\) है।

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Question 38/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (5x-2)²+(5x+2)² ) का सरल रूप क्या है?

What is the simplified form of ( (5x-2)²+(5x+2)² )?

Explanation opens after your attempt

Correct Answer

A. \(50x^2+8\)

Step 1

Concept

( (u-v)²+(u+v)²=2u^-2+2v^-2 ). With (u=5x), (v=2), it is \(50x^2+8\).

Step 2

Why this answer is correct

The correct answer is A. \(50x^2+8\). ( (u-v)²+(u+v)²=2u^-2+2v^-2 ). With (u=5x), (v=2), it is \(50x^2+8\).

Step 3

Exam Tip

( (u-v)²+(u+v)²=2u^-2+2v^-2 ) है। (u=5x), (v=2), इसलिए \(50x^2+8\) है।

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Question 39/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (7a+3b)²+(7a-3b)² ) में (ab) वाला पद क्यों नहीं बचता?

Why does the (ab)-term not remain in ( (7a+3b)²+(7a-3b)² )?

Explanation opens after your attempt

Correct Answer

A. क्योंकि (+42ab) और (-42ab) कट जाते हैंBecause (+42ab) and (-42ab) cancel

Step 1

Concept

The middle terms in the two squares have opposite signs. They cancel when added.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि (+42ab) और (-42ab) कट जाते हैं / Because (+42ab) and (-42ab) cancel. The middle terms in the two squares have opposite signs. They cancel when added.

Step 3

Exam Tip

दोनों वर्गों में बीच के पद विपरीत चिन्ह के होते हैं। जोड़ने पर वे कट जाते हैं।

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Question 40/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+7)²-\(x^2+49\) ) का सरल रूप क्या है?

What is the simplified form of ( (x+7)²-\(x^2+49\) )?

Explanation opens after your attempt

Correct Answer

B. (14x)

Step 1

Concept

( (x+7)²=x^-2+14x+49 ). Subtracting \(x^2+49\) leaves (14x).

Step 2

Why this answer is correct

The correct answer is B. (14x). ( (x+7)²=x^-2+14x+49 ). Subtracting \(x^2+49\) leaves (14x).

Step 3

Exam Tip

( (x+7)²=x^-2+14x+49 ) है। \(x^2+49\) घटाने पर (14x) बचता है।

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Question 41/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (4x-5)²-\(16x^2+25\) ) का सरल रूप क्या है?

What is the simplified form of ( (4x-5)²-\(16x^2+25\) )?

Explanation opens after your attempt

Correct Answer

B. (-40x)

Step 1

Concept

( (4x-5)²=16x^-2-40x+25 ). Subtracting \(16x^2+25\) leaves (-40x).

Step 2

Why this answer is correct

The correct answer is B. (-40x). ( (4x-5)²=16x^-2-40x+25 ). Subtracting \(16x^2+25\) leaves (-40x).

Step 3

Exam Tip

( (4x-5)²=16x^-2-40x+25 ) है। \(16x^2+25\) घटाने पर (-40x) बचता है।

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Question 42/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b)²+(a-b)²-\(2b^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (a+b)²+(a-b)²-\(2b^2\) )?

Explanation opens after your attempt

Correct Answer

A. \(2a^2\)

Step 1

Concept

The sum is first \(2a^2+2b^2\). Subtracting \(2b^2\) leaves \(2a^2\).

Step 2

Why this answer is correct

The correct answer is A. \(2a^2\). The sum is first \(2a^2+2b^2\). Subtracting \(2b^2\) leaves \(2a^2\).

Step 3

Exam Tip

पहले योग \(2a^2+2b^2\) है। \(2b^2\) घटाने पर \(2a^2\) बचता है।

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Question 43/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+y+z)²-(x+y-z)²=40z ) है। यदि (x+y=5) हो तो यह क्यों सही है?

( (x+y+z)²-(x+y-z)²=40z ). If (x+y=5), why is this correct?

Explanation opens after your attempt

Correct Answer

A. क्योंकि पहचान से (4z(x+y)=20z) आता हैBecause identity gives (4z(x+y)=20z)

Step 1

Concept

Treat it as ( ((x+y)+z)²-((x+y)-z)² ). The result is (4z(x+y)=20z), so (40z) is not correct.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि पहचान से (4z(x+y)=20z) आता है / Because identity gives (4z(x+y)=20z). Treat it as ( ((x+y)+z)²-((x+y)-z)² ). The result is (4z(x+y)=20z), so (40z) is not correct.

Step 3

Exam Tip

इसे ( ((x+y)+z)²-((x+y)-z)² ) मानें। परिणाम (4z(x+y)=20z) है, इसलिए (40z) सही नहीं है।

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Question 44/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+3)²+(2x-3)²=100 ) हो तो \(x^2\) का मान क्या है?

If ( (2x+3)²+(2x-3)²=100 ), what is the value of \(x^2\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{41}{4} \)

Step 1

Concept

By identity the sum is (2(2x)²+2(3)²=8x^-2+18). From \(8x^2+18=100\), \(x^2=\frac{41}{4}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{41}{4} \). By identity the sum is (2(2x)²+2(3)²=8x^-2+18). From \(8x^2+18=100\), \(x^2=\frac{41}{4}\).

Step 3

Exam Tip

पहचान से योग (2(2x)²+2(3)²=8x^-2+18) है। \(8x^2+18=100\), इसलिए \(x^2=\frac{41}{4}\) है।

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Question 45/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+1)²-(x-1)²+(x+2)²-(x-2)² ) का सरल रूप क्या है?

What is the simplified form of ( (x+1)²-(x-1)²+(x+2)²-(x-2)² )?

Explanation opens after your attempt

Correct Answer

B. (12x)

Step 1

Concept

The first difference is (4x) and the second is (8x). Total is (12x).

Step 2

Why this answer is correct

The correct answer is B. (12x). The first difference is (4x) and the second is (8x). Total is (12x).

Step 3

Exam Tip

पहला अंतर (4x) और दूसरा (8x) है। कुल (12x) मिलता है।

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Question 46/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3x+1)²-(3x-2)² ) का सरल रूप क्या है?

What is the simplified form of ( (3x+1)²-(3x-2)² )?

Explanation opens after your attempt

Correct Answer

A. (18x-3)

Step 1

Concept

Apply (A^-2-B^-2=(A+B)(A-B)). Here (A+B=6x-1) and (A-B=3), so it is (18x-3).

Step 2

Why this answer is correct

The correct answer is A. (18x-3). Apply (A^-2-B^-2=(A+B)(A-B)). Here (A+B=6x-1) and (A-B=3), so it is (18x-3).

Step 3

Exam Tip

(A^-2-B^-2=(A+B)(A-B)) लगाएँ। (A+B=6x-1) और (A-B=3), इसलिए (18x-3) है।

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Question 47/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+2)(x+6)-(x+3)(x+5) ) का सरल रूप क्या है?

What is the simplified form of ( (x+2)(x+6)-(x+3)(x+5) )?

Explanation opens after your attempt

Correct Answer

A. ( -3 )

Step 1

Concept

The first product is \(x^2+8x+12\) and the second is \(x^2+8x+15\). Their difference is (-3).

Step 2

Why this answer is correct

The correct answer is A. ( -3 ). The first product is \(x^2+8x+12\) and the second is \(x^2+8x+15\). Their difference is (-3).

Step 3

Exam Tip

पहला गुणनफल \(x^2+8x+12\) और दूसरा \(x^2+8x+15\) है। अंतर (-3) है।

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Question 48/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x-1)(2x+7)-(2x+1)(2x+5) ) का सरल रूप क्या है?

What is the simplified form of ( (2x-1)(2x+7)-(2x+1)(2x+5) )?

Explanation opens after your attempt

Correct Answer

A. ( -12 )

Step 1

Concept

The first product is \(4x^2+12x-7\) and the second is \(4x^2+12x+5\). The difference is (-12).

Step 2

Why this answer is correct

The correct answer is A. ( -12 ). The first product is \(4x^2+12x-7\) and the second is \(4x^2+12x+5\). The difference is (-12).

Step 3

Exam Tip

पहला गुणनफल \(4x^2+12x-7\) और दूसरा \(4x^2+12x+5\) है। अंतर (-12) है।

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Question 49/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( x^4-81 \) का गुणनखंड रूप पहचान के अनुसार कौन सा है?

According to identities, what is the factor form of \( x^4-81 \)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(x^-4-81=\(x^2\)²-9²). First get ( \(x^2+9\)\(x^2-9\) ), then (x^-2-9=(x+3)(x-3)).

Step 2

Why this answer is correct

The correct answer is A. ( \(x^2+9\)(x+3)(x-3) ). (x^-4-81=\(x^2\)²-9²). First get ( \(x^2+9\)\(x^2-9\) ), then (x^-2-9=(x+3)(x-3)).

Step 3

Exam Tip

(x^-4-81=\(x^2\)²-9²) है। पहले ( \(x^2+9\)\(x^2-9\) ), फिर (x^-2-9=(x+3)(x-3)) करें।

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Question 50/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+4)²-(x-6)² ) का सरल रूप क्या है?

What is the simplified form of ( (x+4)²-(x-6)² )?

Explanation opens after your attempt

Correct Answer

A. (20x-20)

Step 1

Concept

Apply (A^-2-B^-2=(A+B)(A-B)). Here (A+B=2x-2) and (A-B=10), so it is (20x-20).

Step 2

Why this answer is correct

The correct answer is A. (20x-20). Apply (A^-2-B^-2=(A+B)(A-B)). Here (A+B=2x-2) and (A-B=10), so it is (20x-20).

Step 3

Exam Tip

(A^-2-B^-2=(A+B)(A-B)) लगाएँ। यहाँ (A+B=2x-2) और (A-B=10), इसलिए (20x-20) है।

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Class 9 Mathematics - Exploring Algebraic Identities - Algebraic identities Expert Quiz

( (2x+3y+4z)2 ) में (xz) वाला पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

( (3a-2b+c)2 ) में (bc) वाला पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

( (x+2)2-(x-3)2 ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (2x-1)2-(2x+5)2 ) का सरल रूप क्या होगा?

Concept

Why this answer is correct

Exam Tip

\( x^2+10x+25-4y^2 \) का गुणनखंड रूप क्या है?

Concept

Why this answer is correct

Exam Tip

\( 9p^2-12pq+4q^2-16 \) का सही गुणनखंड रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

( (a+b+c)2-(a-b-c)2 ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (2x+y)2+(2x-y)2-8x-2 ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (3m+n)2-(3m-n)2=48mn ) हो तो \(n\neq0\) के लिए (m) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (x+4)(x-6)+(x-4)(x+6) ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (x+4)(x-6)-(x-4)(x+6) ) का सरल रूप क्या है?

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( (x-2)(x+5)(x-7) ) में \(x^2\) का गुणांक क्या होगा?

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( (x+1)(x-3)(x+8) ) में स्थिर पद क्या है?

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( (2x+3)(2x-5)(2x+1) ) में \(x^2\) का गुणांक क्या होगा?

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( (2a-b)2-\(4a^2+b^2\) ) का सरल रूप क्या है?

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( (x+y)2+(x-y)2-\(2x^2\) ) का सरल रूप क्या है?

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( (a+b)2+(a-b)2=50 ) और (a=3) हो तो \(b^2\) कितना है?

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( (p+q)2-(p-q)2=36 ) और (p=3) हो तो (q) क्या है?

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\( 1004^2-996^2 \) का मान क्या है?

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\( 503^2+497^2 \) को पहचान से निकालने पर मान क्या होगा?

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( (2x+3y+4z)² ) में (xz) वाला पद क्या होगा?

( (3a-2b+c)² ) में (bc) वाला पद कौन सा है?

( (x+2)²-(x-3)² ) का सरल रूप क्या है?

( (2x-1)²-(2x+5)² ) का सरल रूप क्या होगा?

( (a+b+c)²-(a-b-c)² ) का सरल रूप क्या है?

( (2x+y)²+(2x-y)²-8x^-2 ) का सरल रूप क्या है?

( (3m+n)²-(3m-n)²=48mn ) हो तो \(n\neq0\) के लिए (m) का मान क्या है?

( (2a-b)²-\(4a^2+b^2\) ) का सरल रूप क्या है?

( (x+y)²+(x-y)²-\(2x^2\) ) का सरल रूप क्या है?

( (a+b)²+(a-b)²=50 ) और (a=3) हो तो \(b^2\) कितना है?

( (p+q)²-(p-q)²=36 ) और (p=3) हो तो (q) क्या है?

( \(x^2+1\)²-x^-4 ) का सरल गुणनखंड रूप क्या है?

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

( (a+2b)²+(a-2b)²-\(2a^2\) ) का सरल रूप क्या है?

( (4x+y)²-(4x-y)² ) को (32xy) के बराबर क्यों लिखा जा सकता है?

( (x+2)²+(x+5)²-2(x+2)(x+5) ) का मान क्या है?

( (2x+7)²+(2x-1)²-2(2x+7)(2x-1) ) का मान क्या है?

( (a+b+c)²-\(a^2+b^2+c^2+2ab\) ) का सरल रूप क्या है?

( (x+2y+z)²-\(x^2+4y^2+z^2\) ) का सरल रूप क्या है?

( (3x-2y+z)² ) में (xy) और (yz) पदों का योग क्या है?

( (2x+3)²-(2x-3)² ) को (24x) के बराबर क्यों माना जाता है?

( (5x-2)²+(5x+2)² ) का सरल रूप क्या है?