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Mathematics Quiz - Class 9 Mathematics Medium Level 64 Quiz

Question 1/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+5)²-(2x-5)² ) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (40x)

Step 1

Concept

This is ( (a+b)²-(a-b)²=4ab ) where (a=2x) and (b=5). Exam tip: use the (4ab) identity quickly.

Step 2

Why this answer is correct

The correct answer is B. (40x). This is ( (a+b)²-(a-b)²=4ab ) where (a=2x) and (b=5). Exam tip: use the (4ab) identity quickly.

Step 3

Exam Tip

यह ( (a+b)²-(a-b)²=4ab ) है जहाँ (a=2x) और (b=5)। परीक्षा में (4ab) पहचान जल्दी लगाएँ।

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Question 2/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3a-4b)² ) का सही विस्तार चुनिए।

Choose the correct expansion of ( (3a-4b)² ).

Explanation opens after your attempt

Correct Answer

A. \(9a^2-24ab+16b^2\)

Step 1

Concept

In ( (a-b)² ) the middle term is negative. Exam tip: keep both coefficient squares and (2ab) correct.

Step 2

Why this answer is correct

The correct answer is A. \(9a^2-24ab+16b^2\). In ( (a-b)² ) the middle term is negative. Exam tip: keep both coefficient squares and (2ab) correct.

Step 3

Exam Tip

( (a-b)² ) में मध्य पद ऋणात्मक होता है। परीक्षा में गुणांक का वर्ग और (2ab) दोनों ध्यान रखें।

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Question 3/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+6)(x-2) ) का विस्तार क्या है?

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

Explanation opens after your attempt

Correct Answer

B. \(x^2+4x-12\)

Step 1

Concept

(6+(-2)=4) and \(6\times(-2)=-12\). Exam tip: check addition and multiplication with signs separately.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+4x-12\). (6+(-2)=4) and \(6\times(-2)=-12\). Exam tip: check addition and multiplication with signs separately.

Step 3

Exam Tip

(6+(-2)=4) और \(6\times(-2)=-12\)। परीक्षा में चिन्हों के साथ जोड़ और गुणन अलग जाँचें।

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Question 4/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 104^2-96^2 \) का मान क्या है?

What is the value of \( 104^2-96^2 \)?

Explanation opens after your attempt

Correct Answer

C. (1600)

Step 1

Concept

Using (a^-2-b^-2=(a+b)(a-b)), \(200\times8=1600\). Exam tip: convert difference of squares into a product.

Step 2

Why this answer is correct

The correct answer is C. (1600). Using (a^-2-b^-2=(a+b)(a-b)), \(200\times8=1600\). Exam tip: convert difference of squares into a product.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)) से \(200\times8=1600\)। परीक्षा में अंतर वर्ग को गुणनफल में बदलें।

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Question 5/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (5p+2q)(5p-2q) ) का गुणनफल क्या है?

What is the product of ( (5p+2q)(5p-2q) )?

Explanation opens after your attempt

Correct Answer

A. \(25p^2-4q^2\)

Step 1

Concept

This is ( (a+b)(a-b)=a^-2-b^-2 ). Exam tip: square ((5p)²) and ((2q)²) correctly.

Step 2

Why this answer is correct

The correct answer is A. \(25p^2-4q^2\). This is ( (a+b)(a-b)=a^-2-b^-2 ). Exam tip: square ((5p)²) and ((2q)²) correctly.

Step 3

Exam Tip

यह ( (a+b)(a-b)=a^-2-b^-2 ) का रूप है। परीक्षा में ((5p)²) और ((2q)²) सही करें।

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Question 6/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+3b+c)² ) में (6ab) किससे आता है?

In ( (a+3b+c)² ), where does (6ab) come from?

Explanation opens after your attempt

Correct Answer

B. \(2\times a\times3b\) सेFrom \(2\times a\times3b\)

Step 1

Concept

In the square of three terms, twice the product of each pair appears. Exam tip: identify the pair for mixed terms.

Step 2

Why this answer is correct

The correct answer is B. \(2\times a\times3b\) से / From \(2\times a\times3b\). In the square of three terms, twice the product of each pair appears. Exam tip: identify the pair for mixed terms.

Step 3

Exam Tip

तीन पदों के वर्ग में हर जोड़े का दुगुना गुणन आता है। परीक्षा में मिश्र पदों की जोड़ी पहचानें।

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Question 7/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+y+3)² ) में (x) वाला रैखिक पद क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (12x)

Step 1

Concept

\(2\times2x\times3=12x\) gives the linear (x) term. Exam tip: identify the mixed term formed with the constant separately.

Step 2

Why this answer is correct

The correct answer is B. (12x). \(2\times2x\times3=12x\) gives the linear (x) term. Exam tip: identify the mixed term formed with the constant separately.

Step 3

Exam Tip

\(2\times2x\times3=12x\) रैखिक (x) पद देता है। परीक्षा में स्थिर पद के साथ बने मिश्र पद को अलग पहचानें।

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Question 8/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x-5)²+(x+5)² ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

On adding, (10x) and (-10x) cancel. Exam tip: notice cancellation of opposite middle terms.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+50\). On adding, (10x) and (-10x) cancel. Exam tip: notice cancellation of opposite middle terms.

Step 3

Exam Tip

जोड़ने पर (10x) और (-10x) कट जाते हैं। परीक्षा में विपरीत मध्य पदों के कटने को पहचानें।

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Question 9/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (m+4)²-\(m^2+16\) ) का मान क्या है?

What is the value of ( (m+4)²-\(m^2+16\) )?

Explanation opens after your attempt

Correct Answer

B. (8m)

Step 1

Concept

( (m+4)²=m^-2+8m+16 ), so subtracting \(m^2+16\) leaves (8m). Exam tip: cancel like terms.

Step 2

Why this answer is correct

The correct answer is B. (8m). ( (m+4)²=m^-2+8m+16 ), so subtracting \(m^2+16\) leaves (8m). Exam tip: cancel like terms.

Step 3

Exam Tip

( (m+4)²=m^-2+8m+16 ) है इसलिए \(m^2+16\) घटाने पर (8m) बचेगा। परीक्षा में समान पद काटें।

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Question 10/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 87\times93 \) को पहचान से निकालने पर उत्तर क्या है?

What is \( 87\times93 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. (8091)

Step 1

Concept

(87\times93=(90-3)(90+3)=90²-3²=8091). Exam tip: use \(a^2-b^2\) for numbers around the same centre.

Step 2

Why this answer is correct

The correct answer is A. (8091). (87\times93=(90-3)(90+3)=90²-3²=8091). Exam tip: use \(a^2-b^2\) for numbers around the same centre.

Step 3

Exam Tip

(87\times93=(90-3)(90+3)=90²-3²=8091)। परीक्षा में समान केंद्र वाली संख्याओं पर \(a^2-b^2\) लगाएँ।

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Question 11/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (4x-3)(4x+3)+9 ) को सरल कीजिए।

Simplify ( (4x-3)(4x+3)+9 ).

Explanation opens after your attempt

Correct Answer

B. \(16x^2\)

Step 1

Concept

( (4x-3)(4x+3)=16x^-2-9 ), and (+9) gives \(16x^2\). Exam tip: identify difference of squares first.

Step 2

Why this answer is correct

The correct answer is B. \(16x^2\). ( (4x-3)(4x+3)=16x^-2-9 ), and (+9) gives \(16x^2\). Exam tip: identify difference of squares first.

Step 3

Exam Tip

( (4x-3)(4x+3)=16x^-2-9 ) और (+9) से \(16x^2\) मिलता है। परीक्षा में पहले अंतर वर्ग पहचानें।

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Question 12/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+2)(x+7) ) में स्थिर पद और (x) का गुणांक क्रमशः क्या हैं?

In ( (x+2)(x+7) ), what are the constant term and coefficient of (x) respectively?

Explanation opens after your attempt

Correct Answer

A. (14) और (9)(14) and (9)

Step 1

Concept

The constant term is \(2\times7=14\) and the coefficient of (x) is (2+7=9). Exam tip: keep sum and product separate.

Step 2

Why this answer is correct

The correct answer is A. (14) और (9) / (14) and (9). The constant term is \(2\times7=14\) and the coefficient of (x) is (2+7=9). Exam tip: keep sum and product separate.

Step 3

Exam Tip

स्थिर पद \(2\times7=14\) और (x) का गुणांक (2+7=9) है। परीक्षा में योग और गुणन अलग रखें।

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Question 13/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( x^2-22x+121 \) का गुणनखंड रूप क्या है?

What is the factor form of \( x^2-22x+121 \)?

Explanation opens after your attempt

Correct Answer

C. ( (x-11)² )

Step 1

Concept

\(121=11^2\) and the middle term is \(-22x=-2\times x\times11\). Exam tip: identify ((a-b)²) from the negative middle term.

Step 2

Why this answer is correct

The correct answer is C. ( (x-11)² ). \(121=11^2\) and the middle term is \(-22x=-2\times x\times11\). Exam tip: identify ((a-b)²) from the negative middle term.

Step 3

Exam Tip

\(121=11^2\) और मध्य पद \(-22x=-2\times x\times11\) है। परीक्षा में ऋणात्मक मध्य पद से ((a-b)²) पहचानें।

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Question 14/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (7a+2b)²-(7a-2b)² ) का मान क्या है?

What is the value of ( (7a+2b)²-(7a-2b)² )?

Explanation opens after your attempt

Correct Answer

C. (56ab)

Step 1

Concept

This is (4AB) where (A=7a) and (B=2b). Exam tip: calculate \(4\times7a\times2b=56ab\).

Step 2

Why this answer is correct

The correct answer is C. (56ab). This is (4AB) where (A=7a) and (B=2b). Exam tip: calculate \(4\times7a\times2b=56ab\).

Step 3

Exam Tip

यह (4AB) है जहाँ (A=7a) और (B=2b)। परीक्षा में \(4\times7a\times2b=56ab\) करें।

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Question 15/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. \(8p^2+18q^2\)

Step 1

Concept

( (A+B)²+(A-B)²=2A^-2+2B^-2 ). Exam tip: mixed terms cancel.

Step 2

Why this answer is correct

The correct answer is A. \(8p^2+18q^2\). ( (A+B)²+(A-B)²=2A^-2+2B^-2 ). Exam tip: mixed terms cancel.

Step 3

Exam Tip

( (A+B)²+(A-B)²=2A^-2+2B^-2 ) है। परीक्षा में मिश्र पद कट जाते हैं।

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Question 16/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 203^2 \) निकालने के लिए सबसे उपयोगी रूप कौन सा है?

Which is the most useful form to find \( 203^2 \)?

Explanation opens after your attempt

Correct Answer

A. ( (200+3)² )

Step 1

Concept

Writing (203) as (200+3) is easy. Exam tip: split a large number near a simple number.

Step 2

Why this answer is correct

The correct answer is A. ( (200+3)² ). Writing (203) as (200+3) is easy. Exam tip: split a large number near a simple number.

Step 3

Exam Tip

(203) को (200+3) लिखना आसान है। परीक्षा में बड़ी संख्या को निकट सरल संख्या से तोड़ें।

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Question 17/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 197^2 \) का मान पहचान से क्या होगा?

What is the value of \( 197^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. (38809)

Step 1

Concept

(197=200-3), so ( (200-3)²=40000-1200+9=38809 ). Exam tip: subtract the middle term in ( (a-b)² ).

Step 2

Why this answer is correct

The correct answer is A. (38809). (197=200-3), so ( (200-3)²=40000-1200+9=38809 ). Exam tip: subtract the middle term in ( (a-b)² ).

Step 3

Exam Tip

(197=200-3) इसलिए ( (200-3)²=40000-1200+9=38809 )। परीक्षा में ( (a-b)² ) में मध्य पद घटाएँ।

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Question 18/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+y)²-\(x^2+y^2\) ) किसके बराबर है?

What is ( (x+y)²-\(x^2+y^2\) ) equal to?

Explanation opens after your attempt

Correct Answer

B. (2xy)

Step 1

Concept

( (x+y)²=x^-2+2xy+y^-2 ), so subtracting \(x^2+y^2\) leaves (2xy). Exam tip: identify the middle term.

Step 2

Why this answer is correct

The correct answer is B. (2xy). ( (x+y)²=x^-2+2xy+y^-2 ), so subtracting \(x^2+y^2\) leaves (2xy). Exam tip: identify the middle term.

Step 3

Exam Tip

( (x+y)²=x^-2+2xy+y^-2 ) है इसलिए \(x^2+y^2\) घटाने पर (2xy) बचता है। परीक्षा में मध्य पद पहचानें।

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Question 19/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (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)

Step 1

Concept

( (x-y)²=x^-2-2xy+y^-2 ), subtracting \(x^2+y^2\) gives (-2xy). Exam tip: watch the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. (-2xy). ( (x-y)²=x^-2-2xy+y^-2 ), subtracting \(x^2+y^2\) gives (-2xy). Exam tip: watch the negative middle term.

Step 3

Exam Tip

( (x-y)²=x^-2-2xy+y^-2 ) से \(x^2+y^2\) घटाने पर (-2xy) मिलता है। परीक्षा में ऋणात्मक मध्य पद पर ध्यान दें।

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Question 20/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b+c)²-\(a^2+b^2+c^2\) ) का मान क्या है?

What is the value of ( (a+b+c)²-\(a^2+b^2+c^2\) )?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

In the square of three terms, the extra mixed terms are (2ab+2bc+2ca). Exam tip: remember all three pairs.

Step 2

Why this answer is correct

The correct answer is B. (2ab+2bc+2ca). In the square of three terms, the extra mixed terms are (2ab+2bc+2ca). Exam tip: remember all three pairs.

Step 3

Exam Tip

तीन पदों के वर्ग में अतिरिक्त मिश्र पद (2ab+2bc+2ca) होते हैं। परीक्षा में सभी तीन जोड़े याद रखें।

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Question 21/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+4)(x-9) ) का विस्तार कौन सा है?

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

Explanation opens after your attempt

Correct Answer

A. \(x^2-5x-36\)

Step 1

Concept

(4+(-9)=-5) and \(4\times(-9)=-36\). Exam tip: add signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-5x-36\). (4+(-9)=-5) and \(4\times(-9)=-36\). Exam tip: add signs carefully.

Step 3

Exam Tip

(4+(-9)=-5) और \(4\times(-9)=-36\)। परीक्षा में चिन्हों को ध्यान से जोड़ें।

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Question 22/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x-8)(x-3) ) में (x) का गुणांक क्या है?

What is the coefficient of (x) in ( (x-8)(x-3) )?

Explanation opens after your attempt

Correct Answer

B. (-11)

Step 1

Concept

((-8)+(-3)=-11), so the coefficient of (x) is (-11). Exam tip: the sum of two negative numbers remains negative.

Step 2

Why this answer is correct

The correct answer is B. (-11). ((-8)+(-3)=-11), so the coefficient of (x) is (-11). Exam tip: the sum of two negative numbers remains negative.

Step 3

Exam Tip

((-8)+(-3)=-11) इसलिए (x) का गुणांक (-11) है। परीक्षा में दो ऋण संख्याओं का योग ऋणात्मक रहता है।

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Question 23/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( x^2-144 \) का सही गुणनखंड रूप क्या है?

What is the correct factor form of \( x^2-144 \)?

Explanation opens after your attempt

Correct Answer

A. ( (x+12)(x-12) )

Step 1

Concept

Since \(144=12^2\), this is the form \(a^2-b^2\). Exam tip: identify perfect squares.

Step 2

Why this answer is correct

The correct answer is A. ( (x+12)(x-12) ). Since \(144=12^2\), this is the form \(a^2-b^2\). Exam tip: identify perfect squares.

Step 3

Exam Tip

\(144=12^2\) इसलिए यह \(a^2-b^2\) का रूप है। परीक्षा में पूर्ण वर्ग पहचानें।

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Question 24/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 9x^2-64y^2 \) का गुणनखंड क्या है?

What are the factors of \( 9x^2-64y^2 \)?

Explanation opens after your attempt

Correct Answer

B. ( (3x+8y)(3x-8y) )

Step 1

Concept

(9x^-2=(3x)²) and (64y^-2=(8y)²). Exam tip: view both terms as squares.

Step 2

Why this answer is correct

The correct answer is B. ( (3x+8y)(3x-8y) ). (9x^-2=(3x)²) and (64y^-2=(8y)²). Exam tip: view both terms as squares.

Step 3

Exam Tip

(9x^-2=(3x)²) और (64y^-2=(8y)²) है। परीक्षा में दोनों पदों को वर्ग बनाकर देखें।

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Question 25/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2a+b+c)² ) में (2bc) के अलावा कौन से मिश्र पद आते हैं?

In ( (2a+b+c)² ), which mixed terms come besides (2bc)?

Explanation opens after your attempt

Correct Answer

A. (4ab) और (4ac)(4ab) and (4ac)

Step 1

Concept

The mixed terms are (2(2a)(b)=4ab) and (2(2a)(c)=4ac). Exam tip: form mixed terms with coefficients.

Step 2

Why this answer is correct

The correct answer is A. (4ab) और (4ac) / (4ab) and (4ac). The mixed terms are (2(2a)(b)=4ab) and (2(2a)(c)=4ac). Exam tip: form mixed terms with coefficients.

Step 3

Exam Tip

मिश्र पद (2(2a)(b)=4ab) और (2(2a)(c)=4ac) होते हैं। परीक्षा में गुणांक सहित मिश्र पद बनाएँ।

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Question 26/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+5)²-(x-5)² ) का मान (80) है तो (x) का मान क्या है?

If ( (x+5)²-(x-5)² ) is (80), what is (x)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

This difference equals (20x), so (20x=80). Exam tip: use the identity first to simplify the equation.

Step 2

Why this answer is correct

The correct answer is B. (4). This difference equals (20x), so (20x=80). Exam tip: use the identity first to simplify the equation.

Step 3

Exam Tip

यह अंतर (20x) के बराबर है इसलिए (20x=80)। परीक्षा में पहले पहचान लगाकर समीकरण सरल करें।

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Question 27/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि ( (x+3)²=x^-2+kx+9 ) है तो (k) का मान क्या होगा?

If ( (x+3)²=x^-2+kx+9 ), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

The middle term is \(2\times x\times3=6x\), so (k=6). Exam tip: find the coefficient from the middle term.

Step 2

Why this answer is correct

The correct answer is B. (6). The middle term is \(2\times x\times3=6x\), so (k=6). Exam tip: find the coefficient from the middle term.

Step 3

Exam Tip

मध्य पद \(2\times x\times3=6x\) है इसलिए (k=6)। परीक्षा में मध्य पद से गुणांक निकालें।

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Question 28/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि ( (x-7)²=x^-2-kx+49 ) है तो (k) कितना है?

If ( (x-7)²=x^-2-kx+49 ), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (14)

Step 1

Concept

The middle term is (-14x), so (k=14). Exam tip: in (-kx), (k) is the positive coefficient.

Step 2

Why this answer is correct

The correct answer is B. (14). The middle term is (-14x), so (k=14). Exam tip: in (-kx), (k) is the positive coefficient.

Step 3

Exam Tip

मध्य पद (-14x) है इसलिए (k=14)। परीक्षा में (-kx) में (k) धनात्मक संख्या है।

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Question 29/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3x+1)²-\(9x^2+1\) ) को सरल कीजिए।

Simplify ( (3x+1)²-\(9x^2+1\) ).

Explanation opens after your attempt

Correct Answer

B. (6x)

Step 1

Concept

( (3x+1)²=9x^-2+6x+1 ). Exam tip: subtract like terms after expansion.

Step 2

Why this answer is correct

The correct answer is B. (6x). ( (3x+1)²=9x^-2+6x+1 ). Exam tip: subtract like terms after expansion.

Step 3

Exam Tip

( (3x+1)²=9x^-2+6x+1 ) है। परीक्षा में वर्ग के बाद समान पद घटाएँ।

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Question 30/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (-40a)

Step 1

Concept

The expansion is \(16a^2-40a+25\), so like terms cancel leaving (-40a). Exam tip: do not forget the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. (-40a). The expansion is \(16a^2-40a+25\), so like terms cancel leaving (-40a). Exam tip: do not forget the negative middle term.

Step 3

Exam Tip

विस्तार \(16a^2-40a+25\) है इसलिए समान पद घटकर (-40a) बचता है। परीक्षा में ऋणात्मक मध्य पद न भूलें।

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Question 31/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 62^2-38^2 \) का मान पहचान से निकालिए।

Find \( 62^2-38^2 \) using an identity.

Explanation opens after your attempt

Correct Answer

A. (2400)

Step 1

Concept

(62²-38²=(62+38)(62-38)=100\times24=2400). Exam tip: do addition and subtraction first.

Step 2

Why this answer is correct

The correct answer is A. (2400). (62²-38²=(62+38)(62-38)=100\times24=2400). Exam tip: do addition and subtraction first.

Step 3

Exam Tip

(62²-38²=(62+38)(62-38)=100\times24=2400)। परीक्षा में जोड़ और घटाव पहले करें।

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Question 32/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 58\times42 \) का मान ( (50+8)(50-8) ) से क्या होगा?

What is the value of \( 58\times42 \) using ( (50+8)(50-8) )?

Explanation opens after your attempt

Correct Answer

A. (2436)

Step 1

Concept

\(50^2-8^2=2500-64=2436\). Exam tip: identify the common centre (50).

Step 2

Why this answer is correct

The correct answer is A. (2436). \(50^2-8^2=2500-64=2436\). Exam tip: identify the common centre (50).

Step 3

Exam Tip

\(50^2-8^2=2500-64=2436\)। परीक्षा में समान केंद्र (50) पहचानें।

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Question 33/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+a)(x+b) ) में (x) का गुणांक क्या होता है?

What is the coefficient of (x) in ( (x+a)(x+b) )?

Explanation opens after your attempt

Correct Answer

C. (a+b)

Step 1

Concept

The expansion is (x^-2+(a+b)x+ab). Exam tip: the coefficient of (x) is the sum of constants.

Step 2

Why this answer is correct

The correct answer is C. (a+b). The expansion is (x^-2+(a+b)x+ab). Exam tip: the coefficient of (x) is the sum of constants.

Step 3

Exam Tip

विस्तार (x^-2+(a+b)x+ab) होता है। परीक्षा में (x) का गुणांक स्थिर पदों का योग होता है।

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Question 34/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x-2)(x+11) ) में स्थिर पद क्या है?

What is the constant term in ( (x-2)(x+11) )?

Explanation opens after your attempt

Correct Answer

B. (-22)

Step 1

Concept

The constant term is ((-2)\times11=-22). Exam tip: multiply the constants to get the constant term.

Step 2

Why this answer is correct

The correct answer is B. (-22). The constant term is ((-2)\times11=-22). Exam tip: multiply the constants to get the constant term.

Step 3

Exam Tip

स्थिर पद ((-2)\times11=-22) है। परीक्षा में स्थिर पद पाने के लिए स्थिर संख्याओं का गुणन करें।

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Question 35/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+3)(2x-7) ) का विस्तार क्या है?

What is the expansion of ( (2x+3)(2x-7) )?

Explanation opens after your attempt

Correct Answer

A. \(4x^2-8x-21\)

Step 1

Concept

( (2x)(2x)=4x^-2 ), ( -14x+6x=-8x ), and \(3\times(-7)=-21\). Exam tip: combine like terms.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2-8x-21\). ( (2x)(2x)=4x^-2 ), ( -14x+6x=-8x ), and \(3\times(-7)=-21\). Exam tip: combine like terms.

Step 3

Exam Tip

( (2x)(2x)=4x^-2 ), ( -14x+6x=-8x ), और \(3\times(-7)=-21\)। परीक्षा में समान पद जोड़ें।

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Question 36/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b)² ) और \(a^2+b^2\) का अंतर क्या है?

What is the difference between ( (a+b)² ) and \(a^2+b^2\)?

Explanation opens after your attempt

Correct Answer

B. (2ab)

Step 1

Concept

( (a+b)²=a^-2+2ab+b^-2 ). Exam tip: a common mistake is leaving out (2ab).

Step 2

Why this answer is correct

The correct answer is B. (2ab). ( (a+b)²=a^-2+2ab+b^-2 ). Exam tip: a common mistake is leaving out (2ab).

Step 3

Exam Tip

( (a+b)²=a^-2+2ab+b^-2 ) होता है। परीक्षा में यह आम गलती है कि (2ab) छोड़ दिया जाता है।

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Question 37/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a-b)² ) और \(a^2-b^2\) का अंतर क्या है?

What is the difference between ( (a-b)² ) and \(a^2-b^2\)?

Explanation opens after your attempt

Correct Answer

A. \(2b^2-2ab\)

Step 1

Concept

( (a-b)²=a^-2-2ab+b^-2 ), so subtracting \(a^2-b^2\) gives \(2b^2-2ab\). Exam tip: keep both identities separate.

Step 2

Why this answer is correct

The correct answer is A. \(2b^2-2ab\). ( (a-b)²=a^-2-2ab+b^-2 ), so subtracting \(a^2-b^2\) gives \(2b^2-2ab\). Exam tip: keep both identities separate.

Step 3

Exam Tip

( (a-b)²=a^-2-2ab+b^-2 ) है इसलिए \(a^2-b^2\) घटाने पर \(2b^2-2ab\) मिलता है। परीक्षा में दोनों पहचान अलग रखें।

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Question 38/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि (x+y=9) और (xy=14) है तो \(x^2+y^2\) कितना होगा?

If (x+y=9) and (xy=14), what is \(x^2+y^2\)?

Explanation opens after your attempt

Correct Answer

A. (53)

Step 1

Concept

(x^-2+y^-2=(x+y)²-2xy=81-28=53). Exam tip: use the given sum and product.

Step 2

Why this answer is correct

The correct answer is A. (53). (x^-2+y^-2=(x+y)²-2xy=81-28=53). Exam tip: use the given sum and product.

Step 3

Exam Tip

(x^-2+y^-2=(x+y)²-2xy=81-28=53)। परीक्षा में दिए गए योग और गुणन का उपयोग करें।

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Question 39/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि (p-q=5) और (pq=6) है तो \(p^2+q^2\) का मान क्या है?

If (p-q=5) and (pq=6), what is \(p^2+q^2\)?

Explanation opens after your attempt

Correct Answer

B. (37)

Step 1

Concept

(p^-2+q^-2=(p-q)²+2pq=25+12=37). Exam tip: rearrange using ( (p-q)²=p^-2-2pq+q^-2 ).

Step 2

Why this answer is correct

The correct answer is B. (37). (p^-2+q^-2=(p-q)²+2pq=25+12=37). Exam tip: rearrange using ( (p-q)²=p^-2-2pq+q^-2 ).

Step 3

Exam Tip

(p^-2+q^-2=(p-q)²+2pq=25+12=37)। परीक्षा में ( (p-q)²=p^-2-2pq+q^-2 ) से रूप बदलें।

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Question 40/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि (a+b=10) और (a-b=4) है तो \(a^2-b^2\) कितना होगा?

If (a+b=10) and (a-b=4), what is \(a^2-b^2\)?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

(a^-2-b^-2=(a+b)(a-b)=10\times4=40). Exam tip: directly use the difference of squares identity.

Step 2

Why this answer is correct

The correct answer is C. (40). (a^-2-b^-2=(a+b)(a-b)=10\times4=40). Exam tip: directly use the difference of squares identity.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)=10\times4=40)। परीक्षा में अंतर वर्ग पहचान का सीधा प्रयोग करें।

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Question 41/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+1)(x+2)(x+3) ) को पहले दो गुणनखंडों से शुरू कर सरल करने पर कौन सा मध्य चरण सही है?

When simplifying ( (x+1)(x+2)(x+3) ) starting with the first two factors, which middle step is correct?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

( (x+1)(x+2)=x^-2+3x+2 ). Exam tip: do long expressions in smaller steps.

Step 2

Why this answer is correct

The correct answer is A. ( \(x^2+3x+2\)(x+3) ). ( (x+1)(x+2)=x^-2+3x+2 ). Exam tip: do long expressions in smaller steps.

Step 3

Exam Tip

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

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Question 42/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

A. (4x+8)

Step 1

Concept

The first part is \(x^2+4x+4\) and the second is \(x^2-4\). Subtraction gives (4x+8).

Step 2

Why this answer is correct

The correct answer is A. (4x+8). The first part is \(x^2+4x+4\) and the second is \(x^2-4\). Subtraction gives (4x+8).

Step 3

Exam Tip

पहला भाग \(x^2+4x+4\) और दूसरा \(x^2-4\) है। घटाने पर (4x+8) मिलता है।

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Question 43/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3x+2)²+(3x-2)² ) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(18x^2+8\)

Step 1

Concept

Use \(2A^2+2B^2\) where (A=3x) and (B=2). Exam tip: mixed terms cancel.

Step 2

Why this answer is correct

The correct answer is A. \(18x^2+8\). Use \(2A^2+2B^2\) where (A=3x) and (B=2). Exam tip: mixed terms cancel.

Step 3

Exam Tip

\(2A^2+2B^2\) लगाएँ जहाँ (A=3x) और (B=2)। परीक्षा में मिश्र पद कटते हैं।

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Question 44/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x-5)² ) में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in ( (2x-5)² )?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

((2x)²=4x^-2), so the coefficient of \(x^2\) is (4). Exam tip: square the coefficient too.

Step 2

Why this answer is correct

The correct answer is B. (4). ((2x)²=4x^-2), so the coefficient of \(x^2\) is (4). Exam tip: square the coefficient too.

Step 3

Exam Tip

((2x)²=4x^-2) इसलिए \(x^2\) का गुणांक (4) है। परीक्षा में गुणांक का भी वर्ग करें।

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Question 45/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

((3y)²=9y^-2). Exam tip: do not forget to square the coefficient in the last term.

Step 2

Why this answer is correct

The correct answer is C. (9). ((3y)²=9y^-2). Exam tip: do not forget to square the coefficient in the last term.

Step 3

Exam Tip

((3y)²=9y^-2) है। परीक्षा में अंतिम पद में गुणांक का वर्ग लेना न भूलें।

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Question 46/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+5)(x-5) ) और ( (x-5)² ) में क्या मुख्य अंतर है?

What is the main difference between ( (x+5)(x-5) ) and ( (x-5)² )?

Explanation opens after your attempt

Correct Answer

A. पहला \(x^2-25\) है और दूसरा \(x^2-10x+25\) हैThe first is \(x^2-25\) and the second is \(x^2-10x+25\)

Step 1

Concept

In opposite-sign product mixed terms cancel but in a square the middle term remains. Exam tip: do not mix the two forms.

Step 2

Why this answer is correct

The correct answer is A. पहला \(x^2-25\) है और दूसरा \(x^2-10x+25\) है / The first is \(x^2-25\) and the second is \(x^2-10x+25\). In opposite-sign product mixed terms cancel but in a square the middle term remains. Exam tip: do not mix the two forms.

Step 3

Exam Tip

विपरीत चिन्ह वाले गुणन में मिश्र पद कटता है पर वर्ग में मध्य पद रहता है। परीक्षा में दोनों रूपों को न मिलाएँ।

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Question 47/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+2y+3z)² ) में (12yz) किस जोड़ी से आता है?

In ( (x+2y+3z)² ), from which pair does (12yz) come?

Explanation opens after your attempt

Correct Answer

C. (2y) और (3z)(2y) and (3z)

Step 1

Concept

\(2\times2y\times3z=12yz\). Exam tip: find the pair for each mixed term.

Step 2

Why this answer is correct

The correct answer is C. (2y) और (3z) / (2y) and (3z). \(2\times2y\times3z=12yz\). Exam tip: find the pair for each mixed term.

Step 3

Exam Tip

\(2\times2y\times3z=12yz\) होता है। परीक्षा में हर मिश्र पद की जोड़ी खोजें।

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Question 48/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a-b+c)² ) में (ab) वाला पद कौन सा होगा?

Which term containing (ab) appears in ( (a-b+c)² )?

Explanation opens after your attempt

Correct Answer

B. (-2ab)

Step 1

Concept

The mixed term of (a) and (-b) is \(2\times a\times(-b)=-2ab\). Exam tip: keep the negative sign with the term.

Step 2

Why this answer is correct

The correct answer is B. (-2ab). The mixed term of (a) and (-b) is \(2\times a\times(-b)=-2ab\). Exam tip: keep the negative sign with the term.

Step 3

Exam Tip

(a) और (-b) का मिश्र पद \(2\times a\times(-b)=-2ab\) है। परीक्षा में ऋण चिन्ह को पद के साथ रखें।

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Question 49/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

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

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

Explanation opens after your attempt

Correct Answer

B. (8xy)

Step 1

Concept

This is (4AB) where (A=2x) and (B=y). Exam tip: calculate \(4\times2x\times y=8xy\).

Step 2

Why this answer is correct

The correct answer is B. (8xy). This is (4AB) where (A=2x) and (B=y). Exam tip: calculate \(4\times2x\times y=8xy\).

Step 3

Exam Tip

यह (4AB) है जहाँ (A=2x) और (B=y)। परीक्षा में \(4\times2x\times y=8xy\) करें।

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Question 50/50 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

यदि ( (x+k)²=x^-2+18x+81 ) है तो (k) का मान क्या होगा?

If ( (x+k)²=x^-2+18x+81 ), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

\(81=9^2\) and (2k=18), so (k=9). Exam tip: verify using both the last term and middle term.

Step 2

Why this answer is correct

The correct answer is B. (9). \(81=9^2\) and (2k=18), so (k=9). Exam tip: verify using both the last term and middle term.

Step 3

Exam Tip

\(81=9^2\) और (2k=18) इसलिए (k=9)। परीक्षा में अंतिम पद और मध्य पद दोनों से जाँच करें।

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Class 9 Mathematics Medium Quiz

( (2x+5)2-(2x-5)2 ) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (3a-4b)2 ) का सही विस्तार चुनिए।

Concept

Why this answer is correct

Exam Tip

( (x+6)(x-2) ) का विस्तार क्या है?

Concept

Why this answer is correct

Exam Tip

\( 104^2-96^2 \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (5p+2q)(5p-2q) ) का गुणनफल क्या है?

Concept

Why this answer is correct

Exam Tip

( (a+3b+c)2 ) में (6ab) किससे आता है?

Concept

Why this answer is correct

Exam Tip

( (2x+y+3)2 ) में (x) वाला रैखिक पद क्या है?

Concept

Why this answer is correct

Exam Tip

( (x-5)2+(x+5)2 ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (m+4)2-\(m^2+16\) ) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( 87\times93 \) को पहचान से निकालने पर उत्तर क्या है?

Concept

Why this answer is correct

Exam Tip

( (4x-3)(4x+3)+9 ) को सरल कीजिए।

Concept

Why this answer is correct

Exam Tip

( (x+2)(x+7) ) में स्थिर पद और (x) का गुणांक क्रमशः क्या हैं?

Concept

Why this answer is correct

Exam Tip

\( x^2-22x+121 \) का गुणनखंड रूप क्या है?

Concept

Why this answer is correct

Exam Tip

( (7a+2b)2-(7a-2b)2 ) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\( 203^2 \) निकालने के लिए सबसे उपयोगी रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

\( 197^2 \) का मान पहचान से क्या होगा?

Concept

Why this answer is correct

Exam Tip

( (x+y)2-\(x^2+y^2\) ) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

( (a+b+c)2-\(a^2+b^2+c^2\) ) का मान क्या है?

Concept

Why this answer is correct

( (2x+5)²-(2x-5)² ) का मान क्या है?

( (3a-4b)² ) का सही विस्तार चुनिए।

( (a+3b+c)² ) में (6ab) किससे आता है?

( (2x+y+3)² ) में (x) वाला रैखिक पद क्या है?

( (x-5)²+(x+5)² ) का सरल रूप क्या है?

( (m+4)²-\(m^2+16\) ) का मान क्या है?

( (7a+2b)²-(7a-2b)² ) का मान क्या है?

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

( (x+y)²-\(x^2+y^2\) ) किसके बराबर है?

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

( (a+b+c)²-\(a^2+b^2+c^2\) ) का मान क्या है?

( (2a+b+c)² ) में (2bc) के अलावा कौन से मिश्र पद आते हैं?

( (x+5)²-(x-5)² ) का मान (80) है तो (x) का मान क्या है?

यदि ( (x+3)²=x^-2+kx+9 ) है तो (k) का मान क्या होगा?

यदि ( (x-7)²=x^-2-kx+49 ) है तो (k) कितना है?

( (3x+1)²-\(9x^2+1\) ) को सरल कीजिए।

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

( (a+b)² ) और \(a^2+b^2\) का अंतर क्या है?

( (a-b)² ) और \(a^2-b^2\) का अंतर क्या है?