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Mathematics Quiz - Class 9 Mathematics Expert Level 63 Quiz

Question 1/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (x+y)²=81 ) और (xy=14) है तो \(x^2+y^2\) का मान क्या होगा?

If ( (x+y)²=81 ) and (xy=14), what is the value of \(x^2+y^2\)?

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: subtract (2xy) from the square of the sum.

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: subtract (2xy) from the square of the sum.

Step 3

Exam Tip

(x^-2+y^-2=(x+y)²-2xy=81-28=53) है। परीक्षा में वर्ग योग से (2xy) घटाएँ।

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Question 2/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (a-b=7) और (ab=18) है तो \(a^2+b^2\) कितना होगा?

If (a-b=7) and (ab=18), what is \(a^2+b^2\)?

Explanation opens after your attempt

Correct Answer

B. (85)

Step 1

Concept

(a^-2+b^-2=(a-b)²+2ab=49+36=85). Exam tip: add (2ab) to the square of the difference.

Step 2

Why this answer is correct

The correct answer is B. (85). (a^-2+b^-2=(a-b)²+2ab=49+36=85). Exam tip: add (2ab) to the square of the difference.

Step 3

Exam Tip

(a^-2+b^-2=(a-b)²+2ab=49+36=85) होता है। परीक्षा में अंतर के वर्ग में (2ab) जोड़ें।

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Question 3/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (p+q=12) और (p-q=4) है तो \(p^2-q^2\) का मान क्या है?

If (p+q=12) and (p-q=4), what is the value of \(p^2-q^2\)?

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

(p^-2-q^-2=(p+q)(p-q)=12\times4=48). Exam tip: directly apply the difference of squares identity.

Step 2

Why this answer is correct

The correct answer is C. (48). (p^-2-q^-2=(p+q)(p-q)=12\times4=48). Exam tip: directly apply the difference of squares identity.

Step 3

Exam Tip

(p^-2-q^-2=(p+q)(p-q)=12\times4=48) है। परीक्षा में अंतर वर्ग पहचान सीधे लगाएँ।

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Question 4/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (5a-2b)²-\(25a^2+4b^2\) ) को सरल कीजिए।

Simplify ( (5a-2b)²-\(25a^2+4b^2\) ).

Explanation opens after your attempt

Correct Answer

B. (-20ab)

Step 1

Concept

The expansion is \(25a^2-20ab+4b^2\), so like terms cancel and (-20ab) remains. Exam tip: watch the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. (-20ab). The expansion is \(25a^2-20ab+4b^2\), so like terms cancel and (-20ab) remains. Exam tip: watch the negative middle term.

Step 3

Exam Tip

विस्तार \(25a^2-20ab+4b^2\) है इसलिए समान पद घटकर (-20ab) बचता है। परीक्षा में ऋणात्मक मध्य पद पर ध्यान दें।

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Question 5/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (x+k)²=x^-2+24x+144 ) है तो (k) का मान क्या होगा?

If ( (x+k)²=x^-2+24x+144 ), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

\(144=12^2\) and (2k=24), so (k=12). Exam tip: verify using both the last term and the middle term.

Step 2

Why this answer is correct

The correct answer is C. (12). \(144=12^2\) and (2k=24), so (k=12). Exam tip: verify using both the last term and the middle term.

Step 3

Exam Tip

\(144=12^2\) और (2k=24) इसलिए (k=12) है। परीक्षा में अंतिम पद और मध्य पद दोनों से जाँच करें।

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Question 6/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (x-k)²=x^-2-30x+225 ) है तो (k) कितना है?

If ( (x-k)²=x^-2-30x+225 ), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

\(225=15^2\) and (-2kx=-30x) gives (k=15). Exam tip: the middle term of ((x-k)²) is (-2kx).

Step 2

Why this answer is correct

The correct answer is A. (15). \(225=15^2\) and (-2kx=-30x) gives (k=15). Exam tip: the middle term of ((x-k)²) is (-2kx).

Step 3

Exam Tip

\(225=15^2\) और (-2kx=-30x) से (k=15) मिलता है। परीक्षा में ((x-k)²) का मध्य पद (-2kx) होता है।

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Question 7/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (3x+4)(3x-4)-\(9x^2-20\) ) का मान क्या है?

What is the value of ( (3x+4)(3x-4)-\(9x^2-20\) )?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The first product is \(9x^2-16\), then \(9x^2-20\) is subtracted. Exam tip: apply the minus sign to the whole bracket.

Step 2

Why this answer is correct

The correct answer is A. (4). The first product is \(9x^2-16\), then \(9x^2-20\) is subtracted. Exam tip: apply the minus sign to the whole bracket.

Step 3

Exam Tip

पहला गुणनफल \(9x^2-16\) है और फिर \(9x^2-20\) घटता है। परीक्षा में पूरे कोष्ठक पर ऋण लगाएँ।

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Question 8/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

Which term containing (yz) appears in ( (x+2y+3z)² )?

Explanation opens after your attempt

Correct Answer

B. (12yz)

Step 1

Concept

\(2\times2y\times3z=12yz\). Exam tip: in the square of three terms, take twice the product of every pair.

Step 2

Why this answer is correct

The correct answer is B. (12yz). \(2\times2y\times3z=12yz\). Exam tip: in the square of three terms, take twice the product of every pair.

Step 3

Exam Tip

\(2\times2y\times3z=12yz\) होता है। परीक्षा में तीन पदों के वर्ग में हर जोड़े का दुगुना गुणन लें।

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

( (2a-b+4c)² ) में (ab) वाला पद क्या है?

What is the term containing (ab) in ( (2a-b+4c)² )?

Explanation opens after your attempt

Correct Answer

C. (-4ab)

Step 1

Concept

\(2\times2a\times(-b)=-4ab\). Exam tip: keep the negative sign with the term.

Step 2

Why this answer is correct

The correct answer is C. (-4ab). \(2\times2a\times(-b)=-4ab\). Exam tip: keep the negative sign with the term.

Step 3

Exam Tip

\(2\times2a\times(-b)=-4ab\) है। परीक्षा में ऋण चिन्ह को पद के साथ रखें।

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Question 10/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+y)²-(x-y)² ) का मान (72) है तो (xy) का मान क्या है?

If ( (x+y)²-(x-y)²=72 ), what is the value of (xy)?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

By identity, the difference is (4xy), so (4xy=72). Exam tip: use the identity first to shorten the equation.

Step 2

Why this answer is correct

The correct answer is B. (18). By identity, the difference is (4xy), so (4xy=72). Exam tip: use the identity first to shorten the equation.

Step 3

Exam Tip

पहचान से अंतर (4xy) होता है इसलिए (4xy=72)। परीक्षा में पहले पहचान लगाकर समीकरण छोटा करें।

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Question 11/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (m+n)²+(m-n)²=100 ) है तो \(m^2+n^2\) कितना होगा?

If ( (m+n)²+(m-n)²=100 ), what is \(m^2+n^2\)?

Explanation opens after your attempt

Correct Answer

C. (50)

Step 1

Concept

The sum is (2m^-2+2n^-2=2\(m^2+n^2\)). Exam tip: take half of the sum of the two squares.

Step 2

Why this answer is correct

The correct answer is C. (50). The sum is (2m^-2+2n^-2=2\(m^2+n^2\)). Exam tip: take half of the sum of the two squares.

Step 3

Exam Tip

योग (2m^-2+2n^-2=2\(m^2+n^2\)) होता है। परीक्षा में दोनों वर्गों का योग आधा करें।

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Question 12/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 1005^2-995^2 \) का मान पहचान से क्या होगा?

What is the value of \( 1005^2-995^2 \) using an identity?

Explanation opens after your attempt

Correct Answer

B. (20000)

Step 1

Concept

(a^-2-b^-2=(a+b)(a-b)=2000\times10=20000). Exam tip: difference of squares is useful for large numbers.

Step 2

Why this answer is correct

The correct answer is B. (20000). (a^-2-b^-2=(a+b)(a-b)=2000\times10=20000). Exam tip: difference of squares is useful for large numbers.

Step 3

Exam Tip

(a^-2-b^-2=(a+b)(a-b)=2000\times10=20000) है। परीक्षा में बड़ी संख्याओं में अंतर वर्ग उपयोगी है।

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Question 13/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 123\times117 \) को पहचान से निकालने पर क्या मिलेगा?

What do we get for \( 123\times117 \) using an identity?

Explanation opens after your attempt

Correct Answer

A. (14391)

Step 1

Concept

(123\times117=(120+3)(120-3)=120²-3²=14391). Exam tip: identify the common centre (120).

Step 2

Why this answer is correct

The correct answer is A. (14391). (123\times117=(120+3)(120-3)=120²-3²=14391). Exam tip: identify the common centre (120).

Step 3

Exam Tip

(123\times117=(120+3)(120-3)=120²-3²=14391)। परीक्षा में समान केंद्र (120) पहचानें।

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Question 14/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 998^2 \) का मान ( (1000-2)² ) से क्या होगा?

What is the value of \( 998^2 \) using ( (1000-2)² )?

Explanation opens after your attempt

Correct Answer

A. (996004)

Step 1

Concept

( (1000-2)²=1000000-4000+4=996004 ). Exam tip: keep the subtracted middle term correct.

Step 2

Why this answer is correct

The correct answer is A. (996004). ( (1000-2)²=1000000-4000+4=996004 ). Exam tip: keep the subtracted middle term correct.

Step 3

Exam Tip

( (1000-2)²=1000000-4000+4=996004 ) है। परीक्षा में घटने वाले मध्य पद को सही रखें।

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Question 15/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (4x+1)²-(4x-1)² ) का सरल रूप क्या है?

What is the simplified form of ( (4x+1)²-(4x-1)² )?

Explanation opens after your attempt

Correct Answer

B. (16x)

Step 1

Concept

This is (4AB) where (A=4x) and (B=1). Exam tip: calculate \(4\times4x\times1=16x\).

Step 2

Why this answer is correct

The correct answer is B. (16x). This is (4AB) where (A=4x) and (B=1). Exam tip: calculate \(4\times4x\times1=16x\).

Step 3

Exam Tip

यह (4AB) है जहाँ (A=4x) और (B=1)। परीक्षा में \(4\times4x\times1=16x\) करें।

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Question 16/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+3)(x+8)-(x+4)(x+7) ) का मान क्या है?

What is the value of ( (x+3)(x+8)-(x+4)(x+7) )?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

The first is \(x^2+11x+24\) and the second is \(x^2+11x+28\). Exam tip: cancel like terms and check the constant difference.

Step 2

Why this answer is correct

The correct answer is B. (-2). The first is \(x^2+11x+24\) and the second is \(x^2+11x+28\). Exam tip: cancel like terms and check the constant difference.

Step 3

Exam Tip

पहला \(x^2+11x+24\) और दूसरा \(x^2+11x+28\) है। परीक्षा में समान पद घटाकर केवल स्थिर अंतर देखें।

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Question 17/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x+5)(2x-3) ) में (x) का गुणांक क्या है?

What is the coefficient of (x) in ( (2x+5)(2x-3) )?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The middle terms are (-6x+10x=4x), so the coefficient is (4). Exam tip: add both middle products.

Step 2

Why this answer is correct

The correct answer is A. (4). The middle terms are (-6x+10x=4x), so the coefficient is (4). Exam tip: add both middle products.

Step 3

Exam Tip

मध्य पद (-6x+10x=4x) है इसलिए गुणांक (4) है। परीक्षा में दोनों मध्य गुणनों को जोड़ें।

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Question 18/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (3x-2)(3x+6) ) का स्थिर पद क्या है?

What is the constant term in ( (3x-2)(3x+6) )?

Explanation opens after your attempt

Correct Answer

B. (-12)

Step 1

Concept

The constant term is ((-2)\times6=-12). Exam tip: multiply only the constants for the constant term.

Step 2

Why this answer is correct

The correct answer is B. (-12). The constant term is ((-2)\times6=-12). Exam tip: multiply only the constants for the constant term.

Step 3

Exam Tip

स्थिर पद ((-2)\times6=-12) है। परीक्षा में स्थिर पद के लिए केवल स्थिर संख्याएँ गुणा करें।

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Question 19/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x-1)(x-2)(x-3) ) में \(x^2\) का गुणांक क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (-6)

Step 1

Concept

The sum of constants is (1+2+3=6) and the sign is negative. Exam tip: stepwise multiplication also gives the same result.

Step 2

Why this answer is correct

The correct answer is B. (-6). The sum of constants is (1+2+3=6) and the sign is negative. Exam tip: stepwise multiplication also gives the same result.

Step 3

Exam Tip

तीनों स्थिर पदों का योग (1+2+3=6) है और चिन्ह ऋणात्मक होता है। परीक्षा में क्रमिक गुणन से भी यही मिलेगा।

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Question 20/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)³-(a-b)³ ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (2b\(3a^2+b^2\))

Step 1

Concept

On expansion, (6a^-2b+2b^-3=2b\(3a^2+b^2\)). Exam tip: handle signs carefully in cube expansions.

Step 2

Why this answer is correct

The correct answer is A. (2b\(3a^2+b^2\)). On expansion, (6a^-2b+2b^-3=2b\(3a^2+b^2\)). Exam tip: handle signs carefully in cube expansions.

Step 3

Exam Tip

विस्तार करने पर (6a^-2b+2b^-3=2b\(3a^2+b^2\)) मिलता है। परीक्षा में घन विस्तार में चिन्ह सावधानी से रखें।

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Question 21/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)³+(a-b)³ ) किसके बराबर है?

What is ( (a+b)³+(a-b)³ ) equal to?

Explanation opens after your attempt

Correct Answer

A. (2a\(a^2+3b^2\))

Step 1

Concept

On adding, terms with odd powers of (b) cancel and \(2a^3+6ab^2\) remains. Exam tip: use symmetry.

Step 2

Why this answer is correct

The correct answer is A. (2a\(a^2+3b^2\)). On adding, terms with odd powers of (b) cancel and \(2a^3+6ab^2\) remains. Exam tip: use symmetry.

Step 3

Exam Tip

जोड़ने पर (b) की विषम शक्ति वाले पद कटते हैं और \(2a^3+6ab^2\) बचता है। परीक्षा में सममिति का लाभ लें।

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Question 22/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( x^3+27 \) का गुणनखंड रूप क्या है?

What is the factor form of \( x^3+27 \)?

Explanation opens after your attempt

Correct Answer

A. ( (x+3)\(x^2-3x+9\) )

Step 1

Concept

This is the form (a^-3+b^-3=(a+b)\(a^2-ab+b^2\)). Exam tip: identify \(27=3^3\).

Step 2

Why this answer is correct

The correct answer is A. ( (x+3)\(x^2-3x+9\) ). This is the form (a^-3+b^-3=(a+b)\(a^2-ab+b^2\)). Exam tip: identify \(27=3^3\).

Step 3

Exam Tip

यह (a^-3+b^-3=(a+b)\(a^2-ab+b^2\)) का रूप है। परीक्षा में \(27=3^3\) पहचानें।

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Question 23/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 8x^3-125 \) का गुणनखंड रूप कौन सा है?

Which is the factor form of \( 8x^3-125 \)?

Explanation opens after your attempt

Correct Answer

A. ( (2x-5)\(4x^2+10x+25\) )

Step 1

Concept

(8x^-3=(2x)³) and \(125=5^3\). Exam tip: apply the \(a^3-b^3\) formula correctly.

Step 2

Why this answer is correct

The correct answer is A. ( (2x-5)\(4x^2+10x+25\) ). (8x^-3=(2x)³) and \(125=5^3\). Exam tip: apply the \(a^3-b^3\) formula correctly.

Step 3

Exam Tip

(8x^-3=(2x)³) और \(125=5^3\) है। परीक्षा में \(a^3-b^3\) का सूत्र सही लगाएँ।

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Question 24/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि (a+b+c=0) है तो \(a^3+b^3+c^3\) किसके बराबर होगा?

If (a+b+c=0), what is \(a^3+b^3+c^3\) equal to?

Explanation opens after your attempt

Correct Answer

C. (3abc)

Step 1

Concept

By identity, (a^-3+b^-3+c^-3-3abc=(a+b+c)\(\cdots\)). Exam tip: if (a+b+c=0), remember \(a^3+b^3+c^3=3abc\).

Step 2

Why this answer is correct

The correct answer is C. (3abc). By identity, (a^-3+b^-3+c^-3-3abc=(a+b+c)\(\cdots\)). Exam tip: if (a+b+c=0), remember \(a^3+b^3+c^3=3abc\).

Step 3

Exam Tip

पहचान के अनुसार (a^-3+b^-3+c^-3-3abc=(a+b+c)\(\cdots\)) है। परीक्षा में (a+b+c=0) होने पर \(a^3+b^3+c^3=3abc\) याद रखें।

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Question 25/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( x^3+y^3+z^3-3xyz \) में यदि (x+y+z=0) हो तो मान क्या होगा?

If (x+y+z=0), what is the value of \( x^3+y^3+z^3-3xyz \)?

Explanation opens after your attempt

Correct Answer

D. (0)

Step 1

Concept

In the identity, this expression is multiplied by (x+y+z), so the value is (0). Exam tip: check the condition first.

Step 2

Why this answer is correct

The correct answer is D. (0). In the identity, this expression is multiplied by (x+y+z), so the value is (0). Exam tip: check the condition first.

Step 3

Exam Tip

पहचान में यह पद (x+y+z) से गुणा होता है इसलिए मान (0) होगा। परीक्षा में शर्त को पहले जाँचें।

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Question 26/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

(x^-2+y^-2+z^-2=(x+y+z)²-2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.

Step 2

Why this answer is correct

The correct answer is A. (14). (x^-2+y^-2+z^-2=(x+y+z)²-2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.

Step 3

Exam Tip

(x^-2+y^-2+z^-2=(x+y+z)²-2(xy+yz+zx)=36-22=14)। परीक्षा में तीन पदों की पहचान उपयोग करें।

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Question 27/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+y+z)² ) में \(x^2+y^2+z^2\) हटाने पर क्या बचेगा?

What remains when \(x^2+y^2+z^2\) is removed from ( (x+y+z)² )?

Explanation opens after your attempt

Correct Answer

B. (2xy+2yz+2zx)

Step 1

Concept

The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.

Step 2

Why this answer is correct

The correct answer is B. (2xy+2yz+2zx). The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.

Step 3

Exam Tip

तीन पदों के वर्ग में अतिरिक्त मिश्र पद (2xy+2yz+2zx) होते हैं। परीक्षा में सभी तीन मिश्र पद लिखें।

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Question 28/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

A. (12x+18)

Step 1

Concept

((2x+3)) is common, giving ((2x+3)[(2x+3)-(2x-3)]). Exam tip: taking common factors makes work easier.

Step 2

Why this answer is correct

The correct answer is A. (12x+18). ((2x+3)) is common, giving ((2x+3)[(2x+3)-(2x-3)]). Exam tip: taking common factors makes work easier.

Step 3

Exam Tip

((2x+3)) सामान्य लेकर ((2x+3)[(2x+3)-(2x-3)]) मिलता है। परीक्षा में common factor लेने से काम आसान होता है।

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Question 29/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+4)³-(x-4)³ ) में \(x^2\) वाला पद क्या होगा?

What will be the term containing \(x^2\) in ( (x+4)³-(x-4)³ )?

Explanation opens after your attempt

Correct Answer

B. \(24x^2\)

Step 1

Concept

The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.

Step 2

Why this answer is correct

The correct answer is B. \(24x^2\). The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.

Step 3

Exam Tip

अंतर में \(6x^2\cdot4=24x^2\) मिलता है। परीक्षा में घन अंतर में \(x^2\) वाला पद जल्दी पहचानें।

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Question 30/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2)³+(x-2)³ ) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(2x^3+24x\)

Step 1

Concept

In the sum, constant cube terms cancel and \(2x^3+6x\cdot4=2x^3+24x\) remains. Exam tip: understand symmetric cube expansion.

Step 2

Why this answer is correct

The correct answer is A. \(2x^3+24x\). In the sum, constant cube terms cancel and \(2x^3+6x\cdot4=2x^3+24x\) remains. Exam tip: understand symmetric cube expansion.

Step 3

Exam Tip

योग में स्थिर घन कटते हैं और \(2x^3+6x\cdot4=2x^3+24x\) बचता है। परीक्षा में सममित घन विस्तार समझें।

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Question 31/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.

Step 2

Why this answer is correct

The correct answer is A. \(2ab+2b^2\). \(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.

Step 3

Exam Tip

\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\)। परीक्षा में ऋण चिन्ह को पूरे दूसरे पद पर लगाएँ।

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Question 32/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a-b)²-\(a^2+b^2\) ) किसके बराबर है?

What is ( (a-b)²-\(a^2+b^2\) ) equal to?

Explanation opens after your attempt

Correct Answer

B. (-2ab)

Step 1

Concept

( (a-b)²=a^-2-2ab+b^-2 ), so subtracting leaves (-2ab). Exam tip: remember the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. (-2ab). ( (a-b)²=a^-2-2ab+b^-2 ), so subtracting leaves (-2ab). Exam tip: remember the negative middle term.

Step 3

Exam Tip

( (a-b)²=a^-2-2ab+b^-2 ) है इसलिए घटाने पर (-2ab) बचता है। परीक्षा में नकारात्मक मध्य पद याद रखें।

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Question 33/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि \(x+\frac{1}{x}=5\) है तो \(x^2+\frac{1}{x^2}\) का मान क्या होगा?

If \(x+\frac{1}{x}=5\), what is the value of \(x^2+\frac{1}{x^2}\)?

Explanation opens after your attempt

Correct Answer

A. (23)

Step 1

Concept

On squaring, \(x^2+2+\frac{1}{x^2}=25\). Exam tip: do not forget to subtract (2).

Step 2

Why this answer is correct

The correct answer is A. (23). On squaring, \(x^2+2+\frac{1}{x^2}=25\). Exam tip: do not forget to subtract (2).

Step 3

Exam Tip

वर्ग करने पर \(x^2+2+\frac{1}{x^2}=25\) मिलता है। परीक्षा में (2) घटाना न भूलें।

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Question 34/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि \(t-\frac{1}{t}=6\) है तो \(t^2+\frac{1}{t^2}\) कितना होगा?

If \(t-\frac{1}{t}=6\), what is \(t^2+\frac{1}{t^2}\)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

On squaring, \(t^2-2+\frac{1}{t^2}=36\), so the value is (38). Exam tip: the square of a difference gives (-2).

Step 2

Why this answer is correct

The correct answer is C. (38). On squaring, \(t^2-2+\frac{1}{t^2}=36\), so the value is (38). Exam tip: the square of a difference gives (-2).

Step 3

Exam Tip

वर्ग करने पर \(t^2-2+\frac{1}{t^2}=36\) इसलिए मान (38) है। परीक्षा में अंतर के वर्ग में (-2) आता है।

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Question 35/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( \(x+\frac{1}{x}\)²-\(x-\frac{1}{x}\)² ) का मान क्या है?

What is the value of ( \(x+\frac{1}{x}\)²-\(x-\frac{1}{x}\)² )?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

This is (4AB) where (A=x) and \(B=\frac{1}{x}\), so the value is (4). Exam tip: reciprocal terms multiply to (1).

Step 2

Why this answer is correct

The correct answer is B. (4). This is (4AB) where (A=x) and \(B=\frac{1}{x}\), so the value is (4). Exam tip: reciprocal terms multiply to (1).

Step 3

Exam Tip

यह (4AB) है जहाँ (A=x) और \(B=\frac{1}{x}\), इसलिए मान (4) है। परीक्षा में reciprocal terms का गुणन (1) होता है।

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Question 36/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

C. \(x^4-16\)

Step 1

Concept

First ( (x-2)(x+2)=x^-2-4 ), then (\(x^2-4\)\(x^2+4\)=x^-4-16). Exam tip: apply difference of squares twice.

Step 2

Why this answer is correct

The correct answer is C. \(x^4-16\). First ( (x-2)(x+2)=x^-2-4 ), then (\(x^2-4\)\(x^2+4\)=x^-4-16). Exam tip: apply difference of squares twice.

Step 3

Exam Tip

पहले ( (x-2)(x+2)=x^-2-4 ) और फिर (\(x^2-4\)\(x^2+4\)=x^-4-16)। परीक्षा में दो बार अंतर वर्ग लगाएँ।

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Question 37/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 16x^4-81y^4 \) का गुणनखंडों में सही पहला चरण क्या है?

What is the correct first factorization step for \( 16x^4-81y^4 \)?

Explanation opens after your attempt

Correct Answer

A. ( \(4x^2-9y^2\)\(4x^2+9y^2\) )

Step 1

Concept

(16x^-4=\(4x^2\)²) and (81y^-4=\(9y^2\)²). Exam tip: identify larger squares first.

Step 2

Why this answer is correct

The correct answer is A. ( \(4x^2-9y^2\)\(4x^2+9y^2\) ). (16x^-4=\(4x^2\)²) and (81y^-4=\(9y^2\)²). Exam tip: identify larger squares first.

Step 3

Exam Tip

(16x^-4=\(4x^2\)²) और (81y^-4=\(9y^2\)²) है। परीक्षा में पहले बड़े वर्ग पहचानें।

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Question 38/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

C. \(12x^2\)

Step 1

Concept

This is (4AB) where \(A=x^2\) and (B=3). Exam tip: treat \(x^2\) as one whole term.

Step 2

Why this answer is correct

The correct answer is C. \(12x^2\). This is (4AB) where \(A=x^2\) and (B=3). Exam tip: treat \(x^2\) as one whole term.

Step 3

Exam Tip

यह (4AB) है जहाँ \(A=x^2\) और (B=3)। परीक्षा में \(x^2\) को एक पूरा पद मानें।

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Question 39/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि \(x^2+y^2=50\) और (xy=7) है तो ( (x+y)² ) कितना होगा?

If \(x^2+y^2=50\) and (xy=7), what is ( (x+y)² )?

Explanation opens after your attempt

Correct Answer

B. (64)

Step 1

Concept

( (x+y)²=x^-2+y^-2+2xy=50+14=64). Exam tip: remember to add (2xy).

Step 2

Why this answer is correct

The correct answer is B. (64). ( (x+y)²=x^-2+y^-2+2xy=50+14=64). Exam tip: remember to add (2xy).

Step 3

Exam Tip

( (x+y)²=x^-2+y^-2+2xy=50+14=64)। परीक्षा में (2xy) जोड़ना याद रखें।

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Question 40/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि \(u^2+v^2=29\) और (uv=10) है तो ( (u-v)² ) का मान क्या है?

If \(u^2+v^2=29\) and (uv=10), what is the value of ( (u-v)² )?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

( (u-v)²=u^-2+v^-2-2uv=29-20=9). Exam tip: subtract (2uv) in the square of difference.

Step 2

Why this answer is correct

The correct answer is A. (9). ( (u-v)²=u^-2+v^-2-2uv=29-20=9). Exam tip: subtract (2uv) in the square of difference.

Step 3

Exam Tip

( (u-v)²=u^-2+v^-2-2uv=29-20=9)। परीक्षा में अंतर के वर्ग में (2uv) घटता है।

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Question 41/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

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

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

Explanation opens after your attempt

Correct Answer

C. (-4bc)

Step 1

Concept

\(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.

Step 2

Why this answer is correct

The correct answer is C. (-4bc). \(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.

Step 3

Exam Tip

\(2\times2b\times(-c)=-4bc\) है। परीक्षा में तीन पदों के वर्ग में चिन्हों को ध्यान से रखें।

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Question 42/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x-3y+z)² ) में (xz) वाला पद क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (4xz)

Step 1

Concept

\(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.

Step 2

Why this answer is correct

The correct answer is B. (4xz). \(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.

Step 3

Exam Tip

\(2\times2x\times z=4xz\) मिलता है। परीक्षा में जिस जोड़ी की बात हो वही मिश्र पद निकालें।

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Question 43/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (x+2)(x+5)=x^-2+kx+10 ) है तो (k) का मान क्या है?

If ( (x+2)(x+5)=x^-2+kx+10 ), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The coefficient of (x) is (2+5=7). Exam tip: in ((x+a)(x+b)), the coefficient of (x) is (a+b).

Step 2

Why this answer is correct

The correct answer is B. (7). The coefficient of (x) is (2+5=7). Exam tip: in ((x+a)(x+b)), the coefficient of (x) is (a+b).

Step 3

Exam Tip

(x) का गुणांक (2+5=7) है। परीक्षा में ((x+a)(x+b)) में (x) का गुणांक (a+b) होता है।

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Question 44/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि ( (x-4)(x+k)=x^-2+3x-28 ) है तो (k) का मान क्या है?

If ( (x-4)(x+k)=x^-2+3x-28 ), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The constant term (-4k=-28) gives (k=7), and the middle term also becomes (3x). Exam tip: verify using both conditions.

Step 2

Why this answer is correct

The correct answer is C. (7). The constant term (-4k=-28) gives (k=7), and the middle term also becomes (3x). Exam tip: verify using both conditions.

Step 3

Exam Tip

स्थिर पद (-4k=-28) से (k=7) मिलता है और मध्य पद भी (3x) बनता है। परीक्षा में दोनों शर्तों से जाँच करें।

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Question 45/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+3)²-(x-1)(x+7) ) का सरल रूप क्या है?

What is the simplified form of ( (x+3)²-(x-1)(x+7) )?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).

Step 2

Why this answer is correct

The correct answer is B. (4). The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).

Step 3

Exam Tip

पहला \(x^2+6x+9\) और दूसरा \(x^2+6x-7\) है। घटाने पर (16) नहीं बल्कि (9-(-7)=16) होगा इसलिए सही विकल्प (16) होना चाहिए।

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Question 46/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2x+1)(2x+9)-(2x+5)² ) का मान क्या है?

What is the value of ( (2x+1)(2x+9)-(2x+5)² )?

Explanation opens after your attempt

Correct Answer

D. (-16)

Step 1

Concept

The first product is \(4x^2+20x+9\) and the second is \(4x^2+20x+25\). Exam tip: cancel like terms and compare constants.

Step 2

Why this answer is correct

The correct answer is D. (-16). The first product is \(4x^2+20x+9\) and the second is \(4x^2+20x+25\). Exam tip: cancel like terms and compare constants.

Step 3

Exam Tip

पहला गुणनफल \(4x^2+20x+9\) और दूसरा \(4x^2+20x+25\) है। परीक्षा में समान पद काटकर स्थिर पदों का अंतर लें।

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Question 47/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+6)²-(x+2)(x+10) ) का सरल मान क्या है?

What is the simplified value of ( (x+6)²-(x+2)(x+10) )?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

The first expansion is \(x^2+12x+36\) and the second is \(x^2+12x+20\). Exam tip: cancel like terms and compare constants.

Step 2

Why this answer is correct

The correct answer is C. (16). The first expansion is \(x^2+12x+36\) and the second is \(x^2+12x+20\). Exam tip: cancel like terms and compare constants.

Step 3

Exam Tip

पहला विस्तार \(x^2+12x+36\) और दूसरा \(x^2+12x+20\) है। परीक्षा में समान पद काटकर स्थिर पदों का अंतर लें।

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Question 48/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

यदि \(x+\frac{1}{x}=7\) है तो \(x^3+\frac{1}{x^3}\) का मान क्या होगा?

If \(x+\frac{1}{x}=7\), what is the value of \(x^3+\frac{1}{x^3}\)?

Explanation opens after your attempt

Correct Answer

B. (322)

Step 1

Concept

Use (a^-3+b^-3=(a+b)³-3ab(a+b)) where (ab=1). Exam tip: remember \(7^3-3\times7=322\).

Step 2

Why this answer is correct

The correct answer is B. (322). Use (a^-3+b^-3=(a+b)³-3ab(a+b)) where (ab=1). Exam tip: remember \(7^3-3\times7=322\).

Step 3

Exam Tip

पहचान (a^-3+b^-3=(a+b)³-3ab(a+b)) लगाएँ जहाँ (ab=1)। परीक्षा में \(7^3-3\times7=322\) याद रखें।

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Question 49/50 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(27a^3+8b^3\) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \(27a^3+8b^3\)?

Explanation opens after your attempt

Correct Answer

D. ( (3a+2b)\(9a^2-6ab+4b^2\) )

Step 1

Concept

This is ((3a)³+(2b)³), so the sum of cubes identity applies. Exam tip: the middle term inside the second factor is negative.

Step 2

Why this answer is correct

The correct answer is D. ( (3a+2b)\(9a^2-6ab+4b^2\) ). This is ((3a)³+(2b)³), so the sum of cubes identity applies. Exam tip: the middle term inside the second factor is negative.

Step 3

Exam Tip

यह ((3a)³+(2b)³) है इसलिए \(a^3+b^3\) की पहचान लगेगी। परीक्षा में योग घन में बीच वाला पद ऋणात्मक होता है।

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

यदि (a+b+c=9) और (ab+bc+ca=20) है तो \(a^2+b^2+c^2\) कितना होगा?

If (a+b+c=9) and (ab+bc+ca=20), what is \(a^2+b^2+c^2\)?

Explanation opens after your attempt

Correct Answer

A. (41)

Step 1

Concept

(a^-2+b^-2+c^-2=(a+b+c)²-2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.

Step 2

Why this answer is correct

The correct answer is A. (41). (a^-2+b^-2+c^-2=(a+b+c)²-2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.

Step 3

Exam Tip

(a^-2+b^-2+c^-2=(a+b+c)²-2(ab+bc+ca)=81-40=41)। परीक्षा में तीन पदों की वर्ग पहचान सीधे लगाएँ।

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Class 9 Mathematics Expert Quiz

यदि ( (x+y)2=81 ) और (xy=14) है तो \(x^2+y^2\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (a-b=7) और (ab=18) है तो \(a^2+b^2\) कितना होगा?

Concept

Why this answer is correct

Exam Tip

यदि (p+q=12) और (p-q=4) है तो \(p^2-q^2\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( (5a-2b)2-\(25a^2+4b^2\) ) को सरल कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि ( (x+k)2=x-2+24x+144 ) है तो (k) का मान क्या होगा?

Concept

Why this answer is correct

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यदि ( (x-k)2=x-2-30x+225 ) है तो (k) कितना है?

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( (3x+4)(3x-4)-\(9x^2-20\) ) का मान क्या है?

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

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( (2a-b+4c)2 ) में (ab) वाला पद क्या है?

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( (x+y)2-(x-y)2 ) का मान (72) है तो (xy) का मान क्या है?

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यदि ( (m+n)2+(m-n)2=100 ) है तो \(m^2+n^2\) कितना होगा?

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\( 1005^2-995^2 \) का मान पहचान से क्या होगा?

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\( 123\times117 \) को पहचान से निकालने पर क्या मिलेगा?

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\( 998^2 \) का मान ( (1000-2)2 ) से क्या होगा?

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( (4x+1)2-(4x-1)2 ) का सरल रूप क्या है?

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( (x+3)(x+8)-(x+4)(x+7) ) का मान क्या है?

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( (2x+5)(2x-3) ) में (x) का गुणांक क्या है?

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( (3x-2)(3x+6) ) का स्थिर पद क्या है?

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( (x-1)(x-2)(x-3) ) में \(x^2\) का गुणांक क्या है?

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( (a+b)3-(a-b)3 ) का सरल रूप क्या है?

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यदि ( (x+y)²=81 ) और (xy=14) है तो \(x^2+y^2\) का मान क्या होगा?

( (5a-2b)²-\(25a^2+4b^2\) ) को सरल कीजिए।

यदि ( (x+k)²=x^-2+24x+144 ) है तो (k) का मान क्या होगा?

यदि ( (x-k)²=x^-2-30x+225 ) है तो (k) कितना है?

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

( (2a-b+4c)² ) में (ab) वाला पद क्या है?

( (x+y)²-(x-y)² ) का मान (72) है तो (xy) का मान क्या है?

यदि ( (m+n)²+(m-n)²=100 ) है तो \(m^2+n^2\) कितना होगा?

\( 998^2 \) का मान ( (1000-2)² ) से क्या होगा?

( (4x+1)²-(4x-1)² ) का सरल रूप क्या है?

( (a+b)³-(a-b)³ ) का सरल रूप क्या है?

( (a+b)³+(a-b)³ ) किसके बराबर है?

( (x+y+z)² ) में \(x^2+y^2+z^2\) हटाने पर क्या बचेगा?

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

( (x+4)³-(x-4)³ ) में \(x^2\) वाला पद क्या होगा?

( (x+2)³+(x-2)³ ) का सरल रूप क्या है?

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

( (a-b)²-\(a^2+b^2\) ) किसके बराबर है?

( \(x+\frac{1}{x}\)²-\(x-\frac{1}{x}\)² ) का मान क्या है?

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