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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 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 2/50 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 3/50 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 4/50 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 5/50 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 6/50 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 7/50 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 8/50 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 9/50 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 10/50 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 11/50 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 12/50 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 13/50 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 14/50 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 15/50 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 16/50 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 17/50 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 18/50 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 19/50 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 20/50 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 21/50 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 22/50 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 23/50 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 24/50 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 25/50 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 26/50 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 27/50 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 28/50 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 29/50 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 30/50 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 31/50 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 32/50 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 33/50 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 34/50 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 35/50 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 36/50 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 37/50 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 38/50 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 39/50 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 40/50 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 41/50 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 42/50 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 43/50 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 44/50 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 45/50 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 46/50 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 47/50 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 48/50 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 49/50 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 50/50 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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Class 9 Mathematics - Exploring Algebraic Identities - Quadratic expressions Hard Quiz

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

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

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

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( (a+b)2-\(a^2+b^2\) ) को सरल कीजिए।

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

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

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\(25p^2-36q^2\) का गुणनखंडन क्या है?

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

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( (5x-2)2-\(25x^2+4\) ) को सरल कीजिए।

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( (x+y)2-(x-y)2-4xy ) का मान क्या है?

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

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

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

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

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\( 1005^2-995^2 \) का सही मान चुनिए।

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

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

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

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

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

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( (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?