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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (3a+4b)²+(3a-4b)² ) को सरल करने पर क्या मिलेगा?

What is obtained by simplifying ( (3a+4b)²+(3a-4b)² )?

Explanation opens after your attempt

Correct Answer

A. \(18a^2+32b^2\)सही परिणाम

Step 1

Concept

Using the sum identity gives (2(3a)²+2(4b)²=18a^-2+32b^-2). Exam tip: notice cancellation of middle terms.

Step 2

Why this answer is correct

The correct answer is A. \(18a^2+32b^2\) / सही परिणाम. Using the sum identity gives (2(3a)²+2(4b)²=18a^-2+32b^-2). Exam tip: notice cancellation of middle terms.

Step 3

Exam Tip

योग पहचान से (2(3a)²+2(4b)²=18a^-2+32b^-2) मिलता है। परीक्षा में मध्य पदों के कटने पर ध्यान दें।

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Question 2/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+y+z)²-x^-2-y^-2-z^-2 ) का सरल रूप कौन-सा है?

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

Explanation opens after your attempt

Correct Answer

B. (2xy+2yz+2zx)सही पद

Step 1

Concept

After removing square terms from a three-term square, only double products remain. Exam tip: remember (2xy), (2yz), (2zx).

Step 2

Why this answer is correct

The correct answer is B. (2xy+2yz+2zx) / सही पद. After removing square terms from a three-term square, only double products remain. Exam tip: remember (2xy), (2yz), (2zx).

Step 3

Exam Tip

तीन पदों के वर्ग में वर्ग पद हटाने पर केवल दोहरे गुणन पद बचते हैं। परीक्षा में (2xy), (2yz), (2zx) याद रखें।

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Question 3/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( x^-2+14x+49-(x+7)² ) का मान क्या होगा?

What is the value of ( x^-2+14x+49-(x+7)² )?

Explanation opens after your attempt

Correct Answer

A. (0)सही मान

Step 1

Concept

(x^-2+14x+49=(x+7)²), so subtraction gives (0). Exam tip: identify perfect square trinomials.

Step 2

Why this answer is correct

The correct answer is A. (0) / सही मान. (x^-2+14x+49=(x+7)²), so subtraction gives (0). Exam tip: identify perfect square trinomials.

Step 3

Exam Tip

(x^-2+14x+49=(x+7)²) है इसलिए घटाने पर (0) मिलता है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।

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Question 4/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)²-\(a^2+b^2\) ) को सरल कीजिए।

Simplify ( (a+b)²-\(a^2+b^2\) ).

Explanation opens after your attempt

Correct Answer

B. (2ab)सही उत्तर

Step 1

Concept

( (a+b)²=a^-2+2ab+b^-2 ). Exam tip: after square terms cancel, (2ab) remains.

Step 2

Why this answer is correct

The correct answer is B. (2ab) / सही उत्तर. ( (a+b)²=a^-2+2ab+b^-2 ). Exam tip: after square terms cancel, (2ab) remains.

Step 3

Exam Tip

( (a+b)²=a^-2+2ab+b^-2 ) होता है। परीक्षा में वर्ग पद कटने के बाद (2ab) बचता है।

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Question 5/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+4)(x-6) ) का सही विस्तार क्या है?

What is the correct expansion of ( (x+4)(x-6) )?

Explanation opens after your attempt

Correct Answer

A. \(x^2-2x-24\)सही विस्तार

Step 1

Concept

The sum of constants is (4+(-6)=-2) and the product is (-24). Exam tip: handle mixed signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-24\) / सही विस्तार. The sum of constants is (4+(-6)=-2) and the product is (-24). Exam tip: handle mixed signs carefully.

Step 3

Exam Tip

स्थिर पदों का योग (4+(-6)=-2) और गुणन (-24) है। परीक्षा में मिश्रित चिह्नों को सावधानी से जोड़ें।

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Question 6/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(9x^2-24xy+16y^2\) का सही रूप कौन-सा है?

Which is the correct form of \(9x^2-24xy+16y^2\)?

Explanation opens after your attempt

Correct Answer

B. ( (3x-4y)² )सही पूर्ण वर्ग

Step 1

Concept

This is ( (3x)²-2\cdot3x\cdot4y+(4y)² ). Exam tip: identify the sign of the middle term.

Step 2

Why this answer is correct

The correct answer is B. ( (3x-4y)² ) / सही पूर्ण वर्ग. This is ( (3x)²-2\cdot3x\cdot4y+(4y)² ). Exam tip: identify the sign of the middle term.

Step 3

Exam Tip

यह ( (3x)²-2\cdot3x\cdot4y+(4y)² ) है। परीक्षा में मध्य पद का चिह्न पहचानें।

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Question 7/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(25p^2-36q^2\) का गुणनखंडन क्या है?

What is the factorisation of \(25p^2-36q^2\)?

Explanation opens after your attempt

Correct Answer

C. ( (5p+6q)(5p-6q) )सही रूप

Step 1

Concept

This is the form ( (5p)²-(6q)² ). Exam tip: take the square roots of both squares correctly.

Step 2

Why this answer is correct

The correct answer is C. ( (5p+6q)(5p-6q) ) / सही रूप. This is the form ( (5p)²-(6q)² ). Exam tip: take the square roots of both squares correctly.

Step 3

Exam Tip

यह ( (5p)²-(6q)² ) का रूप है। परीक्षा में दोनों वर्गों के वर्गमूल सही लें।

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Question 8/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2m+n)²-(2m-n)² ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (8mn)सही मान

Step 1

Concept

This is the (4ab) identity where (a=2m) and (b=n). Exam tip: take the full value (2m) for (a).

Step 2

Why this answer is correct

The correct answer is B. (8mn) / सही मान. This is the (4ab) identity where (a=2m) and (b=n). Exam tip: take the full value (2m) for (a).

Step 3

Exam Tip

यह (4ab) पहचान है जहाँ (a=2m) और (b=n) हैं। परीक्षा में (a) का पूरा मान (2m) लें।

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Question 9/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (5x-2)²-\(25x^2+4\) ) को सरल कीजिए।

Simplify ( (5x-2)²-\(25x^2+4\) ).

Explanation opens after your attempt

Correct Answer

B. - (20x)सही उत्तर

Step 1

Concept

( (5x-2)²=25x^-2-20x+4 ). Exam tip: square and constant terms cancel after subtraction.

Step 2

Why this answer is correct

The correct answer is B. - (20x) / सही उत्तर. ( (5x-2)²=25x^-2-20x+4 ). Exam tip: square and constant terms cancel after subtraction.

Step 3

Exam Tip

( (5x-2)²=25x^-2-20x+4 ) है। परीक्षा में घटाने पर वर्ग और स्थिर पद कट जाते हैं।

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Question 10/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+y)²-(x-y)²-4xy ) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (0)सही मान

Step 1

Concept

The difference of the first two terms is (4xy), and then (4xy) is subtracted. Exam tip: simplify in order.

Step 2

Why this answer is correct

The correct answer is A. (0) / सही मान. The difference of the first two terms is (4xy), and then (4xy) is subtracted. Exam tip: simplify in order.

Step 3

Exam Tip

पहले दो पदों का अंतर (4xy) है और फिर (4xy) घटता है। परीक्षा में क्रम से सरल करें।

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Question 11/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+2b+c)² ) में (bc) और (ac) वाले पदों का योग क्या होगा?

In ( (a+2b+c)² ), what is the sum of the terms containing (bc) and (ac)?

Explanation opens after your attempt

Correct Answer

B. (4bc+2ac)सही योग

Step 1

Concept

The (bc) term is \(2\cdot2b\cdot c=4bc\) and the (ac) term is (2ac). Exam tip: use double product for each pair.

Step 2

Why this answer is correct

The correct answer is B. (4bc+2ac) / सही योग. The (bc) term is \(2\cdot2b\cdot c=4bc\) and the (ac) term is (2ac). Exam tip: use double product for each pair.

Step 3

Exam Tip

(bc) पद \(2\cdot2b\cdot c=4bc\) और (ac) पद (2ac) है। परीक्षा में हर जोड़ी का दोहरा गुणन करें।

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Question 12/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x+3y+4z)² ) में (yz) वाला पद कौन-सा होगा?

Which term contains (yz) in ( (2x+3y+4z)² )?

Explanation opens after your attempt

Correct Answer

C. (24yz)सही दोहरा गुणन

Step 1

Concept

The (yz) term is \(2\cdot3y\cdot4z=24yz\). Exam tip: do not forget the factor (2) in double products.

Step 2

Why this answer is correct

The correct answer is C. (24yz) / सही दोहरा गुणन. The (yz) term is \(2\cdot3y\cdot4z=24yz\). Exam tip: do not forget the factor (2) in double products.

Step 3

Exam Tip

(yz) पद \(2\cdot3y\cdot4z=24yz\) है। परीक्षा में दोहरे गुणन में (2) लगाना न भूलें।

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Question 13/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2)(x+5)-(x+3)(x+4) ) का मान क्या है?

What is the value of ( (x+2)(x+5)-(x+3)(x+4) )?

Explanation opens after your attempt

Correct Answer

A. - (2)सही मान

Step 1

Concept

The first expansion is \(x^2+7x+10\) and the second is \(x^2+7x+12\). Exam tip: after like terms cancel, subtract constants.

Step 2

Why this answer is correct

The correct answer is A. - (2) / सही मान. The first expansion is \(x^2+7x+10\) and the second is \(x^2+7x+12\). Exam tip: after like terms cancel, subtract constants.

Step 3

Exam Tip

पहला विस्तार \(x^2+7x+10\) और दूसरा \(x^2+7x+12\) है। परीक्षा में समान पद कटने के बाद स्थिर पद घटाएँ।

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Question 14/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x-8)(x+2) ) में (x) का गुणांक और स्थिर पद कौन-से हैं?

What are the coefficient of (x) and the constant term in ( (x-8)(x+2) )?

Explanation opens after your attempt

Correct Answer

B. - (6) और - (16)सही जोड़ा

Step 1

Concept

The sum of constants is (-8+2=-6) and the product is (-16). Exam tip: check both signs separately.

Step 2

Why this answer is correct

The correct answer is B. - (6) और - (16) / सही जोड़ा. The sum of constants is (-8+2=-6) and the product is (-16). Exam tip: check both signs separately.

Step 3

Exam Tip

स्थिर पदों का योग (-8+2=-6) और गुणन (-16) है। परीक्षा में दोनों संकेत अलग-अलग जाँचें।

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Question 15/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 1005^2-995^2 \) का सही मान चुनिए।

Choose the correct value of \( 1005^2-995^2 \).

Explanation opens after your attempt

Correct Answer

B. (20000)सही मान

Step 1

Concept

By difference of squares, ( (1005+995)(1005-995)=2000\cdot10=20000 ). Exam tip: verify arithmetic carefully.

Step 2

Why this answer is correct

The correct answer is B. (20000) / सही मान. By difference of squares, ( (1005+995)(1005-995)=2000\cdot10=20000 ). Exam tip: verify arithmetic carefully.

Step 3

Exam Tip

वर्गों के अंतर से ( (1005+995)(1005-995)=2000\cdot10=20000 )। परीक्षा में पिछली गणना की जाँच करें।

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Question 16/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 299^2 \) को ( (300-1)² ) से निकालने पर मान क्या होगा?

Using ( (300-1)² ), what is the value of \( 299^2 \)?

Explanation opens after your attempt

Correct Answer

A. (89401)सही मान

Step 1

Concept

\(299^2=90000-600+1=89401\). Exam tip: subtract \(2\cdot300\cdot1\).

Step 2

Why this answer is correct

The correct answer is A. (89401) / सही मान. \(299^2=90000-600+1=89401\). Exam tip: subtract \(2\cdot300\cdot1\).

Step 3

Exam Tip

\(299^2=90000-600+1=89401\) है। परीक्षा में \(2\cdot300\cdot1\) घटाएँ।

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Question 17/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 405^2 \) को पहचान से निकालने पर सही मान क्या है?

What is the correct value of \( 405^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. (164025)सही मान

Step 1

Concept

(405²=(400+5)²=160000+4000+25=164025). Exam tip: add both (2ab) and \(b^2\).

Step 2

Why this answer is correct

The correct answer is A. (164025) / सही मान. (405²=(400+5)²=160000+4000+25=164025). Exam tip: add both (2ab) and \(b^2\).

Step 3

Exam Tip

(405²=(400+5)²=160000+4000+25=164025)। परीक्षा में (2ab) और \(b^2\) दोनों जोड़ें।

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Question 18/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

B. (28a)सही मान

Step 1

Concept

This is (4ab) where (a=7a) and (b=1), so (28a) is obtained. Exam tip: distinguish symbols and full terms.

Step 2

Why this answer is correct

The correct answer is B. (28a) / सही मान. This is (4ab) where (a=7a) and (b=1), so (28a) is obtained. Exam tip: distinguish symbols and full terms.

Step 3

Exam Tip

यह (4ab) है जहाँ (a=7a) और (b=1), इसलिए (28a) मिलता है। परीक्षा में प्रतीक और पद में फर्क रखें।

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Question 19/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x+5)²+(2x-5)²-8x^-2 ) का मान क्या है?

What is the value of ( (2x+5)²+(2x-5)²-8x^-2 )?

Explanation opens after your attempt

Correct Answer

B. (50)सही मान

Step 1

Concept

The sum of the first two squares is \(8x^2+50\). After subtracting \(8x^2\), (50) remains.

Step 2

Why this answer is correct

The correct answer is B. (50) / सही मान. The sum of the first two squares is \(8x^2+50\). After subtracting \(8x^2\), (50) remains.

Step 3

Exam Tip

पहले दो वर्गों का योग \(8x^2+50\) है। फिर \(8x^2\) घटाने पर (50) बचता है।

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Question 20/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (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. (4c(a+b))सही रूप

Step 1

Concept

Take (A=a+b) and use ( (A+c)²-(A-c)²=4Ac ). Exam tip: group terms before applying identities.

Step 2

Why this answer is correct

The correct answer is A. (4c(a+b)) / सही रूप. Take (A=a+b) and use ( (A+c)²-(A-c)²=4Ac ). Exam tip: group terms before applying identities.

Step 3

Exam Tip

इसे (A=a+b) मानकर ( (A+c)²-(A-c)²=4Ac ) लगाएँ। परीक्षा में समूह बनाकर पहचान लगाएँ।

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Question 21/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

A. \(2y^2\)सही मान

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 22/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (3p+q)²-(3p-q)²-12pq ) का मान क्या है?

What is the value of ( (3p+q)²-(3p-q)²-12pq )?

Explanation opens after your attempt

Correct Answer

A. (0)सही मान

Step 1

Concept

The difference of the first two squares is \(4\cdot3p\cdot q=12pq\). After subtracting (12pq), (0) is obtained.

Step 2

Why this answer is correct

The correct answer is A. (0) / सही मान. The difference of the first two squares is \(4\cdot3p\cdot q=12pq\). After subtracting (12pq), (0) is obtained.

Step 3

Exam Tip

पहले दो वर्गों का अंतर \(4\cdot3p\cdot q=12pq\) है। फिर (12pq) घटाने पर (0) मिलता है।

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Question 23/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2y)²-x^-2-4y^-2 ) को सरल करने पर क्या मिलेगा?

What is obtained by simplifying ( (x+2y)²-x^-2-4y^-2 )?

Explanation opens after your attempt

Correct Answer

B. (4xy)सही पद

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 24/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(4x^2+12xy+9y^2\) किसका पूर्ण वर्ग है?

\(4x^2+12xy+9y^2\) is the perfect square of what?

Explanation opens after your attempt

Correct Answer

A. ( (2x+3y)² )सही रूप

Step 1

Concept

(4x^-2=(2x)²), (9y^-2=(3y)²), and the middle term is (12xy). Exam tip: check both square roots.

Step 2

Why this answer is correct

The correct answer is A. ( (2x+3y)² ) / सही रूप. (4x^-2=(2x)²), (9y^-2=(3y)²), and the middle term is (12xy). Exam tip: check both square roots.

Step 3

Exam Tip

(4x^-2=(2x)²), (9y^-2=(3y)²) और मध्य पद (12xy) है। परीक्षा में दोनों वर्गमूल देखें।

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Question 25/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(16a^2-40ab+25b^2\) का गुणनखंडन कौन-सा है?

Which is the factorisation of \(16a^2-40ab+25b^2\)?

Explanation opens after your attempt

Correct Answer

B. ( (4a-5b)² )सही पूर्ण वर्ग

Step 1

Concept

This is ( (4a)²-2\cdot4a\cdot5b+(5b)² ). Exam tip: identify the minus square from the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. ( (4a-5b)² ) / सही पूर्ण वर्ग. This is ( (4a)²-2\cdot4a\cdot5b+(5b)² ). Exam tip: identify the minus square from the negative middle term.

Step 3

Exam Tip

यह ( (4a)²-2\cdot4a\cdot5b+(5b)² ) है। परीक्षा में ऋण मध्य पद से घटाव वर्ग पहचानें।

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Question 26/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+1)(x+2)(x+3) ) में पहले ( (x+1)(x+3) ) लगाने पर कौन-सा रूप मिलेगा?

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

Explanation opens after your attempt

Correct Answer

A. \(x^2+4x+3\)सही आंशिक विस्तार

Step 1

Concept

( (x+1)(x+3)=x^-2+4x+3 ). Exam tip: expand long expressions in small steps.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+4x+3\) / सही आंशिक विस्तार. ( (x+1)(x+3)=x^-2+4x+3 ). Exam tip: expand long expressions in small steps.

Step 3

Exam Tip

( (x+1)(x+3)=x^-2+4x+3 ) है। परीक्षा में लंबी अभिव्यक्ति को छोटे चरणों में फैलाएँ।

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Question 27/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+1)(x+2)(x+3) ) का पूरा विस्तार क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(x^3+6x^2+11x+6\)सही विस्तार

Step 1

Concept

Expand two factors first and then multiply by the third. Exam tip: keep expansion systematic.

Step 2

Why this answer is correct

The correct answer is A. \(x^3+6x^2+11x+6\) / सही विस्तार. Expand two factors first and then multiply by the third. Exam tip: keep expansion systematic.

Step 3

Exam Tip

पहले दो गुणनखंडों को फैलाकर फिर तीसरे से गुणा करें। परीक्षा में क्रमबद्ध विस्तार रखें।

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Question 28/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)³ ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (a+b)³ )?

Explanation opens after your attempt

Correct Answer

B. \(a^3+3a^2b+3ab^2+b^3\)सही विस्तार

Step 1

Concept

( (a+b)³ ) contains both \(3a^2b\) and \(3ab^2\). Exam tip: remember the four terms of the cube identity.

Step 2

Why this answer is correct

The correct answer is B. \(a^3+3a^2b+3ab^2+b^3\) / सही विस्तार. ( (a+b)³ ) contains both \(3a^2b\) and \(3ab^2\). Exam tip: remember the four terms of the cube identity.

Step 3

Exam Tip

( (a+b)³ ) में \(3a^2b\) और \(3ab^2\) दोनों आते हैं। परीक्षा में घन पहचान के चार पद याद रखें।

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Question 29/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

B. ऋणnegative

Step 1

Concept

( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ). Exam tip: remember the sign pattern.

Step 2

Why this answer is correct

The correct answer is B. ऋण / negative. ( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ). Exam tip: remember the sign pattern.

Step 3

Exam Tip

( (a-b)³=a^-3-3a^-2b+3ab^-2-b^-3 ) है। परीक्षा में चिह्नों का क्रम याद रखें।

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Question 30/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2)³ ) का विस्तार क्या है?

What is the expansion of ( (x+2)³ )?

Explanation opens after your attempt

Correct Answer

A. \(x^3+6x^2+12x+8\)सही विस्तार

Step 1

Concept

( (x+2)³=x^-3+3x^-2\cdot2+3x\cdot4+8 ). Exam tip: keep both terms with coefficient (3).

Step 2

Why this answer is correct

The correct answer is A. \(x^3+6x^2+12x+8\) / सही विस्तार. ( (x+2)³=x^-3+3x^-2\cdot2+3x\cdot4+8 ). Exam tip: keep both terms with coefficient (3).

Step 3

Exam Tip

( (x+2)³=x^-3+3x^-2\cdot2+3x\cdot4+8 ) है। परीक्षा में (3ab) वाले दोनों पद रखें।

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Question 31/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x-1)³ ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (2x-1)³ )?

Explanation opens after your attempt

Correct Answer

A. \(8x^3-12x^2+6x-1\)सही विस्तार

Step 1

Concept

In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: write the cube of (2x) as \(8x^3\).

Step 2

Why this answer is correct

The correct answer is A. \(8x^3-12x^2+6x-1\) / सही विस्तार. In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: write the cube of (2x) as \(8x^3\).

Step 3

Exam Tip

घटाव के घन में चिह्न (+), (-), (+), (-) के क्रम में आते हैं। परीक्षा में (2x) का घन \(8x^3\) लिखें।

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Question 32/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( a^3+b^3 \) का गुणनखंडन क्या है?

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

Explanation opens after your attempt

Correct Answer

A. ( (a+b)\(a^2-ab+b^2\) )सही रूप

Step 1

Concept

In sum of cubes, the second factor is \(a^2-ab+b^2\). Exam tip: keep the middle sign negative.

Step 2

Why this answer is correct

The correct answer is A. ( (a+b)\(a^2-ab+b^2\) ) / सही रूप. In sum of cubes, the second factor is \(a^2-ab+b^2\). Exam tip: keep the middle sign negative.

Step 3

Exam Tip

घनों के योग में दूसरा गुणनखंड \(a^2-ab+b^2\) होता है। परीक्षा में बीच का चिह्न ऋण रखें।

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Question 33/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( a^3-b^3 \) किसके बराबर है?

What is \( a^3-b^3 \) equal to?

Explanation opens after your attempt

Correct Answer

A. ( (a-b)\(a^2+ab+b^2\) )सही गुणनखंड

Step 1

Concept

In difference of cubes, ( (a-b)\(a^2+ab+b^2\) ) appears. Exam tip: keep cube and square identities separate.

Step 2

Why this answer is correct

The correct answer is A. ( (a-b)\(a^2+ab+b^2\) ) / सही गुणनखंड. In difference of cubes, ( (a-b)\(a^2+ab+b^2\) ) appears. Exam tip: keep cube and square identities separate.

Step 3

Exam Tip

घनों के अंतर में ( (a-b)\(a^2+ab+b^2\) ) आता है। परीक्षा में घन और वर्ग पहचान अलग रखें।

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Question 34/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 27x^3+8y^3 \) का गुणनखंडन चुनिए।

Choose the factorisation of \( 27x^3+8y^3 \).

Explanation opens after your attempt

Correct Answer

A. ( (3x+2y)\(9x^2-6xy+4y^2\) )सही रूप

Step 1

Concept

This is ( (3x)³+(2y)³ ). Exam tip: identify cube roots (3x) and (2y).

Step 2

Why this answer is correct

The correct answer is A. ( (3x+2y)\(9x^2-6xy+4y^2\) ) / सही रूप. This is ( (3x)³+(2y)³ ). Exam tip: identify cube roots (3x) and (2y).

Step 3

Exam Tip

यह ( (3x)³+(2y)³ ) है। परीक्षा में घनमूल (3x) और (2y) पहचानें।

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Question 35/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 64m^3-125n^3 \) का सही गुणनखंडन क्या है?

What is the correct factorisation of \( 64m^3-125n^3 \)?

Explanation opens after your attempt

Correct Answer

A. ( (4m-5n)\(16m^2+20mn+25n^2\) )सही रूप

Step 1

Concept

This is ( (4m)³-(5n)³ ). Exam tip: in difference of cubes, the second factor has all positive terms.

Step 2

Why this answer is correct

The correct answer is A. ( (4m-5n)\(16m^2+20mn+25n^2\) ) / सही रूप. This is ( (4m)³-(5n)³ ). Exam tip: in difference of cubes, the second factor has all positive terms.

Step 3

Exam Tip

यह ( (4m)³-(5n)³ ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड सभी धन पदों वाला होता है।

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Question 36/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (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

A. (3ab(a+b))सही रूप

Step 1

Concept

( (a+b)³=a^-3+3a^-2b+3ab^-2+b^-3 ). The two middle terms form (3ab(a+b)).

Step 2

Why this answer is correct

The correct answer is A. (3ab(a+b)) / सही रूप. ( (a+b)³=a^-3+3a^-2b+3ab^-2+b^-3 ). The two middle terms form (3ab(a+b)).

Step 3

Exam Tip

( (a+b)³=a^-3+3a^-2b+3ab^-2+b^-3 ) है। बीच के दो पद (3ab(a+b)) बनाते हैं।

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Question 37/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

A. - (3ab(a-b))सही रूप

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 38/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (x+y=10) और (xy=21) हो तो \(x^2+y^2\) का मान क्या है?

If (x+y=10) and (xy=21), what is the value of \(x^2+y^2\)?

Explanation opens after your attempt

Correct Answer

A. (58)सही मान

Step 1

Concept

(x^-2+y^-2=(x+y)²-2xy=100-42=58). Exam tip: subtract (2xy) from the square of the sum.

Step 2

Why this answer is correct

The correct answer is A. (58) / सही मान. (x^-2+y^-2=(x+y)²-2xy=100-42=58). Exam tip: subtract (2xy) from the square of the sum.

Step 3

Exam Tip

(x^-2+y^-2=(x+y)²-2xy=100-42=58)। परीक्षा में योग के वर्ग से (2xy) घटाएँ।

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Question 39/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (a-b=6) और (ab=16) हो तो \(a^2+b^2\) कितना होगा?

If (a-b=6) and (ab=16), what is \(a^2+b^2\)?

Explanation opens after your attempt

Correct Answer

A. (68)सही मान

Step 1

Concept

From ( (a-b)²=a^-2-2ab+b^-2 ), \(a^2+b^2=36+32=68\). Exam tip: add (2ab).

Step 2

Why this answer is correct

The correct answer is A. (68) / सही मान. From ( (a-b)²=a^-2-2ab+b^-2 ), \(a^2+b^2=36+32=68\). Exam tip: add (2ab).

Step 3

Exam Tip

( (a-b)²=a^-2-2ab+b^-2 ) से \(a^2+b^2=36+32=68\)। परीक्षा में (2ab) जोड़ें।

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Question 40/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (p+q=9) और \(p^2+q^2=45\) हो तो (pq) क्या होगा?

If (p+q=9) and \(p^2+q^2=45\), what is (pq)?

Explanation opens after your attempt

Correct Answer

A. (18)सही मान

Step 1

Concept

Using ( (p+q)²=p^-2+2pq+q^-2 ), (81=45+2pq), so (pq=18). Exam tip: find (2pq) first.

Step 2

Why this answer is correct

The correct answer is A. (18) / सही मान. Using ( (p+q)²=p^-2+2pq+q^-2 ), (81=45+2pq), so (pq=18). Exam tip: find (2pq) first.

Step 3

Exam Tip

( (p+q)²=p^-2+2pq+q^-2 ) से (81=45+2pq) इसलिए (pq=18)। परीक्षा में पहले (2pq) निकालें।

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Question 41/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (m+n=12) और (m-n=4) हो तो (mn) का मान क्या है?

If (m+n=12) and (m-n=4), what is the value of (mn)?

Explanation opens after your attempt

Correct Answer

A. (32)सही मान

Step 1

Concept

From ( (m+n)²-(m-n)²=4mn ), (144-16=128=4mn). Therefore (mn=32).

Step 2

Why this answer is correct

The correct answer is A. (32) / सही मान. From ( (m+n)²-(m-n)²=4mn ), (144-16=128=4mn). Therefore (mn=32).

Step 3

Exam Tip

( (m+n)²-(m-n)²=4mn ) से (144-16=128=4mn)। इसलिए (mn=32) है।

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Question 42/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+5)³-(x-5)³ ) में \(x^2\) वाला पद क्या होगा?

What will be the term containing \(x^2\) in ( (x+5)³-(x-5)³ )?

Explanation opens after your attempt

Correct Answer

A. \(30x^2\)सही पद

Step 1

Concept

On expanding cubes, \(+15x^2\) and (-\(-15x^2\)) combine to give \(30x^2\). Exam tip: signs change in subtraction.

Step 2

Why this answer is correct

The correct answer is A. \(30x^2\) / सही पद. On expanding cubes, \(+15x^2\) and (-\(-15x^2\)) combine to give \(30x^2\). Exam tip: signs change in subtraction.

Step 3

Exam Tip

घनों को फैलाने पर \(+15x^2\) और (-\(-15x^2\)) मिलकर \(30x^2\) देते हैं। परीक्षा में घटाव में चिह्न बदलता है।

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Question 43/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

A. \(30x^2+250\)सही रूप

Step 1

Concept

The \(x^3\) and (x) terms of both cubes cancel. Exam tip: expand fully and cancel like terms.

Step 2

Why this answer is correct

The correct answer is A. \(30x^2+250\) / सही रूप. The \(x^3\) and (x) terms of both cubes cancel. Exam tip: expand fully and cancel like terms.

Step 3

Exam Tip

दोनों घनों के \(x^3\) और (x) वाले पद कट जाते हैं। परीक्षा में पूरी तरह विस्तार करके समान पद हटाएँ।

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Question 44/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2a+b)³ ) में \(a^2b\) का गुणांक क्या होगा?

What is the coefficient of \(a^2b\) in ( (2a+b)³ )?

Explanation opens after your attempt

Correct Answer

A. (6)सही गुणांक

Step 1

Concept

(3(2a)²b=12a^-2b), so the coefficient is (12). Exam tip: square ((2a)²) correctly.

Step 2

Why this answer is correct

The correct answer is A. (6) / सही गुणांक. (3(2a)²b=12a^-2b), so the coefficient is (12). Exam tip: square ((2a)²) correctly.

Step 3

Exam Tip

(3(2a)²b=12a^-2b) है, इसलिए गुणांक (12) होगा। परीक्षा में ((2a)²) को सही वर्ग करें।

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Question 45/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2a+b)³ ) में \(a^2b\) का सही गुणांक चुनिए।

Choose the correct coefficient of \(a^2b\) in ( (2a+b)³ ).

Explanation opens after your attempt

Correct Answer

B. (12)सही गुणांक

Step 1

Concept

( (2a+b)³=8a^-3+12a^-2b+6ab^-2+b^-3 ). Exam tip: apply powers to the whole term.

Step 2

Why this answer is correct

The correct answer is B. (12) / सही गुणांक. ( (2a+b)³=8a^-3+12a^-2b+6ab^-2+b^-3 ). Exam tip: apply powers to the whole term.

Step 3

Exam Tip

( (2a+b)³=8a^-3+12a^-2b+6ab^-2+b^-3 ) है। परीक्षा में पूरे पद का घात लगाएँ।

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Question 46/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b+c)²-\(a^2+b^2+c^2+2ab\) ) को सरल कीजिए।

Simplify ( (a+b+c)²-\(a^2+b^2+c^2+2ab\) ).

Explanation opens after your attempt

Correct Answer

A. (2bc+2ca)सही परिणाम

Step 1

Concept

The square of three terms contains (2ab), (2bc), (2ca). After subtracting the given part, (2bc+2ca) remains.

Step 2

Why this answer is correct

The correct answer is A. (2bc+2ca) / सही परिणाम. The square of three terms contains (2ab), (2bc), (2ca). After subtracting the given part, (2bc+2ca) remains.

Step 3

Exam Tip

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

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Question 47/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2y+3z)² ) में (xz) वाला पद और (yz) वाला पद मिलकर क्या बनाते हैं?

In ( (x+2y+3z)² ), what do the (xz) term and the (yz) term together form?

Explanation opens after your attempt

Correct Answer

A. (6xz+12yz)सही योग

Step 1

Concept

The (xz) term is \(2\cdot x\cdot3z=6xz\) and the (yz) term is \(2\cdot2y\cdot3z=12yz\). Exam tip: find each pair separately.

Step 2

Why this answer is correct

The correct answer is A. (6xz+12yz) / सही योग. The (xz) term is \(2\cdot x\cdot3z=6xz\) and the (yz) term is \(2\cdot2y\cdot3z=12yz\). Exam tip: find each pair separately.

Step 3

Exam Tip

(xz) पद \(2\cdot x\cdot3z=6xz\) और (yz) पद \(2\cdot2y\cdot3z=12yz\) है। परीक्षा में हर जोड़ी अलग निकालें।

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Question 48/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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 ), so equality needs (2ab=0). Exam tip: understand the role of the middle term.

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 ), so equality needs (2ab=0). Exam tip: understand the role of the middle term.

Step 3

Exam Tip

( (a+b)²=a^-2+2ab+b^-2 ) है, इसलिए समानता के लिए (2ab=0) चाहिए। परीक्षा में मध्य पद की भूमिका समझें।

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Question 49/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (x+y+z=6) और (xy+yz+zx=11) हो तो \(x^2+y^2+z^2\) का मान क्या है?

If (x+y+z=6) and (xy+yz+zx=11), what is the value of \(x^2+y^2+z^2\)?

Explanation opens after your attempt

Correct Answer

A. (14)सही मान

Step 1

Concept

Using ( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ), \(36=x^2+y^2+z^2+22\). Exam tip: apply the three-term identity directly.

Step 2

Why this answer is correct

The correct answer is A. (14) / सही मान. Using ( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ), \(36=x^2+y^2+z^2+22\). Exam tip: apply the three-term identity directly.

Step 3

Exam Tip

( (x+y+z)²=x^-2+y^-2+z^-2+2(xy+yz+zx) ) से \(36=x^2+y^2+z^2+22\) है। परीक्षा में तीन पदों की पहचान सीधे लगाएँ।

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Question 50/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(8x^3+27\) का सही गुणनखंडन कौन-सा है?

Which is the correct factorisation of \(8x^3+27\)?

Explanation opens after your attempt

Correct Answer

A. ( (2x+3)\(4x^2-6x+9\) )सही रूप

Step 1

Concept

This is ( (2x)³+3³ ), so the sum of cubes identity applies. Exam tip: identify cube roots first.

Step 2

Why this answer is correct

The correct answer is A. ( (2x+3)\(4x^2-6x+9\) ) / सही रूप. This is ( (2x)³+3³ ), so the sum of cubes identity applies. Exam tip: identify cube roots first.

Step 3

Exam Tip

यह ( (2x)³+3³ ) है, इसलिए घनों के योग की पहचान लगती है। परीक्षा में घनमूल पहले पहचानें।

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Question 51/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. \(8x^2+18y^2\)

Step 1

Concept

Use ( (a+b)²+(a-b)²=2a^-2+2b^-2 ). Here (a=2x) and (b=3y).

Step 2

Why this answer is correct

The correct answer is B. \(8x^2+18y^2\). Use ( (a+b)²+(a-b)²=2a^-2+2b^-2 ). Here (a=2x) and (b=3y).

Step 3

Exam Tip

( (a+b)²+(a-b)²=2a^-2+2b^-2 ) लगाएँ। यहाँ (a=2x) और (b=3y) है।

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Question 52/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (16ab)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). With (u=4a) and (v=b), the result is (16ab).

Step 2

Why this answer is correct

The correct answer is B. (16ab). ( (u+v)²-(u-v)²=4uv ). With (u=4a) and (v=b), the result is (16ab).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) होता है। (u=4a) और (v=b) रखने पर (16ab) मिलता है।

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Question 53/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

C. ( (3x-5)² )

Step 1

Concept

(9x^-2=(3x)²) and \(25=5^2\). The middle term is negative, so ( (3x-5)² ) is correct.

Step 2

Why this answer is correct

The correct answer is C. ( (3x-5)² ). (9x^-2=(3x)²) and \(25=5^2\). The middle term is negative, so ( (3x-5)² ) is correct.

Step 3

Exam Tip

(9x^-2=(3x)²) और \(25=5^2\) है। बीच का पद ऋणात्मक है इसलिए ( (3x-5)² ) सही है।

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Question 54/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2p-3q+r)² ) में (pq) वाला पद कौन सा है?

Which is the (pq)-term in ( (2p-3q+r)² )?

Explanation opens after your attempt

Correct Answer

C. (-12pq)

Step 1

Concept

Twice the product of (2p) and (-3q) is (-12pq). Exam tip: check both sign and coefficient.

Step 2

Why this answer is correct

The correct answer is C. (-12pq). Twice the product of (2p) and (-3q) is (-12pq). Exam tip: check both sign and coefficient.

Step 3

Exam Tip

(2p) और (-3q) का दोगुना गुणनफल (-12pq) है। परीक्षा में चिन्ह के साथ गुणांक भी देखें।

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Question 55/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 121a^2-49b^2 \) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \( 121a^2-49b^2 \)?

Explanation opens after your attempt

Correct Answer

A. ( (11a+7b)(11a-7b) )

Step 1

Concept

This is ( (11a)²-(7b)² ). For difference of squares, use (a^-2-b^-2=(a+b)(a-b)).

Step 2

Why this answer is correct

The correct answer is A. ( (11a+7b)(11a-7b) ). This is ( (11a)²-(7b)² ). For difference of squares, use (a^-2-b^-2=(a+b)(a-b)).

Step 3

Exam Tip

यह ( (11a)²-(7b)² ) है। अंतर के वर्गों में (a^-2-b^-2=(a+b)(a-b)) लगता है।

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Question 56/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3x-4)(3x+7) ) में (x) का गुणांक क्या है?

What is the coefficient of (x) in ( (3x-4)(3x+7) )?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

The cross terms are (21x) and (-12x). Their sum is (9x).

Step 2

Why this answer is correct

The correct answer is B. (9). The cross terms are (21x) and (-12x). Their sum is (9x).

Step 3

Exam Tip

क्रॉस पद (21x) और (-12x) हैं। उनका योग (9x) है।

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Question 57/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (-5x-36)

Step 1

Concept

( (x+4)(x-9)=x^-2-5x-36 ). Subtracting \(x^2\) leaves (-5x-36).

Step 2

Why this answer is correct

The correct answer is B. (-5x-36). ( (x+4)(x-9)=x^-2-5x-36 ). Subtracting \(x^2\) leaves (-5x-36).

Step 3

Exam Tip

( (x+4)(x-9)=x^-2-5x-36 ) है। \(x^2\) घटाने पर (-5x-36) बचता है।

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Question 58/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (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

D. (4b(a+c))

Step 1

Concept

Treat it as ( ((a+c)+b)²-((a+c)-b)² ). It gives (4(a+c)b=4b(a+c)).

Step 2

Why this answer is correct

The correct answer is D. (4b(a+c)). Treat it as ( ((a+c)+b)²-((a+c)-b)² ). It gives (4(a+c)b=4b(a+c)).

Step 3

Exam Tip

इसे ( ((a+c)+b)²-((a+c)-b)² ) मानें। (4(a+c)b=4b(a+c)) मिलेगा।

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Question 59/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+5)²-4x^-2 ) का गुणनखंड रूप क्या है?

What is the factor form of ( (2x+5)²-4x^-2 )?

Explanation opens after your attempt

Correct Answer

A. (5(4x+5))

Step 1

Concept

This is ( (2x+5)²-(2x)² ). The factors simplify to (5(4x+5)).

Step 2

Why this answer is correct

The correct answer is A. (5(4x+5)). This is ( (2x+5)²-(2x)² ). The factors simplify to (5(4x+5)).

Step 3

Exam Tip

यह ( (2x+5)²-(2x)² ) है। गुणनखंड (5(4x+5)) बनते हैं।

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Question 60/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 1008^2-992^2 \) का मान क्या है?

What is the value of \( 1008^2-992^2 \)?

Explanation opens after your attempt

Correct Answer

B. (32000)

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), \(2000\cdot16=32000\). Exam tip: do not calculate both squares separately.

Step 2

Why this answer is correct

The correct answer is B. (32000). Using (a^-2-b^-2=(a+b)(a-b)), \(2000\cdot16=32000\). Exam tip: do not calculate both squares separately.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(2000\cdot16=32000\) है। परीक्षा में दोनों वर्ग अलग-अलग न निकालें।

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Question 61/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 997^2 \) का मान सर्वसमिका से क्या होगा?

Using identity, what is the value of \( 997^2 \)?

Explanation opens after your attempt

Correct Answer

A. (994009)

Step 1

Concept

(997=1000-3) and ( (1000-3)²=1000000-6000+9 ). Therefore (994009) is correct.

Step 2

Why this answer is correct

The correct answer is A. (994009). (997=1000-3) and ( (1000-3)²=1000000-6000+9 ). Therefore (994009) is correct.

Step 3

Exam Tip

(997=1000-3) है और ( (1000-3)²=1000000-6000+9 ) है। इसलिए (994009) सही है।

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Question 62/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

This is (a^-2+b^-2-2ab=(a-b)²). Here (a=x+2) and (b=x+3), so the result is (1).

Step 2

Why this answer is correct

The correct answer is A. (1). This is (a^-2+b^-2-2ab=(a-b)²). Here (a=x+2) and (b=x+3), so the result is (1).

Step 3

Exam Tip

यह (a^-2+b^-2-2ab=(a-b)²) है। यहाँ (a=x+2) और (b=x+3), इसलिए परिणाम (1) है।

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Question 63/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2a+3b+4c)² ) में (bc) वाला पद क्या होगा?

What will be the (bc)-term in ( (2a+3b+4c)² )?

Explanation opens after your attempt

Correct Answer

B. (24bc)

Step 1

Concept

From (3b) and (4c), \(2\cdot3b\cdot4c=24bc\). Exam tip: take twice every pair product.

Step 2

Why this answer is correct

The correct answer is B. (24bc). From (3b) and (4c), \(2\cdot3b\cdot4c=24bc\). Exam tip: take twice every pair product.

Step 3

Exam Tip

(3b) और (4c) से \(2\cdot3b\cdot4c=24bc\) मिलता है। परीक्षा में हर जोड़े का दोगुना लें।

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Question 64/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (-40mn)

Step 1

Concept

The order is reversed, so ( (u-v)²-(u+v)²=-4uv ). With (u=5m), (v=2n), the result is (-40mn).

Step 2

Why this answer is correct

The correct answer is B. (-40mn). The order is reversed, so ( (u-v)²-(u+v)²=-4uv ). With (u=5m), (v=2n), the result is (-40mn).

Step 3

Exam Tip

क्रम उल्टा है, इसलिए ( (u-v)²-(u+v)²=-4uv ) होगा। (u=5m), (v=2n), इसलिए (-40mn) है।

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Question 65/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

First identify (x^-2+2xy+y^-2=(x+y)²). Then apply difference of squares to ( (x+y)²-5² ).

Step 2

Why this answer is correct

The correct answer is A. ( (x+y+5)(x+y-5) ). First identify (x^-2+2xy+y^-2=(x+y)²). Then apply difference of squares to ( (x+y)²-5² ).

Step 3

Exam Tip

पहले (x^-2+2xy+y^-2=(x+y)²) पहचानें। फिर ( (x+y)²-5² ) पर अंतर के वर्ग लगाएँ।

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Question 66/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 67/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+6)(x-4)(x+1) ) में पहले दो गुणनखंडों का सही प्रसार क्या है?

What is the correct expansion of the first two factors in ( (x+6)(x-4)(x+1) )?

Explanation opens after your attempt

Correct Answer

A. \(x^2+2x-24\)

Step 1

Concept

( (x+6)(x-4)=x^-2+2x-24 ). Exam tip: make the first step correct before moving ahead.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x-24\). ( (x+6)(x-4)=x^-2+2x-24 ). Exam tip: make the first step correct before moving ahead.

Step 3

Exam Tip

( (x+6)(x-4)=x^-2+2x-24 ) है। परीक्षा में आगे बढ़ने से पहले प्रथम चरण सही करें।

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Question 68/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b)²+(b+c)²+(c+a)² ) में (ab) वाला पद कुल कितना है?

What is the total (ab)-term in ( (a+b)²+(b+c)²+(c+a)² )?

Explanation opens after your attempt

Correct Answer

B. (2ab)

Step 1

Concept

Only ( (a+b)² ) gives (2ab). The other two squares do not produce an (ab)-term.

Step 2

Why this answer is correct

The correct answer is B. (2ab). Only ( (a+b)² ) gives (2ab). The other two squares do not produce an (ab)-term.

Step 3

Exam Tip

केवल ( (a+b)² ) से (2ab) आता है। बाकी दो वर्गों में (ab) पद नहीं बनता।

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Question 69/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (12xy)

Step 1

Concept

The first difference is (4xy) and the second is (8xy). The total is (12xy).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 70/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x-5)(2x+5)+25 ) का सरल रूप क्या है?

What is the simplified form of ( (2x-5)(2x+5)+25 )?

Explanation opens after your attempt

Correct Answer

A. \(4x^2\)

Step 1

Concept

( (2x-5)(2x+5)=4x^-2-25 ). Adding (25) leaves \(4x^2\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2\). ( (2x-5)(2x+5)=4x^-2-25 ). Adding (25) leaves \(4x^2\).

Step 3

Exam Tip

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

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Question 71/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

This is (a^-2+b^-2-2ab=(a-b)²). Since ( (x+3)-(x+4)=-1 ), the square is (1).

Step 2

Why this answer is correct

The correct answer is B. (1). This is (a^-2+b^-2-2ab=(a-b)²). Since ( (x+3)-(x+4)=-1 ), the square is (1).

Step 3

Exam Tip

यह (a^-2+b^-2-2ab=(a-b)²) है। ( (x+3)-(x+4)=-1 ), इसलिए वर्ग (1) है।

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Question 72/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3a+2b)²-(3a-2b)² ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (24ab)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). With (u=3a), (v=2b), the result is (24ab).

Step 2

Why this answer is correct

The correct answer is B. (24ab). ( (u+v)²-(u-v)²=4uv ). With (u=3a), (v=2b), the result is (24ab).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। (u=3a), (v=2b) रखने पर (24ab) है।

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Question 73/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+2)(x+5)-(x+3)(x+4) ) का सरल रूप क्या है?

What is the simplified form of ( (x+2)(x+5)-(x+3)(x+4) )?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

The first product is \(x^2+7x+10\) and the second is \(x^2+7x+12\). The difference is (-2).

Step 2

Why this answer is correct

The correct answer is B. (-2). The first product is \(x^2+7x+10\) and the second is \(x^2+7x+12\). The difference is (-2).

Step 3

Exam Tip

पहला गुणनफल \(x^2+7x+10\) और दूसरा \(x^2+7x+12\) है। अंतर (-2) है।

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Question 74/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b)²-(a-b)² ) को (8) के बराबर दिया गया है। यदि (a=2) है तो (b) क्या होगा?

( (a+b)²-(a-b)² ) is given equal to (8). If (a=2), what is (b)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

By identity the result is (4ab). \(4\cdot2\cdot b=8\), so (b=1).

Step 2

Why this answer is correct

The correct answer is A. (1). By identity the result is (4ab). \(4\cdot2\cdot b=8\), so (b=1).

Step 3

Exam Tip

पहचान से परिणाम (4ab) है। \(4\cdot2\cdot b=8\), इसलिए (b=1) है।

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Question 75/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+y+z)² ) में यदि (x=1), (y=2), (z=3) हों तो पहचान से मान क्या है?

Using identity, what is the value of ( (x+y+z)² ) if (x=1), (y=2), (z=3)?

Explanation opens after your attempt

Correct Answer

B. (36)

Step 1

Concept

The sum is (1+2+3=6), and its square is (36). The identity with squares and pair terms gives the same value.

Step 2

Why this answer is correct

The correct answer is B. (36). The sum is (1+2+3=6), and its square is (36). The identity with squares and pair terms gives the same value.

Step 3

Exam Tip

योग (1+2+3=6) है और वर्ग (36) होगा। पहचान में वर्ग और जोड़ीदार पद भी यही मान देते हैं।

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Question 76/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+1)²-(2x-1)²=40 ) हो तो (x) का मान क्या है?

If ( (2x+1)²-(2x-1)²=40 ), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). Here (u=2x), (v=1), so (8x=40) and (x=5).

Step 2

Why this answer is correct

The correct answer is B. (5). ( (u+v)²-(u-v)²=4uv ). Here (u=2x), (v=1), so (8x=40) and (x=5).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। यहाँ (u=2x), (v=1), इसलिए (8x=40) और (x=5) है।

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Question 77/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+1)(x+2)(x+3) ) के प्रसार में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in the expansion of ( (x+1)(x+2)(x+3) )?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

For three linear factors, the coefficient of \(x^2\) is (1+2+3=6). Exam tip: you can also check by expanding the first two factors.

Step 2

Why this answer is correct

The correct answer is C. (6). For three linear factors, the coefficient of \(x^2\) is (1+2+3=6). Exam tip: you can also check by expanding the first two factors.

Step 3

Exam Tip

तीन रैखिक पदों में \(x^2\) का गुणांक (1+2+3=6) होता है। परीक्षा में पहले दो पदों को खोलकर भी जाँच सकते हैं।

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Question 78/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The coefficient of \(x^2\) is the sum of constants (-2+3+5=6). Exam tip: add with signs.

Step 2

Why this answer is correct

The correct answer is A. (6). The coefficient of \(x^2\) is the sum of constants (-2+3+5=6). Exam tip: add with signs.

Step 3

Exam Tip

\(x^2\) का गुणांक स्थिर संख्याओं का योग (-2+3+5=6) है। परीक्षा में चिन्ह के साथ जोड़ें।

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Question 79/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (4xy)

Step 1

Concept

( (x+2y)²=x^-2+4xy+4y^-2 ). Subtracting \(x^2+4y^2\) leaves (4xy).

Step 2

Why this answer is correct

The correct answer is B. (4xy). ( (x+2y)²=x^-2+4xy+4y^-2 ). Subtracting \(x^2+4y^2\) leaves (4xy).

Step 3

Exam Tip

( (x+2y)²=x^-2+4xy+4y^-2 ) है। \(x^2+4y^2\) घटाने पर (4xy) बचता है।

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Question 80/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (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)

Step 1

Concept

( (3x-2y)²=9x^-2-12xy+4y^-2 ). Subtracting \(9x^2+4y^2\) leaves (-12xy).

Step 2

Why this answer is correct

The correct answer is B. (-12xy). ( (3x-2y)²=9x^-2-12xy+4y^-2 ). Subtracting \(9x^2+4y^2\) leaves (-12xy).

Step 3

Exam Tip

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

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Question 81/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+3)²+(2x-3)² ) में स्थिर पद कितना है?

What is the constant term in ( (2x+3)²+(2x-3)² )?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

Each square has constant term (9) and (9). Therefore the total constant term is (18).

Step 2

Why this answer is correct

The correct answer is B. (18). Each square has constant term (9) and (9). Therefore the total constant term is (18).

Step 3

Exam Tip

दोनों वर्गों में स्थिर पद (9) और (9) हैं। इसलिए कुल स्थिर पद (18) है।

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Question 82/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 64x^2+80x+25 \) का पूर्ण वर्ग रूप क्या है?

What is the perfect square form of \( 64x^2+80x+25 \)?

Explanation opens after your attempt

Correct Answer

A. ( (8x+5)² )

Step 1

Concept

(64x^-2=(8x)²), \(25=5^2\), and the middle term is \(2\cdot8x\cdot5=80x\).

Step 2

Why this answer is correct

The correct answer is A. ( (8x+5)² ). (64x^-2=(8x)²), \(25=5^2\), and the middle term is \(2\cdot8x\cdot5=80x\).

Step 3

Exam Tip

(64x^-2=(8x)²), \(25=5^2\) और बीच का पद \(2\cdot8x\cdot5=80x\) है।

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Question 83/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 25m^2-70mn+49n^2 \) किसका वर्ग है?

\( 25m^2-70mn+49n^2 \) is the square of what?

Explanation opens after your attempt

Correct Answer

C. ( (5m-7n)² )

Step 1

Concept

(25m^-2=(5m)²) and (49n^-2=(7n)²). The middle term (-70mn) makes it ( (5m-7n)² ).

Step 2

Why this answer is correct

The correct answer is C. ( (5m-7n)² ). (25m^-2=(5m)²) and (49n^-2=(7n)²). The middle term (-70mn) makes it ( (5m-7n)² ).

Step 3

Exam Tip

(25m^-2=(5m)²) और (49n^-2=(7n)²) है। बीच का पद (-70mn) इसे ( (5m-7n)² ) बनाता है।

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Question 84/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. \(x^4-a^4\)

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 85/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+3y)²+(2x-3y)²-\(8x^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (2x+3y)²+(2x-3y)²-\(8x^2\) )?

Explanation opens after your attempt

Correct Answer

A. \(18y^2\)

Step 1

Concept

The sum is first \(8x^2+18y^2\). Subtracting \(8x^2\) leaves \(18y^2\).

Step 2

Why this answer is correct

The correct answer is A. \(18y^2\). The sum is first \(8x^2+18y^2\). Subtracting \(8x^2\) leaves \(18y^2\).

Step 3

Exam Tip

पहले योग \(8x^2+18y^2\) है। \(8x^2\) घटाने पर \(18y^2\) बचता है।

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Question 86/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. \(2x^2-30\)

Step 1

Concept

The first is \(x^2+2x-15\) and the second is \(x^2-2x-15\). Adding gives \(2x^2-30\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-30\). The first is \(x^2+2x-15\) and the second is \(x^2-2x-15\). Adding gives \(2x^2-30\).

Step 3

Exam Tip

पहला \(x^2+2x-15\) और दूसरा \(x^2-2x-15\) है। जोड़ने पर \(2x^2-30\) मिलता है।

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Question 87/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (4x)

Step 1

Concept

The two products are \(x^2+2x-15\) and \(x^2-2x-15\). Their difference is (4x).

Step 2

Why this answer is correct

The correct answer is B. (4x). The two products are \(x^2+2x-15\) and \(x^2-2x-15\). Their difference is (4x).

Step 3

Exam Tip

दोनों गुणनफल क्रमशः \(x^2+2x-15\) और \(x^2-2x-15\) हैं। अंतर (4x) है।

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Question 88/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b+c)² ) में यदि केवल \(a^2+b^2+c^2\) लिखा गया हो तो कौन से पद छूट गए?

If only \(a^2+b^2+c^2\) is written for ( (a+b+c)² ), which terms are missing?

Explanation opens after your attempt

Correct Answer

B. (2ab+2bc+2ca)

Step 1

Concept

The square of three terms also includes twice the pair products. Exam tip: always write (2ab+2bc+2ca).

Step 2

Why this answer is correct

The correct answer is B. (2ab+2bc+2ca). The square of three terms also includes twice the pair products. Exam tip: always write (2ab+2bc+2ca).

Step 3

Exam Tip

तीन पदों के वर्ग में जोड़ीदार दोगुने पद भी आते हैं। परीक्षा में (2ab+2bc+2ca) अवश्य लिखें।

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Question 89/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 202^2-198^2 \) का मान क्या है?

What is the value of \( 202^2-198^2 \)?

Explanation opens after your attempt

Correct Answer

A. (1600)

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), \(400\cdot4=1600\). Exam tip: quickly find sum and difference.

Step 2

Why this answer is correct

The correct answer is A. (1600). Using (a^-2-b^-2=(a+b)(a-b)), \(400\cdot4=1600\). Exam tip: quickly find sum and difference.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(400\cdot4=1600\) मिलता है। परीक्षा में योग और अंतर जल्दी निकालें।

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Question 90/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 51^2+49^2 \) को पहचान से सरल करने पर कौन सा मान मिलेगा?

What value is obtained by simplifying \( 51^2+49^2 \) using identity?

Explanation opens after your attempt

Correct Answer

B. (5002)

Step 1

Concept

Treat it as ( (50+1)²+(50-1)² ). \(2\cdot50^2+2\cdot1^2=5002\).

Step 2

Why this answer is correct

The correct answer is B. (5002). Treat it as ( (50+1)²+(50-1)² ). \(2\cdot50^2+2\cdot1^2=5002\).

Step 3

Exam Tip

इसे ( (50+1)²+(50-1)² ) मानें। \(2\cdot50^2+2\cdot1^2=5002\) है।

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Question 91/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 51^2-49^2 \) का मान क्या है?

What is the value of \( 51^2-49^2 \)?

Explanation opens after your attempt

Correct Answer

B. (200)

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), \(100\cdot2=200\). Exam tip: no need to calculate the squares.

Step 2

Why this answer is correct

The correct answer is B. (200). Using (a^-2-b^-2=(a+b)(a-b)), \(100\cdot2=200\). Exam tip: no need to calculate the squares.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(100\cdot2=200\) है। परीक्षा में वर्ग निकालने की जरूरत नहीं है।

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Question 92/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+2y)²-(x-2y)² ) और (8xy) के बीच क्या संबंध है?

What is the relation between ( (x+2y)²-(x-2y)² ) and (8xy)?

Explanation opens after your attempt

Correct Answer

A. दोनों बराबर हैंThey are equal

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). With (u=x), (v=2y), it gives (8xy).

Step 2

Why this answer is correct

The correct answer is A. दोनों बराबर हैं / They are equal. ( (u+v)²-(u-v)²=4uv ). With (u=x), (v=2y), it gives (8xy).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। (u=x), (v=2y), इसलिए (8xy) मिलता है।

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Question 93/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. \(x^4-1\)

Step 1

Concept

First ( (x-1)(x+1)=x^-2-1 ). Then ( \(x^2-1\)\(x^2+1\)=x^-4-1 ).

Step 2

Why this answer is correct

The correct answer is A. \(x^4-1\). First ( (x-1)(x+1)=x^-2-1 ). Then ( \(x^2-1\)\(x^2+1\)=x^-4-1 ).

Step 3

Exam Tip

पहले ( (x-1)(x+1)=x^-2-1 ) है। फिर ( \(x^2-1\)\(x^2+1\)=x^-4-1 ) होगा।

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Question 94/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. (8x+8)

Step 1

Concept

Treat it as (A^-2-B^-2=(A+B)(A-B)). Here (A-B=2) and (A+B=4x+4), so it is (8x+8).

Step 2

Why this answer is correct

The correct answer is A. (8x+8). Treat it as (A^-2-B^-2=(A+B)(A-B)). Here (A-B=2) and (A+B=4x+4), so it is (8x+8).

Step 3

Exam Tip

इसे (A^-2-B^-2=(A+B)(A-B)) मानें। यहाँ (A-B=2) और (A+B=4x+4), इसलिए (8x+8) है।

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Question 95/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3x+5)²-(3x-1)² ) का सरल रूप क्या है?

What is the simplified form of ( (3x+5)²-(3x-1)² )?

Explanation opens after your attempt

Correct Answer

A. (36x+24)

Step 1

Concept

Use (A^-2-B^-2=(A+B)(A-B)). (A-B=6) and (A+B=6x+4), so the result is (36x+24).

Step 2

Why this answer is correct

The correct answer is A. (36x+24). Use (A^-2-B^-2=(A+B)(A-B)). (A-B=6) and (A+B=6x+4), so the result is (36x+24).

Step 3

Exam Tip

(A^-2-B^-2=(A+B)(A-B)) लगाएँ। (A-B=6) और (A+B=6x+4), इसलिए (36x+24) है।

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Question 96/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+a)²-(x-a)²=24x ) है। यदि (a=3) हो तो यह कथन किस कारण सही है?

( (x+a)²-(x-a)²=24x ). If (a=3), why is this statement correct?

Explanation opens after your attempt

Correct Answer

B. क्योंकि पहचान से (4ax=24x) होता हैBecause identity gives (4ax=24x)

Step 1

Concept

( (x+a)²-(x-a)²=4ax ). With (a=3), it gives (12x), so the given statement is not correct.

Step 2

Why this answer is correct

The correct answer is B. क्योंकि पहचान से (4ax=24x) होता है / Because identity gives (4ax=24x). ( (x+a)²-(x-a)²=4ax ). With (a=3), it gives (12x), so the given statement is not correct.

Step 3

Exam Tip

( (x+a)²-(x-a)²=4ax ) है। (a=3) रखने पर (12x) मिलेगा, इसलिए दिया कथन सही नहीं है।

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Question 97/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b+c)² ) में यदि (a+b+c=10) हो तो पूरा मान कितना होगा?

If (a+b+c=10), what is the complete value of ( (a+b+c)² )?

Explanation opens after your attempt

Correct Answer

C. (100)

Step 1

Concept

If the whole sum is (10), its square is (100). Exam tip: directly square the given sum.

Step 2

Why this answer is correct

The correct answer is C. (100). If the whole sum is (10), its square is (100). Exam tip: directly square the given sum.

Step 3

Exam Tip

यदि पूरा योग (10) है तो उसका वर्ग (100) होगा। परीक्षा में दिए गए योग का सीधे वर्ग लें।

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Question 98/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 99/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (12xy)

Step 1

Concept

( (u+v)²-(u-v)²=4uv ). Here (u=x) and (v=3y), so the result is (12xy).

Step 2

Why this answer is correct

The correct answer is B. (12xy). ( (u+v)²-(u-v)²=4uv ). Here (u=x) and (v=3y), so the result is (12xy).

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) है। यहाँ (u=x) और (v=3y), इसलिए (12xy) मिलता है।

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Question 100/150 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( x^2+6x+9-y^2 \) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \( x^2+6x+9-y^2 \)?

Explanation opens after your attempt

Correct Answer

C. ( (x+3+y)(x+3-y) )

Step 1

Concept

First identify (x^-2+6x+9=(x+3)²). Then apply the difference of squares identity to ( (x+3)²-y^-2 ).

Step 2

Why this answer is correct

The correct answer is C. ( (x+3+y)(x+3-y) ). First identify (x^-2+6x+9=(x+3)²). Then apply the difference of squares identity to ( (x+3)²-y^-2 ).

Step 3

Exam Tip

पहले (x^-2+6x+9=(x+3)²) पहचानें। फिर ( (x+3)²-y^-2 ) पर अंतर के वर्गों की सर्वसमिका लगाएँ।

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Question 101/150 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 102/150 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 103/150 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 104/150 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 105/150 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 106/150 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 107/150 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 108/150 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 109/150 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 110/150 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 111/150 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 112/150 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 113/150 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 114/150 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 115/150 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 116/150 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 117/150 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 118/150 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 119/150 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 120/150 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 121/150 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 122/150 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 123/150 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 124/150 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 125/150 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 126/150 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 127/150 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 128/150 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 129/150 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 130/150 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 131/150 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 132/150 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 133/150 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 134/150 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 135/150 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 136/150 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 137/150 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 138/150 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 139/150 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 140/150 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 141/150 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 142/150 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 143/150 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 144/150 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 145/150 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 146/150 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 147/150 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 148/150 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 149/150 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 150/150 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 - Algebraic identities Hard Quiz

( (3a+4b)2+(3a-4b)2 ) को सरल करने पर क्या मिलेगा?

Concept

Why this answer is correct

Exam Tip

( (x+y+z)2-x-2-y-2-z-2 ) का सरल रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

( x-2+14x+49-(x+7)2 ) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

( (a+b)2-\(a^2+b^2\) ) को सरल कीजिए।

Concept

Why this answer is correct

Exam Tip

( (x+4)(x-6) ) का सही विस्तार क्या है?

Concept

Why this answer is correct

Exam Tip

\(9x^2-24xy+16y^2\) का सही रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

\(25p^2-36q^2\) का गुणनखंडन क्या है?

Concept

Why this answer is correct

Exam Tip

( (2m+n)2-(2m-n)2 ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (5x-2)2-\(25x^2+4\) ) को सरल कीजिए।

Concept

Why this answer is correct

Exam Tip

( (x+y)2-(x-y)2-4xy ) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (a+2b+c)2 ) में (bc) और (ac) वाले पदों का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

( (2x+3y+4z)2 ) में (yz) वाला पद कौन-सा होगा?

Concept

Why this answer is correct

Exam Tip

( (x+2)(x+5)-(x+3)(x+4) ) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (x-8)(x+2) ) में (x) का गुणांक और स्थिर पद कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

\( 1005^2-995^2 \) का सही मान चुनिए।

Concept

Why this answer is correct

Exam Tip

\( 299^2 \) को ( (300-1)2 ) से निकालने पर मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\( 405^2 \) को पहचान से निकालने पर सही मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

( (2x+5)2+(2x-5)2-8x-2 ) का मान क्या 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

( (3a+4b)²+(3a-4b)² ) को सरल करने पर क्या मिलेगा?

( (x+y+z)²-x^-2-y^-2-z^-2 ) का सरल रूप कौन-सा है?

( x^-2+14x+49-(x+7)² ) का मान क्या होगा?

( (a+b)²-\(a^2+b^2\) ) को सरल कीजिए।

( (2m+n)²-(2m-n)² ) का सरल रूप क्या है?

( (5x-2)²-\(25x^2+4\) ) को सरल कीजिए।

( (x+y)²-(x-y)²-4xy ) का मान क्या है?

( (a+2b+c)² ) में (bc) और (ac) वाले पदों का योग क्या होगा?

( (2x+3y+4z)² ) में (yz) वाला पद कौन-सा होगा?

\( 299^2 \) को ( (300-1)² ) से निकालने पर मान क्या होगा?

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

( (2x+5)²+(2x-5)²-8x^-2 ) का मान क्या है?

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

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

( (3p+q)²-(3p-q)²-12pq ) का मान क्या है?

( (x+2y)²-x^-2-4y^-2 ) को सरल करने पर क्या मिलेगा?

( (a+b)³ ) का सही विस्तार कौन-सा है?

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

( (x+2)³ ) का विस्तार क्या है?

( (2x-1)³ ) का सही विस्तार कौन-सा है?

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

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