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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+7)² ) का पूरा विस्तार कौन-सा है?

Which is the complete expansion of ( (x+7)² )?

Explanation opens after your attempt

Correct Answer

A. \(x^2+14x+49\)सही विस्तार

Step 1

Concept

( (x+7)²=x^-2+2\cdot x\cdot7+49 ). Exam tip: always include the (2ab) term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+14x+49\) / सही विस्तार. ( (x+7)²=x^-2+2\cdot x\cdot7+49 ). Exam tip: always include the (2ab) term.

Step 3

Exam Tip

( (x+7)²=x^-2+2\cdot x\cdot7+49 ) होता है। परीक्षा में (2ab) पद जरूर लिखें।

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Question 2/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x-5)² ) का सही प्रसार कौन सा है?

What is the correct expansion of ( (2x-5)² )?

Explanation opens after your attempt

Correct Answer

B. \(4x^2-20x+25\)

Step 1

Concept

Use ( (a-b)²=a^-2-2ab+b^-2 ). Here the middle term is \(-2\cdot2x\cdot5=-20x\).

Step 2

Why this answer is correct

The correct answer is B. \(4x^2-20x+25\). Use ( (a-b)²=a^-2-2ab+b^-2 ). Here the middle term is \(-2\cdot2x\cdot5=-20x\).

Step 3

Exam Tip

( (a-b)²=a^-2-2ab+b^-2 ) लगाएँ। यहाँ बीच का पद \(-2\cdot2x\cdot5=-20x\) है।

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Question 3/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3y-4)² ) में मध्य पद क्या होगा?

What is the middle term in ( (3y-4)² )?

Explanation opens after your attempt

Correct Answer

D. - (24y)ऋण मध्य पद

Step 1

Concept

The middle term is \(-2\cdot3y\cdot4=-24y\). Exam tip: do not ignore the negative sign.

Step 2

Why this answer is correct

The correct answer is D. - (24y) / ऋण मध्य पद. The middle term is \(-2\cdot3y\cdot4=-24y\). Exam tip: do not ignore the negative sign.

Step 3

Exam Tip

मध्य पद \(-2\cdot3y\cdot4=-24y\) है। परीक्षा में ऋण चिह्न को न छोड़ें।

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Question 4/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3a+4b)(3a-4b) ) का सरल रूप क्या है?

What is the simplified form of ( (3a+4b)(3a-4b) )?

Explanation opens after your attempt

Correct Answer

D. \(9a^2-16b^2\)

Step 1

Concept

This is the form ( (u+v)(u-v)=u^-2-v^-2 ). With (u=3a) and (v=4b), it gives \(9a^2-16b^2\).

Step 2

Why this answer is correct

The correct answer is D. \(9a^2-16b^2\). This is the form ( (u+v)(u-v)=u^-2-v^-2 ). With (u=3a) and (v=4b), it gives \(9a^2-16b^2\).

Step 3

Exam Tip

यह ( (u+v)(u-v)=u^-2-v^-2 ) का रूप है। (u=3a) और (v=4b) रखने पर \(9a^2-16b^2\) मिलता है।

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Question 5/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2a+5b)² ) का सही विस्तार चुनिए।

Choose the correct expansion of ( (2a+5b)² ).

Explanation opens after your attempt

Correct Answer

B. \(4a^2+20ab+25b^2\)सही विस्तार

Step 1

Concept

Since \(2\cdot2a\cdot5b=20ab\), the middle term is (20ab). Exam tip: square complete terms.

Step 2

Why this answer is correct

The correct answer is B. \(4a^2+20ab+25b^2\) / सही विस्तार. Since \(2\cdot2a\cdot5b=20ab\), the middle term is (20ab). Exam tip: square complete terms.

Step 3

Exam Tip

\(2\cdot2a\cdot5b=20ab\) इसलिए मध्य पद (20ab) है। परीक्षा में पूरे पदों का वर्ग करें।

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Question 6/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( x^2+12x+36 \) किसका पूर्ण वर्ग है?

\( x^2+12x+36 \) is the perfect square of what?

Explanation opens after your attempt

Correct Answer

A. ( (x+6)² )

Step 1

Concept

\(36=6^2\) and \(12x=2\cdot x\cdot6\). Therefore it is ( (x+6)² ).

Step 2

Why this answer is correct

The correct answer is A. ( (x+6)² ). \(36=6^2\) and \(12x=2\cdot x\cdot6\). Therefore it is ( (x+6)² ).

Step 3

Exam Tip

\(36=6^2\) और \(12x=2\cdot x\cdot6\) है। इसलिए यह ( (x+6)² ) है।

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Question 7/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (p+9)(p-9) ) को सरल करने पर क्या मिलेगा?

What do we get after simplifying ( (p+9)(p-9) )?

Explanation opens after your attempt

Correct Answer

C. \(p^2-81\)वर्गों का अंतर

Step 1

Concept

This is the form ( (a+b)(a-b)=a^-2-b^-2 ). Exam tip: identify opposite signs.

Step 2

Why this answer is correct

The correct answer is C. \(p^2-81\) / वर्गों का अंतर. This is the form ( (a+b)(a-b)=a^-2-b^-2 ). Exam tip: identify opposite signs.

Step 3

Exam Tip

यह ( (a+b)(a-b)=a^-2-b^-2 ) का रूप है। परीक्षा में विपरीत चिह्नों को पहचानें।

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Question 8/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 96\times104 \) का मान पहचान से क्या होगा?

Using an identity, what is the value of \( 96\times104 \)?

Explanation opens after your attempt

Correct Answer

C. (9984)

Step 1

Concept

(96\times104=(100-4)(100+4)). Using \(a^2-b^2\), we get (10000-16=9984).

Step 2

Why this answer is correct

The correct answer is C. (9984). (96\times104=(100-4)(100+4)). Using \(a^2-b^2\), we get (10000-16=9984).

Step 3

Exam Tip

(96\times104=(100-4)(100+4)) है। \(a^2-b^2\) से (10000-16=9984) मिलता है।

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Question 9/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 98^2 \) को पहचान से निकालने के लिए सबसे उपयोगी रूप कौन-सा है?

Which form is most useful for finding \( 98^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. ( (100-2)² )निकट पूर्ण संख्या

Step 1

Concept

Since (98=100-2), ( (100-2)² ) makes calculation easy. Exam tip: choose a nearby round number.

Step 2

Why this answer is correct

The correct answer is A. ( (100-2)² ) / निकट पूर्ण संख्या. Since (98=100-2), ( (100-2)² ) makes calculation easy. Exam tip: choose a nearby round number.

Step 3

Exam Tip

(98=100-2) इसलिए ( (100-2)² ) से गणना आसान होती है। परीक्षा में निकट पूर्ण संख्या चुनें।

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Question 10/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+3)²-(x-3)² ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

D. (12x)

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

( (u+v)²-(u-v)²=4uv ) होता है। यहाँ (u=x) और (v=3) है, इसलिए (12x) मिलेगा।

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Question 11/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+3)(x+8) ) में (x) का गुणांक क्या होगा?

What will be the coefficient of (x) in ( (x+3)(x+8) )?

Explanation opens after your attempt

Correct Answer

B. (11)स्थिर पदों का योग

Step 1

Concept

( (x+3)(x+8)=x^-2+11x+24 ). Exam tip: the coefficient of (x) is the sum of constants.

Step 2

Why this answer is correct

The correct answer is B. (11) / स्थिर पदों का योग. ( (x+3)(x+8)=x^-2+11x+24 ). Exam tip: the coefficient of (x) is the sum of constants.

Step 3

Exam Tip

( (x+3)(x+8)=x^-2+11x+24 ) होता है। परीक्षा में (x) का गुणांक स्थिर पदों के योग से मिलता है।

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Question 12/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (m^-6)(m+2) ) का विस्तार क्या है?

What is the expansion of ( (m^-6)(m+2) )?

Explanation opens after your attempt

Correct Answer

A. \(m^2-4m-12\)सही विस्तार

Step 1

Concept

The sum of constants is (-6+2=-4) and product is (-12). Exam tip: pay attention to signs.

Step 2

Why this answer is correct

The correct answer is A. \(m^2-4m-12\) / सही विस्तार. The sum of constants is (-6+2=-4) and product is (-12). Exam tip: pay attention to signs.

Step 3

Exam Tip

स्थिर पदों का योग (-6+2=-4) और गुणन (-12) है। परीक्षा में चिह्नों का ध्यान रखें।

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Question 13/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( x^2+18x+81 \) किसका पूर्ण वर्ग है?

\( x^2+18x+81 \) is the perfect square of what?

Explanation opens after your attempt

Correct Answer

B. ( (x+9)² )सही रूप

Step 1

Concept

\(81=9^2\) and \(18x=2\cdot x\cdot9\). Exam tip: check the square root of the last term.

Step 2

Why this answer is correct

The correct answer is B. ( (x+9)² ) / सही रूप. \(81=9^2\) and \(18x=2\cdot x\cdot9\). Exam tip: check the square root of the last term.

Step 3

Exam Tip

\(81=9^2\) और \(18x=2\cdot x\cdot9\) है। परीक्षा में अंतिम पद का वर्गमूल देखें।

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Question 14/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( y^2-20y+100 \) को किस रूप में लिखा जा सकता है?

In which form can \( y^2-20y+100 \) be written?

Explanation opens after your attempt

Correct Answer

C. ( (y-10)² )सही रूप

Step 1

Concept

\(100=10^2\) and \(-20y=-2\cdot y\cdot10\). Exam tip: identify the minus square from the negative middle term.

Step 2

Why this answer is correct

The correct answer is C. ( (y-10)² ) / सही रूप. \(100=10^2\) and \(-20y=-2\cdot y\cdot10\). Exam tip: identify the minus square from the negative middle term.

Step 3

Exam Tip

\(100=10^2\) और \(-20y=-2\cdot y\cdot10\) है। परीक्षा में ऋण मध्य पद से घटाव वाला वर्ग पहचानें।

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Question 15/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 64a^2-25b^2 \) का सही गुणनखंडन क्या है?

What is the correct factorisation of \( 64a^2-25b^2 \)?

Explanation opens after your attempt

Correct Answer

C. ( (8a+5b)(8a-5b) )सही गुणनखंड

Step 1

Concept

This is ( (8a)²-(5b)² ). Exam tip: identify both terms as squares.

Step 2

Why this answer is correct

The correct answer is C. ( (8a+5b)(8a-5b) ) / सही गुणनखंड. This is ( (8a)²-(5b)² ). Exam tip: identify both terms as squares.

Step 3

Exam Tip

यह ( (8a)²-(5b)² ) है। परीक्षा में दोनों पदों को वर्ग के रूप में पहचानें।

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Question 16/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b)²+(a-b)² ) को सरल करने पर क्या मिलता है?

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

Explanation opens after your attempt

Correct Answer

B. \(2a^2+2b^2\)सही योग

Step 1

Concept

When the expansions are added, (+2ab) and (-2ab) cancel. Exam tip: add like terms.

Step 2

Why this answer is correct

The correct answer is B. \(2a^2+2b^2\) / सही योग. When the expansions are added, (+2ab) and (-2ab) cancel. Exam tip: add like terms.

Step 3

Exam Tip

दोनों विस्तार जोड़ने पर (+2ab) और (-2ab) कट जाते हैं। परीक्षा में समान पदों को जोड़ें।

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Question 17/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+y+4)² ) में (8x) किस जोड़ी से आता है?

In ( (x+y+4)² ), from which pair does (8x) come?

Explanation opens after your attempt

Correct Answer

B. (x) और (4)pair (x) and (4)

Step 1

Concept

\(8x=2\cdot x\cdot4\). Exam tip: identify pair products in the square of three terms.

Step 2

Why this answer is correct

The correct answer is B. (x) और (4) / pair (x) and (4). \(8x=2\cdot x\cdot4\). Exam tip: identify pair products in the square of three terms.

Step 3

Exam Tip

\(8x=2\cdot x\cdot4\) से आता है। परीक्षा में तीन पदों के वर्ग में जोड़ी गुणन पहचानें।

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Question 18/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b+c)² ) में कुल कितने दोहरे गुणन पद होते हैं?

How many double product terms are there in ( (a+b+c)² )?

Explanation opens after your attempt

Correct Answer

B. (3)तीन जोड़ी पद

Step 1

Concept

The double product terms are (2ab), (2bc), and (2ca). Exam tip: form three different pairs.

Step 2

Why this answer is correct

The correct answer is B. (3) / तीन जोड़ी पद. The double product terms are (2ab), (2bc), and (2ca). Exam tip: form three different pairs.

Step 3

Exam Tip

दोहरे गुणन पद (2ab), (2bc), और (2ca) हैं। परीक्षा में तीन अलग-अलग जोड़ियाँ बनाएं।

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Question 19/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (p+q+r)² ) में (2qr) क्यों आता है?

Why does (2qr) appear in ( (p+q+r)² )?

Explanation opens after your attempt

Correct Answer

A. क्योंकि (q) और (r) की जोड़ी का दोहरा गुणन होता हैBecause the pair (q) and (r) gives a double product

Step 1

Concept

In a three-term square, each pair gives a product term multiplied by (2). Exam tip: think in pairs.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि (q) और (r) की जोड़ी का दोहरा गुणन होता है / Because the pair (q) and (r) gives a double product. In a three-term square, each pair gives a product term multiplied by (2). Exam tip: think in pairs.

Step 3

Exam Tip

तीन पदों के वर्ग में हर दो पदों की जोड़ी से (2) गुणा पद आता है। परीक्षा में जोड़ी आधारित सोच रखें।

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Question 20/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

What will be the term containing (xy) in ( (2x+3y+z)² )?

Explanation opens after your attempt

Correct Answer

C. (12xy)सही दोहरा गुणन

Step 1

Concept

The (xy) term is \(2\cdot2x\cdot3y=12xy\). Exam tip: apply double product.

Step 2

Why this answer is correct

The correct answer is C. (12xy) / सही दोहरा गुणन. The (xy) term is \(2\cdot2x\cdot3y=12xy\). Exam tip: apply double product.

Step 3

Exam Tip

(xy) पद \(2\cdot2x\cdot3y=12xy\) है। परीक्षा में दोहरा गुणन लगाएँ।

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Question 21/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 103^2 \) का मान पहचान से निकालिए।

Find the value of \( 103^2 \) using an identity.

Explanation opens after your attempt

Correct Answer

A. (10609)

Step 1

Concept

(103²=(100+3)²=10000+600+9=10609). Exam tip: do not forget to add (2ab).

Step 2

Why this answer is correct

The correct answer is A. (10609). (103²=(100+3)²=10000+600+9=10609). Exam tip: do not forget to add (2ab).

Step 3

Exam Tip

(103²=(100+3)²=10000+600+9=10609)। परीक्षा में (2ab) जोड़ना न भूलें।

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Question 22/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 97^2 \) का मान ( (100-3)² ) से क्या होगा?

What is the value of \( 97^2 \) using ( (100-3)² )?

Explanation opens after your attempt

Correct Answer

A. (9409)

Step 1

Concept

\(97^2=10000-600+9=9409\). Exam tip: note the negative middle term.

Step 2

Why this answer is correct

The correct answer is A. (9409). \(97^2=10000-600+9=9409\). Exam tip: note the negative middle term.

Step 3

Exam Tip

\(97^2=10000-600+9=9409\) है। परीक्षा में घटाव वाले मध्य पद पर ध्यान दें।

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Question 23/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 54^2-46^2 \) को जल्दी कैसे सरल किया जा सकता है?

How can \( 54^2-46^2 \) be simplified quickly?

Explanation opens after your attempt

Correct Answer

A. ( (54+46)(54-46) )वर्गों का अंतर

Step 1

Concept

This is (a^-2-b^-2=(a+b)(a-b)). Exam tip: use this identity in difference of large squares.

Step 2

Why this answer is correct

The correct answer is A. ( (54+46)(54-46) ) / वर्गों का अंतर. This is (a^-2-b^-2=(a+b)(a-b)). Exam tip: use this identity in difference of large squares.

Step 3

Exam Tip

यह (a^-2-b^-2=(a+b)(a-b)) है। परीक्षा में बड़े वर्गों के अंतर में यह पहचान लगाएँ।

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Question 24/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 54^2-46^2 \) का सही मान क्या है?

What is the correct value of \( 54^2-46^2 \)?

Explanation opens after your attempt

Correct Answer

A. (800)

Step 1

Concept

( (54+46)(54-46)=100\cdot8=800 ). Exam tip: multiply the sum and difference.

Step 2

Why this answer is correct

The correct answer is A. (800). ( (54+46)(54-46)=100\cdot8=800 ). Exam tip: multiply the sum and difference.

Step 3

Exam Tip

( (54+46)(54-46)=100\cdot8=800 ) होता है। परीक्षा में योग और अंतर का गुणन करें।

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Question 25/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (5a-2b)² ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (5a-2b)² )?

Explanation opens after your attempt

Correct Answer

C. \(25a^2-20ab+4b^2\)सही विस्तार

Step 1

Concept

The middle term is \(-2\cdot5a\cdot2b=-20ab\). Exam tip: square with coefficients.

Step 2

Why this answer is correct

The correct answer is C. \(25a^2-20ab+4b^2\) / सही विस्तार. The middle term is \(-2\cdot5a\cdot2b=-20ab\). Exam tip: square with coefficients.

Step 3

Exam Tip

मध्य पद \(-2\cdot5a\cdot2b=-20ab\) है। परीक्षा में गुणांक सहित वर्ग करें।

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Question 26/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (7m+3n)(7m-3n) ) को सरल कीजिए।

Simplify ( (7m+3n)(7m-3n) ).

Explanation opens after your attempt

Correct Answer

A. \(49m^2-9n^2\)सही परिणाम

Step 1

Concept

This is ( (7m)²-(3n)² ). Exam tip: identify the ( (a+b)(a-b) ) identity.

Step 2

Why this answer is correct

The correct answer is A. \(49m^2-9n^2\) / सही परिणाम. This is ( (7m)²-(3n)² ). Exam tip: identify the ( (a+b)(a-b) ) identity.

Step 3

Exam Tip

यह ( (7m)²-(3n)² ) है। परीक्षा में ( (a+b)(a-b) ) पहचान पहचानें।

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Question 27/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x-4)(x+9) ) का विस्तार क्या है?

What is the expansion of ( (x-4)(x+9) )?

Explanation opens after your attempt

Correct Answer

B. \(x^2+5x-36\)सही विस्तार

Step 1

Concept

The sum of constants is (5) and the product is (-36). Exam tip: be careful with mixed signs.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+5x-36\) / सही विस्तार. The sum of constants is (5) and the product is (-36). Exam tip: be careful with mixed signs.

Step 3

Exam Tip

स्थिर पदों का योग (5) और गुणन (-36) है। परीक्षा में मिश्रित चिह्नों में सावधानी रखें।

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Question 28/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x-7)(2x+7) ) में कौन-सा पद नहीं आएगा?

Which term will not appear in ( (2x-7)(2x+7) )?

Explanation opens after your attempt

Correct Answer

C. (28x)मध्य पद

Step 1

Concept

Due to opposite signs, the middle term cancels. Exam tip: ( (a+b)(a-b) ) has no middle term.

Step 2

Why this answer is correct

The correct answer is C. (28x) / मध्य पद. Due to opposite signs, the middle term cancels. Exam tip: ( (a+b)(a-b) ) has no middle term.

Step 3

Exam Tip

विपरीत चिह्नों के कारण मध्य पद कट जाता है। परीक्षा में ( (a+b)(a-b) ) में मध्य पद नहीं आता।

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Question 29/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

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

Explanation opens after your attempt

Correct Answer

B. (8ab)सही मान

Step 1

Concept

This uses the (4ab) identity with second term (2b), so \(4\cdot a\cdot2b=8ab\). Exam tip: take the full second term.

Step 2

Why this answer is correct

The correct answer is B. (8ab) / सही मान. This uses the (4ab) identity with second term (2b), so \(4\cdot a\cdot2b=8ab\). Exam tip: take the full second term.

Step 3

Exam Tip

यह (4ab) पहचान है जहाँ दूसरा पद (2b) है, इसलिए \(4\cdot a\cdot2b=8ab\)। परीक्षा में दूसरे पद को पूरा लें।

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Question 30/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3x+2)²+(3x-2)² ) को सरल करने पर क्या मिलेगा?

What is obtained by simplifying ( (3x+2)²+(3x-2)² )?

Explanation opens after your attempt

Correct Answer

A. \(18x^2+8\)सही परिणाम

Step 1

Concept

Using the sum identity gives (2(3x)²+2(2)²=18x^-2+8). Exam tip: middle terms cancel.

Step 2

Why this answer is correct

The correct answer is A. \(18x^2+8\) / सही परिणाम. Using the sum identity gives (2(3x)²+2(2)²=18x^-2+8). Exam tip: middle terms cancel.

Step 3

Exam Tip

योग पहचान से (2(3x)²+2(2)²=18x^-2+8) मिलता है। परीक्षा में मध्य पद कटते हैं।

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Question 31/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( x^2-49 \) को गुणनखंडों में लिखिए।

Write \( x^2-49 \) in factors.

Explanation opens after your attempt

Correct Answer

B. ( (x+7)(x-7) )सही रूप

Step 1

Concept

Since \(49=7^2\), (x^-2-49=(x+7)(x-7)). Exam tip: identify square roots.

Step 2

Why this answer is correct

The correct answer is B. ( (x+7)(x-7) ) / सही रूप. Since \(49=7^2\), (x^-2-49=(x+7)(x-7)). Exam tip: identify square roots.

Step 3

Exam Tip

\(49=7^2\) इसलिए (x^-2-49=(x+7)(x-7))। परीक्षा में वर्गमूल पहचानें।

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Question 32/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 121-4y^2 \) का गुणनखंडन क्या है?

What is the factorisation of \( 121-4y^2 \)?

Explanation opens after your attempt

Correct Answer

A. ( (11+2y)(11-2y) )सही रूप

Step 1

Concept

\(121=11^2\) and (4y^-2=(2y)²). Exam tip: identify both squares.

Step 2

Why this answer is correct

The correct answer is A. ( (11+2y)(11-2y) ) / सही रूप. \(121=11^2\) and (4y^-2=(2y)²). Exam tip: identify both squares.

Step 3

Exam Tip

\(121=11^2\) और (4y^-2=(2y)²) है। परीक्षा में दोनों वर्गों को पहचानें।

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Question 33/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+5)² ) और \(x^2+25\) में अंतर क्या है?

What is the difference between ( (x+5)² ) and \(x^2+25\)?

Explanation opens after your attempt

Correct Answer

B. ( (x+5)² ) में (10x) अतिरिक्त होता है( (x+5)² ) has extra (10x)

Step 1

Concept

( (x+5)²=x^-2+10x+25 ). Exam tip: do not omit the middle term.

Step 2

Why this answer is correct

The correct answer is B. ( (x+5)² ) में (10x) अतिरिक्त होता है / ( (x+5)² ) has extra (10x). ( (x+5)²=x^-2+10x+25 ). Exam tip: do not omit the middle term.

Step 3

Exam Tip

( (x+5)²=x^-2+10x+25 ) है। परीक्षा में मध्य पद छोड़ने की गलती न करें।

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Question 34/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2p-3)² ) और \(4p^2-9\) में सही अंतर कौन-सा है?

What is the correct difference between ( (2p-3)² ) and \(4p^2-9\)?

Explanation opens after your attempt

Correct Answer

A. पहला \(4p^2-12p+9\) है और दूसरा ((2p+3)(2p-3)) हैFirst is \(4p^2-12p+9\) and second is ((2p+3)(2p-3))

Step 1

Concept

One is a perfect square and the other is difference of squares. Exam tip: distinguish bracket square from difference of squares.

Step 2

Why this answer is correct

The correct answer is A. पहला \(4p^2-12p+9\) है और दूसरा ((2p+3)(2p-3)) है / First is \(4p^2-12p+9\) and second is ((2p+3)(2p-3)). One is a perfect square and the other is difference of squares. Exam tip: distinguish bracket square from difference of squares.

Step 3

Exam Tip

एक पूर्ण वर्ग है और दूसरा वर्गों का अंतर है। परीक्षा में कोष्ठक वर्ग और वर्गों के अंतर को अलग पहचानें।

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Question 35/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+b+c)² ) में \(a^2+b^2+c^2\) के अलावा कौन-सा भाग जुड़ता है?

Apart from \(a^2+b^2+c^2\), what part is added in ( (a+b+c)² )?

Explanation opens after your attempt

Correct Answer

B. (2ab+2bc+2ca)सही भाग

Step 1

Concept

In the square of three terms, the double product of each pair is added. Exam tip: remember (2ab+2bc+2ca).

Step 2

Why this answer is correct

The correct answer is B. (2ab+2bc+2ca) / सही भाग. In the square of three terms, the double product of each pair is added. Exam tip: remember (2ab+2bc+2ca).

Step 3

Exam Tip

तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन जुड़ता है। परीक्षा में (2ab+2bc+2ca) याद रखें।

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Question 36/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

What is the term containing (yz) in ( (x+2y+3z)² )?

Explanation opens after your attempt

Correct Answer

C. (12yz)दोहरा गुणन

Step 1

Concept

The (yz) term is \(2\cdot2y\cdot3z=12yz\). Exam tip: do not forget the factor (2).

Step 2

Why this answer is correct

The correct answer is C. (12yz) / दोहरा गुणन. The (yz) term is \(2\cdot2y\cdot3z=12yz\). Exam tip: do not forget the factor (2).

Step 3

Exam Tip

(yz) पद \(2\cdot2y\cdot3z=12yz\) है। परीक्षा में (2) गुणक लगाना न भूलें।

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Question 37/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (4x+5)² ) का स्थिर पद कौन-सा है?

What is the constant term in ( (4x+5)² )?

Explanation opens after your attempt

Correct Answer

C. (25)सही स्थिर पद

Step 1

Concept

The constant term is \(5^2=25\). Exam tip: square the last number for the constant term.

Step 2

Why this answer is correct

The correct answer is C. (25) / सही स्थिर पद. The constant term is \(5^2=25\). Exam tip: square the last number for the constant term.

Step 3

Exam Tip

स्थिर पद \(5^2=25\) होता है। परीक्षा में स्थिर पद के लिए अंतिम संख्या का वर्ग करें।

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Question 38/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (6a-5b)² ) में (ab) का गुणांक क्या होगा?

What will be the coefficient of (ab) in ( (6a-5b)² )?

Explanation opens after your attempt

Correct Answer

C. - (60)सही गुणांक

Step 1

Concept

The middle term is \(-2\cdot6a\cdot5b=-60ab\). Exam tip: check both coefficient and sign.

Step 2

Why this answer is correct

The correct answer is C. - (60) / सही गुणांक. The middle term is \(-2\cdot6a\cdot5b=-60ab\). Exam tip: check both coefficient and sign.

Step 3

Exam Tip

मध्य पद \(-2\cdot6a\cdot5b=-60ab\) है। परीक्षा में गुणांक और चिह्न दोनों देखें।

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Question 39/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+6)(x-1) ) में स्थिर पद क्या है?

What is the constant term in ( (x+6)(x-1) )?

Explanation opens after your attempt

Correct Answer

B. - (6)सही स्थिर पद

Step 1

Concept

The constant term is (6\cdot(-1)=-6). Exam tip: multiply the constants.

Step 2

Why this answer is correct

The correct answer is B. - (6) / सही स्थिर पद. The constant term is (6\cdot(-1)=-6). Exam tip: multiply the constants.

Step 3

Exam Tip

स्थिर पद (6\cdot(-1)=-6) है। परीक्षा में स्थिर पदों का गुणन करें।

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Question 40/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+6)(x-1) ) में (x) का गुणांक कौन-सा है?

What is the coefficient of (x) in ( (x+6)(x-1) )?

Explanation opens after your attempt

Correct Answer

A. (5)सही गुणांक

Step 1

Concept

The sum of constants is (6+(-1)=5). Exam tip: take the coefficient of (x) from the sum of constants.

Step 2

Why this answer is correct

The correct answer is A. (5) / सही गुणांक. The sum of constants is (6+(-1)=5). Exam tip: take the coefficient of (x) from the sum of constants.

Step 3

Exam Tip

स्थिर पदों का योग (6+(-1)=5) है। परीक्षा में (x) का गुणांक स्थिर पदों के योग से लें।

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Question 41/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 1002^2 \) के लिए कौन-सा पहचान रूप सबसे उपयुक्त है?

Which identity form is most suitable for \( 1002^2 \)?

Explanation opens after your attempt

Correct Answer

A. ( (1000+2)² )सही रूप

Step 1

Concept

Since (1002=1000+2), the square of sum identity is useful. Exam tip: use a nearby base for large numbers.

Step 2

Why this answer is correct

The correct answer is A. ( (1000+2)² ) / सही रूप. Since (1002=1000+2), the square of sum identity is useful. Exam tip: use a nearby base for large numbers.

Step 3

Exam Tip

(1002=1000+2) इसलिए योग के वर्ग की पहचान उपयोगी है। परीक्षा में बड़ी संख्याओं में निकट आधार लें।

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Question 42/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 1002^2 \) का मान क्या है?

What is the value of \( 1002^2 \)?

Explanation opens after your attempt

Correct Answer

A. (1004004)सही मान

Step 1

Concept

\(1002^2=1000000+4000+4=1004004\). Exam tip: add \(2\cdot1000\cdot2\).

Step 2

Why this answer is correct

The correct answer is A. (1004004) / सही मान. \(1002^2=1000000+4000+4=1004004\). Exam tip: add \(2\cdot1000\cdot2\).

Step 3

Exam Tip

\(1002^2=1000000+4000+4=1004004\) है। परीक्षा में \(2\cdot1000\cdot2\) जोड़ें।

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Question 43/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 999^2 \) को किस रूप में निकालना सबसे आसान है?

Which form is easiest for finding \( 999^2 \)?

Explanation opens after your attempt

Correct Answer

B. ( (1000-1)² )सही रूप

Step 1

Concept

Since (999=1000-1), use the square of difference identity. Exam tip: take nearby base (1000).

Step 2

Why this answer is correct

The correct answer is B. ( (1000-1)² ) / सही रूप. Since (999=1000-1), use the square of difference identity. Exam tip: take nearby base (1000).

Step 3

Exam Tip

(999=1000-1) इसलिए घटाव के वर्ग की पहचान लगाएँ। परीक्षा में निकट आधार (1000) लें।

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Question 44/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (a+3b)²-(a-3b)² ) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (12ab)सही मान

Step 1

Concept

We get \(4\cdot a\cdot3b=12ab\). Exam tip: take the coefficient (3) with (b) fully.

Step 2

Why this answer is correct

The correct answer is C. (12ab) / सही मान. We get \(4\cdot a\cdot3b=12ab\). Exam tip: take the coefficient (3) with (b) fully.

Step 3

Exam Tip

\(4\cdot a\cdot3b=12ab\) मिलता है। परीक्षा में (b) के साथ गुणांक (3) को पूरा लें।

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Question 45/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

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

Explanation opens after your attempt

Correct Answer

A. (40x)सही परिणाम

Step 1

Concept

\(4\cdot5x\cdot4=80x\), not (40x). Exam tip: calculate (4ab) carefully.

Step 2

Why this answer is correct

The correct answer is A. (40x) / सही परिणाम. \(4\cdot5x\cdot4=80x\), not (40x). Exam tip: calculate (4ab) carefully.

Step 3

Exam Tip

\(4\cdot5x\cdot4=80x\) नहीं, ध्यान दें: (a=5x), (b=4), इसलिए (4ab=80x)।

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Question 46/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (5x+4)²-(5x-4)² ) का सही मान कौन-सा है?

Which is the correct value of ( (5x+4)²-(5x-4)² )?

Explanation opens after your attempt

Correct Answer

B. (80x)सही मान

Step 1

Concept

In ( (a+b)²-(a-b)²=4ab ), (a=5x) and (b=4), so (80x) is obtained. Exam tip: take the full (a).

Step 2

Why this answer is correct

The correct answer is B. (80x) / सही मान. In ( (a+b)²-(a-b)²=4ab ), (a=5x) and (b=4), so (80x) is obtained. Exam tip: take the full (a).

Step 3

Exam Tip

( (a+b)²-(a-b)²=4ab ) में (a=5x) और (b=4) है, इसलिए (80x) मिलता है। परीक्षा में पूरे (a) को लें।

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Question 47/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

What is the term containing (bc) in ( (2a+b+c)² )?

Explanation opens after your attempt

Correct Answer

B. (2bc)सही पद

Step 1

Concept

The pair (b) and (c) gives (2bc). Exam tip: take the double product of every pair.

Step 2

Why this answer is correct

The correct answer is B. (2bc) / सही पद. The pair (b) and (c) gives (2bc). Exam tip: take the double product of every pair.

Step 3

Exam Tip

(b) और (c) की जोड़ी से (2bc) आता है। परीक्षा में हर जोड़ी का दोहरा गुणन करें।

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Question 48/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (3u+2v+1)² ) में स्थिर पद क्या होगा?

What will be the constant term in ( (3u+2v+1)² )?

Explanation opens after your attempt

Correct Answer

A. (1)सही स्थिर पद

Step 1

Concept

The constant term is \(1^2=1\). Exam tip: the constant term comes from the square of the constant number.

Step 2

Why this answer is correct

The correct answer is A. (1) / सही स्थिर पद. The constant term is \(1^2=1\). Exam tip: the constant term comes from the square of the constant number.

Step 3

Exam Tip

स्थिर पद \(1^2=1\) है। परीक्षा में स्थिर पद केवल स्थिर संख्या के वर्ग से आता है।

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Question 49/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (x+y)²-x^-2-y^-2 ) को सरल कीजिए।

Simplify ( (x+y)²-x^-2-y^-2 ).

Explanation opens after your attempt

Correct Answer

B. (2xy)सही परिणाम

Step 1

Concept

( (x+y)²=x^-2+2xy+y^-2 ), so \(x^2\) and \(y^2\) cancel leaving (2xy). Exam tip: expand and subtract.

Step 2

Why this answer is correct

The correct answer is B. (2xy) / सही परिणाम. ( (x+y)²=x^-2+2xy+y^-2 ), so \(x^2\) and \(y^2\) cancel leaving (2xy). Exam tip: expand and subtract.

Step 3

Exam Tip

( (x+y)²=x^-2+2xy+y^-2 ), इसलिए \(x^2\) और \(y^2\) कटकर (2xy) बचता है। परीक्षा में विस्तार के बाद घटाएँ।

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Question 50/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

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

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

Explanation opens after your attempt

Correct Answer

B. - (2xy)सही परिणाम

Step 1

Concept

( (x-y)²=x^-2-2xy+y^-2 ), so (-2xy) remains. Exam tip: check the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. - (2xy) / सही परिणाम. ( (x-y)²=x^-2-2xy+y^-2 ), so (-2xy) remains. Exam tip: check the negative middle term.

Step 3

Exam Tip

( (x-y)²=x^-2-2xy+y^-2 ), इसलिए (-2xy) बचता है। परीक्षा में ऋण मध्य पद देखें।

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Question 51/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

( (2x+3)(2x-3) ) और ( (2x-3)² ) में मुख्य अंतर क्या है?

What is the main difference between ( (2x+3)(2x-3) ) and ( (2x-3)² )?

Explanation opens after your attempt

Correct Answer

A. पहला वर्गों का अंतर है, दूसरा पूर्ण वर्ग हैFirst is difference of squares, second is perfect square

Step 1

Concept

( (2x+3)(2x-3)=4x^-2-9 ) and ( (2x-3)²=4x^-2-12x+9 ). Exam tip: identify signs and brackets.

Step 2

Why this answer is correct

The correct answer is A. पहला वर्गों का अंतर है, दूसरा पूर्ण वर्ग है / First is difference of squares, second is perfect square. ( (2x+3)(2x-3)=4x^-2-9 ) and ( (2x-3)²=4x^-2-12x+9 ). Exam tip: identify signs and brackets.

Step 3

Exam Tip

( (2x+3)(2x-3)=4x^-2-9 ) और ( (2x-3)²=4x^-2-12x+9 )। परीक्षा में चिह्न और कोष्ठक पहचानें।

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Question 52/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

\( 39^2 \) को ( (40-1)² ) से निकालने पर कौन-सा मध्य पद घटेगा?

When finding \( 39^2 \) using ( (40-1)² ), which middle term will be subtracted?

Explanation opens after your attempt

Correct Answer

B. (80)सही मध्य पद

Step 1

Concept

( (40-1)²=40²-2\cdot40\cdot1+1 ), so (80) is subtracted. Exam tip: subtract (2ab).

Step 2

Why this answer is correct

The correct answer is B. (80) / सही मध्य पद. ( (40-1)²=40²-2\cdot40\cdot1+1 ), so (80) is subtracted. Exam tip: subtract (2ab).

Step 3

Exam Tip

( (40-1)²=40²-2\cdot40\cdot1+1 ), इसलिए (80) घटेगा। परीक्षा में (2ab) घटाएँ।

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Question 53/53 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 62

बीजीय पहचानों का सही उपयोग कब सबसे अधिक लाभ देता है?

When is the correct use of algebraic identities most useful?

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Correct Answer

A. जब व्यंजक को जल्दी विस्तार, सरल या गुणनखंड करना होWhen an expression has to be expanded, simplified or factorised quickly

Step 1

Concept

Identities make long calculations shorter and systematic. Exam tip: identify the identity first, then solve.

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Why this answer is correct

The correct answer is A. जब व्यंजक को जल्दी विस्तार, सरल या गुणनखंड करना हो / When an expression has to be expanded, simplified or factorised quickly. Identities make long calculations shorter and systematic. Exam tip: identify the identity first, then solve.

Step 3

Exam Tip

पहचानें लंबी गणना को छोटा और व्यवस्थित करती हैं। परीक्षा में पहले पहचान पहचानें फिर हल करें।

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

( (x+7)2 ) का पूरा विस्तार कौन-सा है?

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( (2x-5)2 ) का सही प्रसार कौन सा है?

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( (3y-4)2 ) में मध्य पद क्या होगा?

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( (3a+4b)(3a-4b) ) का सरल रूप क्या है?

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( (2a+5b)2 ) का सही विस्तार चुनिए।

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\( x^2+12x+36 \) किसका पूर्ण वर्ग है?

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( (p+9)(p-9) ) को सरल करने पर क्या मिलेगा?

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\( 96\times104 \) का मान पहचान से क्या होगा?

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\( 98^2 \) को पहचान से निकालने के लिए सबसे उपयोगी रूप कौन-सा है?

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( (x+3)2-(x-3)2 ) का सरल रूप क्या है?

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( (x+3)(x+8) ) में (x) का गुणांक क्या होगा?

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( (m-6)(m+2) ) का विस्तार क्या है?

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\( x^2+18x+81 \) किसका पूर्ण वर्ग है?

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\( y^2-20y+100 \) को किस रूप में लिखा जा सकता है?

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\( 64a^2-25b^2 \) का सही गुणनखंडन क्या है?

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( (a+b)2+(a-b)2 ) को सरल करने पर क्या मिलता है?

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( (x+y+4)2 ) में (8x) किस जोड़ी से आता है?

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( (a+b+c)2 ) में कुल कितने दोहरे गुणन पद होते हैं?

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( (p+q+r)2 ) में (2qr) क्यों आता है?

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

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( (x+7)² ) का पूरा विस्तार कौन-सा है?

( (2x-5)² ) का सही प्रसार कौन सा है?

( (3y-4)² ) में मध्य पद क्या होगा?

( (2a+5b)² ) का सही विस्तार चुनिए।

( (x+3)²-(x-3)² ) का सरल रूप क्या है?

( (m^-6)(m+2) ) का विस्तार क्या है?

( (a+b)²+(a-b)² ) को सरल करने पर क्या मिलता है?

( (x+y+4)² ) में (8x) किस जोड़ी से आता है?

( (a+b+c)² ) में कुल कितने दोहरे गुणन पद होते हैं?

( (p+q+r)² ) में (2qr) क्यों आता है?

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

\( 97^2 \) का मान ( (100-3)² ) से क्या होगा?

( (5a-2b)² ) का सही विस्तार कौन-सा है?

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

( (3x+2)²+(3x-2)² ) को सरल करने पर क्या मिलेगा?

( (x+5)² ) और \(x^2+25\) में अंतर क्या है?

( (2p-3)² ) और \(4p^2-9\) में सही अंतर कौन-सा है?

( (a+b+c)² ) में \(a^2+b^2+c^2\) के अलावा कौन-सा भाग जुड़ता है?

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

( (4x+5)² ) का स्थिर पद कौन-सा है?

( (6a-5b)² ) में (ab) का गुणांक क्या होगा?