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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (4x+3y)²-(4x-3y)² ) का सरल रूप क्या है?

What is the simplified form of ( (4x+3y)²-(4x-3y)² )?

Explanation opens after your attempt

Correct Answer

B. (48xy)सही मान

Step 1

Concept

This uses ( (a+b)²-(a-b)²=4ab ) where (a=4x) and (b=3y). Exam tip: take full terms as (a) and (b).

Step 2

Why this answer is correct

The correct answer is B. (48xy) / सही मान. This uses ( (a+b)²-(a-b)²=4ab ) where (a=4x) and (b=3y). Exam tip: take full terms as (a) and (b).

Step 3

Exam Tip

यह ( (a+b)²-(a-b)²=4ab ) है जहाँ (a=4x) और (b=3y) हैं। परीक्षा में पूरे पदों को (a) और (b) मानें।

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Question 2/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (5a+2b)²+(5a-2b)² ) को सरल करने पर क्या मिलेगा?

What is obtained by simplifying ( (5a+2b)²+(5a-2b)² )?

Explanation opens after your attempt

Correct Answer

A. \(50a^2+8b^2\)सही परिणाम

Step 1

Concept

Using the sum identity gives (2(5a)²+2(2b)²=50a^-2+8b^-2). Exam tip: notice cancellation of middle terms.

Step 2

Why this answer is correct

The correct answer is A. \(50a^2+8b^2\) / सही परिणाम. Using the sum identity gives (2(5a)²+2(2b)²=50a^-2+8b^-2). Exam tip: notice cancellation of middle terms.

Step 3

Exam Tip

योग पहचान से (2(5a)²+2(2b)²=50a^-2+8b^-2) मिलता है। परीक्षा में मध्य पदों के कटने को पहचानें।

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Question 3/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2p+q+r)² ) में (pq) और (pr) वाले पदों का योग क्या होगा?

In ( (2p+q+r)² ), what is the sum of the terms containing (pq) and (pr)?

Explanation opens after your attempt

Correct Answer

B. (4pq+4pr)सही योग

Step 1

Concept

The (pq) term is \(2\cdot2p\cdot q=4pq\) and the (pr) term is (4pr). Exam tip: use double product for every pair.

Step 2

Why this answer is correct

The correct answer is B. (4pq+4pr) / सही योग. The (pq) term is \(2\cdot2p\cdot q=4pq\) and the (pr) term is (4pr). Exam tip: use double product for every pair.

Step 3

Exam Tip

(pq) पद \(2\cdot2p\cdot q=4pq\) और (pr) पद (4pr) है। परीक्षा में हर जोड़ी का दोहरा गुणन करें।

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Question 4/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\(9x^2+30xy+25y^2\) किसका पूर्ण वर्ग है?

\(9x^2+30xy+25y^2\) is the perfect square of what?

Explanation opens after your attempt

Correct Answer

C. ( (3x+5y)² )सही रूप

Step 1

Concept

(9x^-2=(3x)²), (25y^-2=(5y)²), and the middle term is (30xy). Exam tip: check both square roots and the middle term.

Step 2

Why this answer is correct

The correct answer is C. ( (3x+5y)² ) / सही रूप. (9x^-2=(3x)²), (25y^-2=(5y)²), and the middle term is (30xy). Exam tip: check both square roots and the middle term.

Step 3

Exam Tip

(9x^-2=(3x)²), (25y^-2=(5y)²) और मध्य पद (30xy) है। परीक्षा में वर्गमूल और मध्य पद दोनों जाँचें।

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Question 5/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\(36m^2-49n^2\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(36m^2-49n^2\)?

Explanation opens after your attempt

Correct Answer

D. ( (6m+7n)(6m-7n) )सही गुणनखंड

Step 1

Concept

This is the form ( (6m)²-(7n)² ). Exam tip: apply the difference of squares identity.

Step 2

Why this answer is correct

The correct answer is D. ( (6m+7n)(6m-7n) ) / सही गुणनखंड. This is the form ( (6m)²-(7n)² ). Exam tip: apply the difference of squares identity.

Step 3

Exam Tip

यह ( (6m)²-(7n)² ) का रूप है। परीक्षा में वर्गों के अंतर की पहचान लगाएँ।

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Question 6/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+9)(x-4) ) में (x) का गुणांक और स्थिर पद कौन-से हैं?

What are the coefficient of (x) and the constant term in ( (x+9)(x-4) )?

Explanation opens after your attempt

Correct Answer

A. (5) और (-36)सही जोड़ा

Step 1

Concept

The sum of constants is (9+(-4)=5) and the product is (-36). Exam tip: check sum and product separately in mixed signs.

Step 2

Why this answer is correct

The correct answer is A. (5) और (-36) / सही जोड़ा. The sum of constants is (9+(-4)=5) and the product is (-36). Exam tip: check sum and product separately in mixed signs.

Step 3

Exam Tip

स्थिर पदों का योग (9+(-4)=5) और गुणन (-36) है। परीक्षा में मिश्रित चिह्नों में योग और गुणन अलग देखें।

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Question 7/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2x+3)²-\(4x^2+9\) ) को सरल कीजिए।

Simplify ( (2x+3)²-\(4x^2+9\) ).

Explanation opens after your attempt

Correct Answer

B. (12x)सही उत्तर

Step 1

Concept

( (2x+3)²=4x^-2+12x+9 ). After subtraction, only (12x) remains.

Step 2

Why this answer is correct

The correct answer is B. (12x) / सही उत्तर. ( (2x+3)²=4x^-2+12x+9 ). After subtraction, only (12x) remains.

Step 3

Exam Tip

( (2x+3)²=4x^-2+12x+9 ) है। घटाने पर केवल (12x) बचता है।

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Question 8/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (3u-2v)²-\(9u^2+4v^2\) ) का मान क्या होगा?

What is the value of ( (3u-2v)²-\(9u^2+4v^2\) )?

Explanation opens after your attempt

Correct Answer

C. (-12uv)सही मान

Step 1

Concept

( (3u-2v)²=9u^-2-12uv+4v^-2 ). Exam tip: pay attention to the negative middle term.

Step 2

Why this answer is correct

The correct answer is C. (-12uv) / सही मान. ( (3u-2v)²=9u^-2-12uv+4v^-2 ). Exam tip: pay attention to the negative middle term.

Step 3

Exam Tip

( (3u-2v)²=9u^-2-12uv+4v^-2 ) है। परीक्षा में ऋण मध्य पद पर ध्यान दें।

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Question 9/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (p+q)²-(p-q)²-4pq ) का मान क्या है?

What is the value of ( (p+q)²-(p-q)²-4pq )?

Explanation opens after your attempt

Correct Answer

A. (0)सही मान

Step 1

Concept

The difference of the first two squares is (4pq), and then (4pq) is subtracted. Exam tip: check remaining terms after applying identity.

Step 2

Why this answer is correct

The correct answer is A. (0) / सही मान. The difference of the first two squares is (4pq), and then (4pq) is subtracted. Exam tip: check remaining terms after applying identity.

Step 3

Exam Tip

पहले दो वर्गों का अंतर (4pq) है और फिर (4pq) घटता है। परीक्षा में पहचान के बाद शेष पद जाँचें।

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Question 10/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

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

Explanation opens after your attempt

Correct Answer

B. \(2x^2\)सही मान

Step 1

Concept

The sum identity gives \(2x^2+2y^2\). Subtracting \(2y^2\) leaves \(2x^2\).

Step 2

Why this answer is correct

The correct answer is B. \(2x^2\) / सही मान. The sum identity gives \(2x^2+2y^2\). Subtracting \(2y^2\) leaves \(2x^2\).

Step 3

Exam Tip

योग पहचान से \(2x^2+2y^2\) मिलता है। \(2y^2\) घटाने पर \(2x^2\) बचता है।

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Question 11/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+3)(x+7)-(x+4)(x+6) ) का मान क्या है?

What is the value of ( (x+3)(x+7)-(x+4)(x+6) )?

Explanation opens after your attempt

Correct Answer

C. (-3)सही मान

Step 1

Concept

The first expansion is \(x^2+10x+21\) and the second is \(x^2+10x+24\). Exam tip: cancel like terms and subtract constants.

Step 2

Why this answer is correct

The correct answer is C. (-3) / सही मान. The first expansion is \(x^2+10x+21\) and the second is \(x^2+10x+24\). Exam tip: cancel like terms and subtract constants.

Step 3

Exam Tip

पहला विस्तार \(x^2+10x+21\) और दूसरा \(x^2+10x+24\) है। परीक्षा में समान पद काटकर स्थिर पद घटाएँ।

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Question 12/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2a+b+c)²-\(4a^2+b^2+c^2\) ) का सरल रूप कौन-सा है?

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

Explanation opens after your attempt

Correct Answer

B. (4ab+2bc+4ac)सही रूप

Step 1

Concept

The pair terms in the square are (4ab), (2bc), and (4ac). Exam tip: take the double product of each pair.

Step 2

Why this answer is correct

The correct answer is B. (4ab+2bc+4ac) / सही रूप. The pair terms in the square are (4ab), (2bc), and (4ac). Exam tip: take the double product of each pair.

Step 3

Exam Tip

तीन पदों के वर्ग में जोड़ी पद (4ab), (2bc), और (4ac) आते हैं। परीक्षा में हर जोड़ी का दोहरा गुणन करें।

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Question 13/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+2y+5z)² ) में (yz) वाला पद कौन-सा होगा?

Which term contains (yz) in ( (x+2y+5z)² )?

Explanation opens after your attempt

Correct Answer

C. (20yz)सही दोहरा गुणन

Step 1

Concept

The (yz) term is \(2\cdot2y\cdot5z=20yz\). Exam tip: do not forget the factor (2) in double products.

Step 2

Why this answer is correct

The correct answer is C. (20yz) / सही दोहरा गुणन. The (yz) term is \(2\cdot2y\cdot5z=20yz\). Exam tip: do not forget the factor (2) in double products.

Step 3

Exam Tip

(yz) पद \(2\cdot2y\cdot5z=20yz\) है। परीक्षा में दोहरे गुणन में (2) लगाना न भूलें।

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Question 14/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 997^2 \) को पहचान से निकालने के लिए सबसे उपयुक्त रूप कौन-सा है?

Which form is most suitable for finding \( 997^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. ( (1000-3)² )सही रूप

Step 1

Concept

Since (997=1000-3), the square of difference identity is useful. Exam tip: choose a nearby base.

Step 2

Why this answer is correct

The correct answer is A. ( (1000-3)² ) / सही रूप. Since (997=1000-3), the square of difference identity is useful. Exam tip: choose a nearby base.

Step 3

Exam Tip

(997=1000-3) इसलिए घटाव के वर्ग की पहचान उपयोगी है। परीक्षा में निकट आधार चुनें।

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Question 15/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 997^2 \) का मान क्या है?

What is the value of \( 997^2 \)?

Explanation opens after your attempt

Correct Answer

A. (994009)सही मान

Step 1

Concept

\(997^2=1000000-6000+9=994009\). Exam tip: subtract \(2\cdot1000\cdot3\).

Step 2

Why this answer is correct

The correct answer is A. (994009) / सही मान. \(997^2=1000000-6000+9=994009\). Exam tip: subtract \(2\cdot1000\cdot3\).

Step 3

Exam Tip

\(997^2=1000000-6000+9=994009\) है। परीक्षा में \(2\cdot1000\cdot3\) घटाएँ।

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Question 16/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 1004^2-996^2 \) का सही मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (16000)सही मान

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), we get \(2000\cdot8=16000\). Exam tip: multiply the sum and difference.

Step 2

Why this answer is correct

The correct answer is B. (16000) / सही मान. Using (a^-2-b^-2=(a+b)(a-b)), we get \(2000\cdot8=16000\). Exam tip: multiply the sum and difference.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(2000\cdot8=16000\) मिलता है। परीक्षा में योग और अंतर का गुणन करें।

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Question 17/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 205^2 \) को पहचान से निकालने पर सही मान क्या है?

What is the correct value of \( 205^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. (42025)सही मान

Step 1

Concept

(205²=(200+5)²=40000+2000+25=42025). Exam tip: add both (2ab) and \(b^2\).

Step 2

Why this answer is correct

The correct answer is A. (42025) / सही मान. (205²=(200+5)²=40000+2000+25=42025). Exam tip: add both (2ab) and \(b^2\).

Step 3

Exam Tip

(205²=(200+5)²=40000+2000+25=42025) होता है। परीक्षा में (2ab) और \(b^2\) दोनों जोड़ें।

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Question 18/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (6x+1)²-(6x-1)² ) का सरल रूप क्या है?

What is the simplified form of ( (6x+1)²-(6x-1)² )?

Explanation opens after your attempt

Correct Answer

B. (24x)सही मान

Step 1

Concept

This is (4ab) where (a=6x) and (b=1), so (24x) is obtained. Exam tip: take the full term for (a).

Step 2

Why this answer is correct

The correct answer is B. (24x) / सही मान. This is (4ab) where (a=6x) and (b=1), so (24x) is obtained. Exam tip: take the full term for (a).

Step 3

Exam Tip

यह (4ab) है जहाँ (a=6x) और (b=1), इसलिए (24x) मिलता है। परीक्षा में (a) का पूरा पद लें।

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Question 19/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (4x+3)²+(4x-3)²-32x^-2 ) का मान क्या है?

What is the value of ( (4x+3)²+(4x-3)²-32x^-2 )?

Explanation opens after your attempt

Correct Answer

B. (18)सही मान

Step 1

Concept

The sum of the first two squares is \(32x^2+18\). After subtracting \(32x^2\), (18) remains.

Step 2

Why this answer is correct

The correct answer is B. (18) / सही मान. The sum of the first two squares is \(32x^2+18\). After subtracting \(32x^2\), (18) remains.

Step 3

Exam Tip

पहले दो वर्गों का योग \(32x^2+18\) है। \(32x^2\) घटाने पर (18) बचता है।

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Question 20/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2x+y)³ ) में \(x^2y\) का गुणांक क्या होगा?

What is the coefficient of \(x^2y\) in ( (2x+y)³ )?

Explanation opens after your attempt

Correct Answer

B. (12)सही गुणांक

Step 1

Concept

(3(2x)²y=12x^-2y). Exam tip: square the whole term (2x).

Step 2

Why this answer is correct

The correct answer is B. (12) / सही गुणांक. (3(2x)²y=12x^-2y). Exam tip: square the whole term (2x).

Step 3

Exam Tip

(3(2x)²y=12x^-2y) है। परीक्षा में (2x) का पूरा वर्ग करें।

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Question 21/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (3a-b)³ ) में \(a^2b\) वाले पद का गुणांक क्या है?

What is the coefficient of the term containing \(a^2b\) in ( (3a-b)³ )?

Explanation opens after your attempt

Correct Answer

B. (-27)सही गुणांक

Step 1

Concept

In the cube of a difference, ( -3(3a)²b=-27a^-2b ) appears. Exam tip: check sign and coefficient together.

Step 2

Why this answer is correct

The correct answer is B. (-27) / सही गुणांक. In the cube of a difference, ( -3(3a)²b=-27a^-2b ) appears. Exam tip: check sign and coefficient together.

Step 3

Exam Tip

घटाव के घन में ( -3(3a)²b=-27a^-2b ) आता है। परीक्षा में चिह्न और गुणांक साथ देखें।

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Question 22/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+4)³-(x-4)³ ) का पूरा सरल रूप क्या है?

What is the complete simplified form of ( (x+4)³-(x-4)³ )?

Explanation opens after your attempt

Correct Answer

A. \(24x^2+128\)सही रूप

Step 1

Concept

In cube expansion, the \(x^3\) and (x) terms cancel. Exam tip: change signs and combine like terms.

Step 2

Why this answer is correct

The correct answer is A. \(24x^2+128\) / सही रूप. In cube expansion, the \(x^3\) and (x) terms cancel. Exam tip: change signs and combine like terms.

Step 3

Exam Tip

घन विस्तार में \(x^3\) और (x) वाले पद कट जाते हैं। परीक्षा में चिह्न बदलकर समान पद जोड़ें।

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Question 23/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( a^3+125b^3 \) का गुणनखंडन क्या है?

What is the factorisation of \( a^3+125b^3 \)?

Explanation opens after your attempt

Correct Answer

A. ( (a+5b)\(a^2-5ab+25b^2\) )सही रूप

Step 1

Concept

This is (a^-3+(5b)³). In sum of cubes, the second factor is \(a^2-5ab+25b^2\).

Step 2

Why this answer is correct

The correct answer is A. ( (a+5b)\(a^2-5ab+25b^2\) ) / सही रूप. This is (a^-3+(5b)³). In sum of cubes, the second factor is \(a^2-5ab+25b^2\).

Step 3

Exam Tip

यह (a^-3+(5b)³) है। घनों के योग में दूसरा गुणनखंड \(a^2-5ab+25b^2\) होता है।

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Question 24/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 64x^3-27y^3 \) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \( 64x^3-27y^3 \).

Explanation opens after your attempt

Correct Answer

B. ( (4x-3y)\(16x^2+12xy+9y^2\) )सही रूप

Step 1

Concept

This is ( (4x)³-(3y)³ ). Exam tip: in difference of cubes, all terms of the second factor are positive.

Step 2

Why this answer is correct

The correct answer is B. ( (4x-3y)\(16x^2+12xy+9y^2\) ) / सही रूप. This is ( (4x)³-(3y)³ ). Exam tip: in difference of cubes, all terms of the second factor are positive.

Step 3

Exam Tip

यह ( (4x)³-(3y)³ ) है। परीक्षा में घनों के अंतर में दूसरे गुणनखंड के सभी पद धन होते हैं।

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Question 25/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (a+b)³-\(a^3+b^3\) ) को गुणनखंड रूप में कैसे लिखा जाएगा?

How will ( (a+b)³-\(a^3+b^3\) ) be written in factor form?

Explanation opens after your attempt

Correct Answer

A. (3ab(a+b))सही रूप

Step 1

Concept

The middle terms \(3a^2b+3ab^2\) form (3ab(a+b)). Exam tip: take the common factor.

Step 2

Why this answer is correct

The correct answer is A. (3ab(a+b)) / सही रूप. The middle terms \(3a^2b+3ab^2\) form (3ab(a+b)). Exam tip: take the common factor.

Step 3

Exam Tip

घन विस्तार के मध्य पद \(3a^2b+3ab^2\) मिलकर (3ab(a+b)) बनाते हैं। परीक्षा में सामान्य गुणनखंड निकालें।

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Question 26/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (a-b)³-\(a^3-b^3\) ) का सरल रूप क्या है?

What is the simplified form of ( (a-b)³-\(a^3-b^3\) )?

Explanation opens after your attempt

Correct Answer

B. (-3ab(a-b))सही रूप

Step 1

Concept

( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ). Subtracting gives (-3ab(a-b)).

Step 2

Why this answer is correct

The correct answer is B. (-3ab(a-b)) / सही रूप. ( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ). Subtracting gives (-3ab(a-b)).

Step 3

Exam Tip

( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ) है। घटाने पर (-3ab(a-b)) मिलता है।

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Question 27/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (x+y=13) और (xy=40) हो तो \(x^2+y^2\) का मान क्या है?

If (x+y=13) and (xy=40), what is the value of \(x^2+y^2\)?

Explanation opens after your attempt

Correct Answer

A. (89)सही मान

Step 1

Concept

(x^-2+y^-2=(x+y)²-2xy=169-80=89). Exam tip: subtract (2xy) from the square of the sum.

Step 2

Why this answer is correct

The correct answer is A. (89) / सही मान. (x^-2+y^-2=(x+y)²-2xy=169-80=89). Exam tip: subtract (2xy) from the square of the sum.

Step 3

Exam Tip

(x^-2+y^-2=(x+y)²-2xy=169-80=89)। परीक्षा में योग के वर्ग से (2xy) घटाएँ।

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Question 28/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (p-q=7) और (pq=18) हो तो \(p^2+q^2\) कितना होगा?

If (p-q=7) and (pq=18), what is \(p^2+q^2\)?

Explanation opens after your attempt

Correct Answer

B. (67)सही मान

Step 1

Concept

From ( (p-q)²=p^-2-2pq+q^-2 ), \(p^2+q^2=49+36=85\). Exam tip: add (2pq) carefully.

Step 2

Why this answer is correct

The correct answer is B. (67) / सही मान. From ( (p-q)²=p^-2-2pq+q^-2 ), \(p^2+q^2=49+36=85\). Exam tip: add (2pq) carefully.

Step 3

Exam Tip

( (p-q)²=p^-2-2pq+q^-2 ) से \(p^2+q^2=49+36=85\) नहीं, सही गणना (49+36=85) है।

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Question 29/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (p-q=7) और (pq=18) हो तो \(p^2+q^2\) का सही मान चुनिए।

If (p-q=7) and (pq=18), choose the correct value of \(p^2+q^2\).

Explanation opens after your attempt

Correct Answer

B. (85)सही मान

Step 1

Concept

(p^-2+q^-2=(p-q)²+2pq=49+36=85). Exam tip: add (2pq).

Step 2

Why this answer is correct

The correct answer is B. (85) / सही मान. (p^-2+q^-2=(p-q)²+2pq=49+36=85). Exam tip: add (2pq).

Step 3

Exam Tip

(p^-2+q^-2=(p-q)²+2pq=49+36=85) है। परीक्षा में (2pq) जोड़ें।

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Question 30/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (m+n=11) और \(m^2+n^2=65\) हो तो (mn) क्या होगा?

If (m+n=11) and \(m^2+n^2=65\), what is (mn)?

Explanation opens after your attempt

Correct Answer

A. (28)सही मान

Step 1

Concept

Using ( (m+n)²=m^-2+2mn+n^-2 ), (121=65+2mn), so (mn=28). Exam tip: find (2mn) first.

Step 2

Why this answer is correct

The correct answer is A. (28) / सही मान. Using ( (m+n)²=m^-2+2mn+n^-2 ), (121=65+2mn), so (mn=28). Exam tip: find (2mn) first.

Step 3

Exam Tip

( (m+n)²=m^-2+2mn+n^-2 ) से (121=65+2mn), इसलिए (mn=28)। परीक्षा में पहले (2mn) निकालें।

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Question 31/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (a+b=15) और (a-b=5) हो तो (ab) का मान क्या है?

If (a+b=15) and (a-b=5), what is the value of (ab)?

Explanation opens after your attempt

Correct Answer

A. (50)सही मान

Step 1

Concept

From ( (a+b)²-(a-b)²=4ab ), (225-25=200=4ab). Therefore (ab=50).

Step 2

Why this answer is correct

The correct answer is A. (50) / सही मान. From ( (a+b)²-(a-b)²=4ab ), (225-25=200=4ab). Therefore (ab=50).

Step 3

Exam Tip

( (a+b)²-(a-b)²=4ab ) से (225-25=200=4ab)। इसलिए (ab=50) है।

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Question 32/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (x+y+z=8) और (xy+yz+zx=19) हो तो \(x^2+y^2+z^2\) क्या है?

If (x+y+z=8) and (xy+yz+zx=19), what is \(x^2+y^2+z^2\)?

Explanation opens after your attempt

Correct Answer

A. (26)सही मान

Step 1

Concept

Using ( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ), (64=S+38), so (S=26).

Step 2

Why this answer is correct

The correct answer is A. (26) / सही मान. Using ( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ), (64=S+38), so (S=26).

Step 3

Exam Tip

( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ) से (64= S+38), इसलिए (S=26)।

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Question 33/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2x+1)(2x+3)(2x+5) ) में पहले ( (2x+1)(2x+5) ) लगाने पर क्या मिलेगा?

When first applying ( (2x+1)(2x+5) ) in ( (2x+1)(2x+3)(2x+5) ), what is obtained?

Explanation opens after your attempt

Correct Answer

A. \(4x^2+12x+5\)सही आंशिक विस्तार

Step 1

Concept

( (2x+1)(2x+5)=4x^-2+12x+5 ). Exam tip: do long multiplication in small steps.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+12x+5\) / सही आंशिक विस्तार. ( (2x+1)(2x+5)=4x^-2+12x+5 ). Exam tip: do long multiplication in small steps.

Step 3

Exam Tip

( (2x+1)(2x+5)=4x^-2+12x+5 ) है। परीक्षा में लंबा गुणन छोटे चरणों में करें।

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Question 34/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+2)(x+4)(x+6) ) का पूरा विस्तार क्या है?

What is the full expansion of ( (x+2)(x+4)(x+6) )?

Explanation opens after your attempt

Correct Answer

A. \(x^3+12x^2+44x+48\)सही विस्तार

Step 1

Concept

Expand two factors first and then multiply by the third. Exam tip: add like terms systematically.

Step 2

Why this answer is correct

The correct answer is A. \(x^3+12x^2+44x+48\) / सही विस्तार. Expand two factors first and then multiply by the third. Exam tip: add like terms systematically.

Step 3

Exam Tip

पहले दो गुणनखंड फैलाएँ और फिर तीसरे से गुणा करें। परीक्षा में समान पदों को व्यवस्थित जोड़ें।

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Question 35/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+2y)²-x^-2-4y^-2-4xy ) का मान क्या है?

What is the value of ( (x+2y)²-x^-2-4y^-2-4xy )?

Explanation opens after your attempt

Correct Answer

A. (0)सही मान

Step 1

Concept

( (x+2y)²=x^-2+4xy+4y^-2 ). Subtracting all terms gives (0).

Step 2

Why this answer is correct

The correct answer is A. (0) / सही मान. ( (x+2y)²=x^-2+4xy+4y^-2 ). Subtracting all terms gives (0).

Step 3

Exam Tip

( (x+2y)²=x^-2+4xy+4y^-2 ) है। सभी पद घटाने पर (0) मिलता है।

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Question 36/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (3x-2y)²-9x^-2-4y^-2 ) का सरल रूप क्या है?

What is the simplified form of ( (3x-2y)²-9x^-2-4y^-2 )?

Explanation opens after your attempt

Correct Answer

B. (-12xy)सही रूप

Step 1

Concept

( (3x-2y)²=9x^-2-12xy+4y^-2 ). After removing square terms, (-12xy) remains.

Step 2

Why this answer is correct

The correct answer is B. (-12xy) / सही रूप. ( (3x-2y)²=9x^-2-12xy+4y^-2 ). After removing square terms, (-12xy) remains.

Step 3

Exam Tip

( (3x-2y)²=9x^-2-12xy+4y^-2 ) है। वर्ग पद हटाने पर (-12xy) बचता है।

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Question 37/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+y+z)²-(x-y+z)² ) में कौन-सा पद नहीं बचेगा?

Which term will not remain in ( (x+y+z)²-(x-y+z)² )?

Explanation opens after your attempt

Correct Answer

C. \(x^2\)नहीं बचेगा

Step 1

Concept

In both squares, \(x^2\), \(y^2\), and \(z^2\) cancel. Exam tip: cancel common square terms.

Step 2

Why this answer is correct

The correct answer is C. \(x^2\) / नहीं बचेगा. In both squares, \(x^2\), \(y^2\), and \(z^2\) cancel. Exam tip: cancel common square terms.

Step 3

Exam Tip

दोनों वर्गों में \(x^2\), \(y^2\), और \(z^2\) कट जाते हैं। परीक्षा में समान वर्ग पद हटाएँ।

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Question 38/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

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

Explanation opens after your attempt

Correct Answer

A. (8a(b+c))सही रूप

Step 1

Concept

Take (A=2a) and (B=b+c), then apply ( (A+B)²-(A-B)²=4AB ). Exam tip: group terms.

Step 2

Why this answer is correct

The correct answer is A. (8a(b+c)) / सही रूप. Take (A=2a) and (B=b+c), then apply ( (A+B)²-(A-B)²=4AB ). Exam tip: group terms.

Step 3

Exam Tip

इसे (A=2a) और (B=b+c) मानकर ( (A+B)²-(A-B)²=4AB ) लगाएँ। परीक्षा में समूह बनाएं।

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Question 39/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

What is the coefficient of \(xy^2\) in ( (5x+2y)³ )?

Explanation opens after your attempt

Correct Answer

B. (60)सही गुणांक

Step 1

Concept

(3(5x)(2y)²=60xy^-2). Exam tip: square the second term completely.

Step 2

Why this answer is correct

The correct answer is B. (60) / सही गुणांक. (3(5x)(2y)²=60xy^-2). Exam tip: square the second term completely.

Step 3

Exam Tip

(3(5x)(2y)²=60xy^-2) है। परीक्षा में दूसरे पद का वर्ग पूरा करें।

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Question 40/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x-3)³ ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (x-3)³ )?

Explanation opens after your attempt

Correct Answer

A. \(x^3-9x^2+27x-27\)सही विस्तार

Step 1

Concept

In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: check both \(3^2\) and \(3^3\).

Step 2

Why this answer is correct

The correct answer is A. \(x^3-9x^2+27x-27\) / सही विस्तार. In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: check both \(3^2\) and \(3^3\).

Step 3

Exam Tip

घटाव के घन में चिह्न (+), (-), (+), (-) क्रम में आते हैं। परीक्षा में \(3^2\) और \(3^3\) दोनों देखें।

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Question 41/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2x+3)³ ) का सही विस्तार क्या है?

What is the correct expansion of ( (2x+3)³ )?

Explanation opens after your attempt

Correct Answer

A. \(8x^3+36x^2+54x+27\)सही विस्तार

Step 1

Concept

( (2x)³=8x^-3 ), (3(2x)²\cdot3=36x^-2), and (3(2x)\cdot9=54x). Exam tip: check the power of every term.

Step 2

Why this answer is correct

The correct answer is A. \(8x^3+36x^2+54x+27\) / सही विस्तार. ( (2x)³=8x^-3 ), (3(2x)²\cdot3=36x^-2), and (3(2x)\cdot9=54x). Exam tip: check the power of every term.

Step 3

Exam Tip

( (2x)³=8x^-3 ), (3(2x)²\cdot3=36x^-2), और (3(2x)\cdot9=54x) है। परीक्षा में हर पद की घात जाँचें।

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Question 42/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 8a^3+27b^3 \) का गुणनखंडन कौन-सा है?

Which is the factorisation of \( 8a^3+27b^3 \)?

Explanation opens after your attempt

Correct Answer

A. ( (2a+3b)\(4a^2-6ab+9b^2\) )सही रूप

Step 1

Concept

This is ( (2a)³+(3b)³ ). Exam tip: identify cube roots and apply the sum of cubes identity.

Step 2

Why this answer is correct

The correct answer is A. ( (2a+3b)\(4a^2-6ab+9b^2\) ) / सही रूप. This is ( (2a)³+(3b)³ ). Exam tip: identify cube roots and apply the sum of cubes identity.

Step 3

Exam Tip

यह ( (2a)³+(3b)³ ) है। परीक्षा में घनमूल पहचानकर घनों के योग की पहचान लगाएँ।

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Question 43/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\(125p^3-8q^3\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(125p^3-8q^3\)?

Explanation opens after your attempt

Correct Answer

A. ( (5p-2q)\(25p^2+10pq+4q^2\) )सही रूप

Step 1

Concept

This is ( (5p)³-(2q)³ ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. ( (5p-2q)\(25p^2+10pq+4q^2\) ) / सही रूप. This is ( (5p)³-(2q)³ ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 3

Exam Tip

यह ( (5p)³-(2q)³ ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।

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Question 44/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

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

Explanation opens after your attempt

Correct Answer

A. (3x(x+1))सही रूप

Step 1

Concept

( (x+1)³=x^-3+3x^-2+3x+1 ). The middle terms form (3x(x+1)).

Step 2

Why this answer is correct

The correct answer is A. (3x(x+1)) / सही रूप. ( (x+1)³=x^-3+3x^-2+3x+1 ). The middle terms form (3x(x+1)).

Step 3

Exam Tip

( (x+1)³=x^-3+3x^-2+3x+1 ) है। बीच के पद (3x(x+1)) बनाते हैं।

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Question 45/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x-2)³-\(x^3-8\) ) का सरल रूप कौन-सा है?

Which is the simplified form of ( (x-2)³-\(x^3-8\) )?

Explanation opens after your attempt

Correct Answer

A. (-6x(x-2))सही रूप

Step 1

Concept

( (x-2)³=x^-3-6x^-2+12x-8 ). Subtracting gives (-6x^-2+12x=-6x(x-2)).

Step 2

Why this answer is correct

The correct answer is A. (-6x(x-2)) / सही रूप. ( (x-2)³=x^-3-6x^-2+12x-8 ). Subtracting gives (-6x^-2+12x=-6x(x-2)).

Step 3

Exam Tip

( (x-2)³=x^-3-6x^-2+12x-8 ) है। घटाने पर (-6x^-2+12x=-6x(x-2)) मिलता है।

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Question 46/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

किस स्थिति में ( (a-b)²=a^-2+b^-2 ) सही हो सकता है?

In which situation can ( (a-b)²=a^-2+b^-2 ) be true?

Explanation opens after your attempt

Correct Answer

A. जब (2ab=0) होwhen (2ab=0)

Step 1

Concept

( (a-b)²=a^-2-2ab+b^-2 ). For equality, the middle term (-2ab) must be zero.

Step 2

Why this answer is correct

The correct answer is A. जब (2ab=0) हो / when (2ab=0). ( (a-b)²=a^-2-2ab+b^-2 ). For equality, the middle term (-2ab) must be zero.

Step 3

Exam Tip

( (a-b)²=a^-2-2ab+b^-2 ) है। समानता के लिए मध्य पद (-2ab) शून्य होना चाहिए।

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Question 47/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

यदि (a+b+c=9) और \(a^2+b^2+c^2=35\) हो तो (ab+bc+ca) क्या होगा?

If (a+b+c=9) and \(a^2+b^2+c^2=35\), what is (ab+bc+ca)?

Explanation opens after your attempt

Correct Answer

A. (23)सही मान

Step 1

Concept

(81=35+2(ab+bc+ca)), so (2(ab+bc+ca)=46) and the value is (23). Exam tip: find the double product sum first.

Step 2

Why this answer is correct

The correct answer is A. (23) / सही मान. (81=35+2(ab+bc+ca)), so (2(ab+bc+ca)=46) and the value is (23). Exam tip: find the double product sum first.

Step 3

Exam Tip

(81=35+2(ab+bc+ca)) इसलिए (2(ab+bc+ca)=46) और मान (23) है। परीक्षा में पहले दोहरा गुणन योग निकालें।

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Question 48/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

What is the sum of the terms containing (xy), (yz), and (xz) in ( (2x+3y+z)² )?

Explanation opens after your attempt

Correct Answer

C. (12xy+6yz+4xz)सही रूप

Step 1

Concept

The (xy) term is (12xy), the (yz) term is (6yz), and the (xz) term is (4xz). Exam tip: find each double product separately.

Step 2

Why this answer is correct

The correct answer is C. (12xy+6yz+4xz) / सही रूप. The (xy) term is (12xy), the (yz) term is (6yz), and the (xz) term is (4xz). Exam tip: find each double product separately.

Step 3

Exam Tip

(xy) पद (12xy), (yz) पद (6yz), और (xz) पद (4xz) है। परीक्षा में हर जोड़ी का दोहरा गुणन अलग निकालें।

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Question 49/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

बीजीय पहचान का उपयोग करते समय सबसे सुरक्षित रणनीति कौन-सी है?

What is the safest strategy while using an algebraic identity?

Explanation opens after your attempt

Correct Answer

A. पहले पदों को पूरे रूप में (a), (b), (c) मानकर चिह्न और घात जाँचनाfirst treat complete terms as (a), (b), (c) and check signs and powers

Step 1

Concept

Most errors occur due to incomplete terms, wrong signs, or wrong powers. Exam tip: identify the whole term before applying the formula.

Step 2

Why this answer is correct

The correct answer is A. पहले पदों को पूरे रूप में (a), (b), (c) मानकर चिह्न और घात जाँचना / first treat complete terms as (a), (b), (c) and check signs and powers. Most errors occur due to incomplete terms, wrong signs, or wrong powers. Exam tip: identify the whole term before applying the formula.

Step 3

Exam Tip

अधिकतर गलती अधूरे पद, गलत चिह्न या गलत घात से होती है। परीक्षा में पूरा पद पहचानकर ही सूत्र लगाएँ।

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Question 50/50 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

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

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

Explanation opens after your attempt

Correct Answer

C. (4y(x+2))सही रूप

Step 1

Concept

Take (A=x+2) and use ( (A+y)²-(A-y)²=4Ay ). Exam tip: group terms and take the complete term.

Step 2

Why this answer is correct

The correct answer is C. (4y(x+2)) / सही रूप. Take (A=x+2) and use ( (A+y)²-(A-y)²=4Ay ). Exam tip: group terms and take the complete term.

Step 3

Exam Tip

इसे (A=x+2) मानकर ( (A+y)²-(A-y)²=4Ay ) लगाएँ। परीक्षा में समूह बनाकर पूरा पद लें।

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Class 9 Mathematics - Exploring Algebraic Identities - Quadratic expressions Hard Quiz

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( (4x+3y)²-(4x-3y)² ) का सरल रूप क्या है?

( (5a+2b)²+(5a-2b)² ) को सरल करने पर क्या मिलेगा?

( (2p+q+r)² ) में (pq) और (pr) वाले पदों का योग क्या होगा?

( (2x+3)²-\(4x^2+9\) ) को सरल कीजिए।

( (3u-2v)²-\(9u^2+4v^2\) ) का मान क्या होगा?

( (p+q)²-(p-q)²-4pq ) का मान क्या है?

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

( (2a+b+c)²-\(4a^2+b^2+c^2\) ) का सरल रूप कौन-सा है?

( (x+2y+5z)² ) में (yz) वाला पद कौन-सा होगा?

( (6x+1)²-(6x-1)² ) का सरल रूप क्या है?

( (4x+3)²+(4x-3)²-32x^-2 ) का मान क्या है?

( (2x+y)³ ) में \(x^2y\) का गुणांक क्या होगा?

( (3a-b)³ ) में \(a^2b\) वाले पद का गुणांक क्या है?

( (x+4)³-(x-4)³ ) का पूरा सरल रूप क्या है?

( (a+b)³-\(a^3+b^3\) ) को गुणनखंड रूप में कैसे लिखा जाएगा?

( (a-b)³-\(a^3-b^3\) ) का सरल रूप क्या है?

( (x+2y)²-x^-2-4y^-2-4xy ) का मान क्या है?

( (3x-2y)²-9x^-2-4y^-2 ) का सरल रूप क्या है?

( (x+y+z)²-(x-y+z)² ) में कौन-सा पद नहीं बचेगा?

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