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Mathematics Quiz - Class 9 Mathematics Hard Level 73 Quiz

Question 1/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(3x^2-5x+7\) में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in \(3x^2-5x+7\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The number attached to \(x^2\) is (3). In exams, identify a coefficient from the numerical part attached to the term.

Step 2

Why this answer is correct

The correct answer is A. (3). The number attached to \(x^2\) is (3). In exams, identify a coefficient from the numerical part attached to the term.

Step 3

Exam Tip

\(x^2\) के साथ लगा संख्या (3) है। परीक्षा में पद का गुणांक उसके साथ लगे संख्यात्मक भाग से पहचानें।

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Question 2/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(5x-2x^2+9\) को मानक रूप में लिखने पर कौन-सा रूप मिलेगा?

When \(5x-2x^2+9\) is written in standard form, which form is obtained?

Explanation opens after your attempt

Correct Answer

A. \(-2x^2+5x+9\)

Step 1

Concept

In standard form, write the \(x^2\) term, then the (x) term, then the constant. In exams, follow descending powers.

Step 2

Why this answer is correct

The correct answer is A. \(-2x^2+5x+9\). In standard form, write the \(x^2\) term, then the (x) term, then the constant. In exams, follow descending powers.

Step 3

Exam Tip

मानक रूप में \(x^2\), फिर (x), फिर स्थिर पद लिखा जाता है। परीक्षा में घटते घात क्रम का ध्यान रखें।

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Question 3/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2+3x-4\) में (x=2) रखने पर मान क्या होगा?

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

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

(2(2)²+3(2)-4=8+6-4=10). In exams, calculate the square first.

Step 2

Why this answer is correct

The correct answer is B. (10). (2(2)²+3(2)-4=8+6-4=10). In exams, calculate the square first.

Step 3

Exam Tip

(2(2)²+3(2)-4=8+6-4=10) है। परीक्षा में पहले वर्ग का मान निकालें।

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Question 4/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-6x+9\) को पूर्ण वर्ग के रूप में कैसे लिखा जाएगा?

How will \(x^2-6x+9\) be written as a perfect square?

Explanation opens after your attempt

Correct Answer

A. ((x-3)²)

Step 1

Concept

\(9=3^2\) and \(-6x=-2\cdot x\cdot3\). In exams, keep the sign of the middle term correct.

Step 2

Why this answer is correct

The correct answer is A. ((x-3)²). \(9=3^2\) and \(-6x=-2\cdot x\cdot3\). In exams, keep the sign of the middle term correct.

Step 3

Exam Tip

\(9=3^2\) और \(-6x=-2\cdot x\cdot3\) है। परीक्षा में मध्य पद का चिन्ह सही रखें।

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Question 5/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(4x^2+12x+9\) का सही पूर्ण वर्ग रूप क्या है?

What is the correct perfect square form of \(4x^2+12x+9\)?

Explanation opens after your attempt

Correct Answer

A. ((2x+3)²)

Step 1

Concept

(4x^-2=(2x)²) and \(9=3^2\). In exams, confirm using the middle term \(2\cdot2x\cdot3\).

Step 2

Why this answer is correct

The correct answer is A. ((2x+3)²). (4x^-2=(2x)²) and \(9=3^2\). In exams, confirm using the middle term \(2\cdot2x\cdot3\).

Step 3

Exam Tip

(4x^-2=(2x)²) और \(9=3^2\) है। परीक्षा में मध्य पद \(2\cdot2x\cdot3\) से पुष्टि करें।

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Question 6/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(9x^2-24x+16\) को पूर्ण वर्ग में बदलने पर क्या मिलेगा?

What is obtained when \(9x^2-24x+16\) is changed into a perfect square?

Explanation opens after your attempt

Correct Answer

B. ((3x-4)²)

Step 1

Concept

(9x^-2=(3x)²), \(16=4^2\), and the middle term is negative. In exams, identify ((a-b)²).

Step 2

Why this answer is correct

The correct answer is B. ((3x-4)²). (9x^-2=(3x)²), \(16=4^2\), and the middle term is negative. In exams, identify ((a-b)²).

Step 3

Exam Tip

(9x^-2=(3x)²), \(16=4^2\) और मध्य पद ऋणात्मक है। परीक्षा में ((a-b)²) पहचानें।

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Question 7/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+7x+12\) में मध्य पद विभाजन के लिए कौन-सी जोड़ी सही है?

For splitting the middle term in \(x^2+7x+12\), which pair is correct?

Explanation opens after your attempt

Correct Answer

A. (3x) और (4x)(3x) and (4x)

Step 1

Concept

(3+4=7) and \(3\cdot4=12\). In exams, check both sum and product.

Step 2

Why this answer is correct

The correct answer is A. (3x) और (4x) / (3x) and (4x). (3+4=7) and \(3\cdot4=12\). In exams, check both sum and product.

Step 3

Exam Tip

(3+4=7) और \(3\cdot4=12\) है। परीक्षा में योग और गुणनफल दोनों जाँचें।

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Question 8/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-9x+20\) के मध्य पद के लिए सही विभाजन क्या है?

What is the correct split of the middle term for \(x^2-9x+20\)?

Explanation opens after your attempt

Correct Answer

A. (-4x) और (-5x)(-4x) and (-5x)

Step 1

Concept

(-4-5=-9) and ((-4)(-5)=20). In exams, when constant is positive and middle term is negative, use two negative signs.

Step 2

Why this answer is correct

The correct answer is A. (-4x) और (-5x) / (-4x) and (-5x). (-4-5=-9) and ((-4)(-5)=20). In exams, when constant is positive and middle term is negative, use two negative signs.

Step 3

Exam Tip

(-4-5=-9) और ((-4)(-5)=20) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद पर दोनों चिह्न ऋण रखें।

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Question 9/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+2x-15\) का गुणनखंड रूप क्या है?

What is the factorised form of \(x^2+2x-15\)?

Explanation opens after your attempt

Correct Answer

A. ((x+5)(x-3))

Step 1

Concept

(5-3=2) and (5\cdot(-3)=-15). In exams, use opposite signs for a negative constant term.

Step 2

Why this answer is correct

The correct answer is A. ((x+5)(x-3)). (5-3=2) and (5\cdot(-3)=-15). In exams, use opposite signs for a negative constant term.

Step 3

Exam Tip

(5-3=2) और (5\cdot(-3)=-15) है। परीक्षा में ऋणात्मक स्थिर पद पर विपरीत चिह्न लें।

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Question 10/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-4x-21\) को गुणनखंडों में लिखिए।

Write \(x^2-4x-21\) in factors.

Explanation opens after your attempt

Correct Answer

A. ((x-7)(x+3))

Step 1

Concept

(-7+3=-4) and ((-7)(3)=-21). In exams, keep the larger factor's sign like the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((x-7)(x+3)). (-7+3=-4) and ((-7)(3)=-21). In exams, keep the larger factor's sign like the middle term.

Step 3

Exam Tip

(-7+3=-4) और ((-7)(3)=-21) है। परीक्षा में बड़े गुणनखंड का चिह्न मध्य पद जैसा रखें।

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Question 11/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2+5x+3\) का सही गुणनखंड कौन-सा है?

Which is the correct factorisation of \(2x^2+5x+3\)?

Explanation opens after your attempt

Correct Answer

A. ((2x+3)(x+1))

Step 1

Concept

Expanding gives \(2x^2+2x+3x+3=2x^2+5x+3\). In exams, verify options by multiplication.

Step 2

Why this answer is correct

The correct answer is A. ((2x+3)(x+1)). Expanding gives \(2x^2+2x+3x+3=2x^2+5x+3\). In exams, verify options by multiplication.

Step 3

Exam Tip

विस्तार करने पर \(2x^2+2x+3x+3=2x^2+5x+3\) मिलता है। परीक्षा में गुणा करके विकल्प जाँचें।

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Question 12/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(3x^2+14x+8\) का गुणनखंड रूप चुनिए।

Choose the factorised form of \(3x^2+14x+8\).

Explanation opens after your attempt

Correct Answer

A. ((3x+2)(x+4))

Step 1

Concept

((3x+2)(x+4)) gives \(3x^2+12x+2x+8\). In exams, check the sum of middle terms.

Step 2

Why this answer is correct

The correct answer is A. ((3x+2)(x+4)). ((3x+2)(x+4)) gives \(3x^2+12x+2x+8\). In exams, check the sum of middle terms.

Step 3

Exam Tip

((3x+2)(x+4)) से \(3x^2+12x+2x+8\) मिलता है। परीक्षा में मध्य पदों का योग देखें।

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Question 13/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2-7x+6\) का सही गुणनखंड क्या है?

What is the correct factorisation of \(2x^2-7x+6\)?

Explanation opens after your attempt

Correct Answer

A. ((2x-3)(x-2))

Step 1

Concept

((2x-3)(x-2)) gives \(2x^2-4x-3x+6\). In exams, add both negative middle terms.

Step 2

Why this answer is correct

The correct answer is A. ((2x-3)(x-2)). ((2x-3)(x-2)) gives \(2x^2-4x-3x+6\). In exams, add both negative middle terms.

Step 3

Exam Tip

((2x-3)(x-2)) से \(2x^2-4x-3x+6\) मिलता है। परीक्षा में दोनों ऋणात्मक मध्य पद जोड़ें।

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Question 14/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(5x^2-13x+6\) के गुणनखंड कौन-से होंगे?

What will be the factors of \(5x^2-13x+6\)?

Explanation opens after your attempt

Correct Answer

A. ((5x-3)(x-2))

Step 1

Concept

((5x-3)(x-2)) gives \(5x^2-10x-3x+6\). In exams, confirm the middle term (-13x).

Step 2

Why this answer is correct

The correct answer is A. ((5x-3)(x-2)). ((5x-3)(x-2)) gives \(5x^2-10x-3x+6\). In exams, confirm the middle term (-13x).

Step 3

Exam Tip

((5x-3)(x-2)) से \(5x^2-10x-3x+6\) मिलता है। परीक्षा में मध्य पद (-13x) की पुष्टि करें।

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Question 15/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(6x^2+x-2\) को गुणनखंडित कीजिए।

Factorise \(6x^2+x-2\).

Explanation opens after your attempt

Correct Answer

A. ((3x+2)(2x-1))

Step 1

Concept

((3x+2)(2x-1)) gives \(6x^2-3x+4x-2\). In exams, add middle terms with opposite signs.

Step 2

Why this answer is correct

The correct answer is A. ((3x+2)(2x-1)). ((3x+2)(2x-1)) gives \(6x^2-3x+4x-2\). In exams, add middle terms with opposite signs.

Step 3

Exam Tip

((3x+2)(2x-1)) से \(6x^2-3x+4x-2\) मिलता है। परीक्षा में विपरीत चिह्न वाले मध्य पद जोड़ें।

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Question 16/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+px+24\) में यदि एक गुणनखंड (x+6) है, तो (p) का मान क्या होगा?

In \(x^2+px+24\), if one factor is (x+6), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

The other factor is (x+4) because \(6\cdot4=24\), so (p=6+4=10). In exams, find the other factor from the constant term.

Step 2

Why this answer is correct

The correct answer is A. (10). The other factor is (x+4) because \(6\cdot4=24\), so (p=6+4=10). In exams, find the other factor from the constant term.

Step 3

Exam Tip

दूसरा गुणनखंड (x+4) होगा क्योंकि \(6\cdot4=24\), इसलिए (p=6+4=10)। परीक्षा में स्थिर पद से दूसरा गुणनखंड खोजें।

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Question 17/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+kx+36\) को ((x+4)(x+9)) के बराबर बनाया गया है। (k) का मान क्या है?

\(x^2+kx+36\) is made equal to ((x+4)(x+9)). What is the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (13)

Step 1

Concept

((x+4)(x+9)=x^-2+13x+36). In exams, add the constant parts of the factors.

Step 2

Why this answer is correct

The correct answer is A. (13). ((x+4)(x+9)=x^-2+13x+36). In exams, add the constant parts of the factors.

Step 3

Exam Tip

((x+4)(x+9)=x^-2+13x+36) है। परीक्षा में गुणनखंडों के स्थिर भाग जोड़ें।

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Question 18/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-11x+k\) के गुणनखंड (x-5) और (x-6) हैं। (k) का मान क्या होगा?

The factors of \(x^2-11x+k\) are (x-5) and (x-6). What will be the value of (k)?

Explanation opens after your attempt

Correct Answer

B. (30)

Step 1

Concept

The constant term is ((-5)(-6)=30). In exams, multiply the constant parts of the factors.

Step 2

Why this answer is correct

The correct answer is B. (30). The constant term is ((-5)(-6)=30). In exams, multiply the constant parts of the factors.

Step 3

Exam Tip

स्थिर पद ((-5)(-6)=30) है। परीक्षा में गुणनखंडों के स्थिर भागों का गुणन करें।

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Question 19/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+8x+c\) को पूर्ण वर्ग बनाने के लिए (c) का मान क्या होना चाहिए?

What should be the value of (c) to make \(x^2+8x+c\) a perfect square?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

Half of (8) is (4), and \(4^2=16\). In exams, square half of the middle coefficient.

Step 2

Why this answer is correct

The correct answer is B. (16). Half of (8) is (4), and \(4^2=16\). In exams, square half of the middle coefficient.

Step 3

Exam Tip

(8) का आधा (4) है और \(4^2=16\) है। परीक्षा में मध्य पद के आधे का वर्ग लें।

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Question 20/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-14x+c\) पूर्ण वर्ग हो, तो (c) का मान क्या होगा?

If \(x^2-14x+c\) is a perfect square, what will be the value of (c)?

Explanation opens after your attempt

Correct Answer

A. (49)

Step 1

Concept

Half of (-14) is (-7), and ((-7)²=49). In exams, even if the sign is negative, the square is positive.

Step 2

Why this answer is correct

The correct answer is A. (49). Half of (-14) is (-7), and ((-7)²=49). In exams, even if the sign is negative, the square is positive.

Step 3

Exam Tip

(-14) का आधा (-7) है और ((-7)²=49) है। परीक्षा में चिह्न चाहे ऋण हो, वर्ग धनात्मक होता है।

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Question 21/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(9x^2-mx+16\) पूर्ण वर्ग है। (m) का मान क्या होगा?

\(9x^2-mx+16\) is a perfect square. What will be the value of (m)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

(9x^-2=(3x)²) and \(16=4^2\), so the middle coefficient is \(2\cdot3\cdot4=24\). In exams, view the negative sign and coefficient separately.

Step 2

Why this answer is correct

The correct answer is C. (24). (9x^-2=(3x)²) and \(16=4^2\), so the middle coefficient is \(2\cdot3\cdot4=24\). In exams, view the negative sign and coefficient separately.

Step 3

Exam Tip

(9x^-2=(3x)²) और \(16=4^2\), इसलिए मध्य गुणांक \(2\cdot3\cdot4=24\) है। परीक्षा में ऋण चिन्ह अलग और गुणांक अलग देखें।

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Question 22/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2+7x+5\) में (x=1) रखने पर मान क्या होगा?

What is the value of \(2x^2+7x+5\) when (x=1)?

Explanation opens after your attempt

Correct Answer

B. (14)

Step 1

Concept

(2(1)²+7(1)+5=14). In exams, when substituting (1), all terms add directly.

Step 2

Why this answer is correct

The correct answer is B. (14). (2(1)²+7(1)+5=14). In exams, when substituting (1), all terms add directly.

Step 3

Exam Tip

(2(1)²+7(1)+5=14) है। परीक्षा में (1) रखने पर सभी पद सीधे जुड़ते हैं।

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Question 23/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(3x^2-2x-8\) में (x=-1) रखने पर मान क्या होगा?

What is the value of \(3x^2-2x-8\) when (x=-1)?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

(3(-1)²-2(-1)-8=3+2-8=-3). In exams, the square of a negative number is positive.

Step 2

Why this answer is correct

The correct answer is A. (-3). (3(-1)²-2(-1)-8=3+2-8=-3). In exams, the square of a negative number is positive.

Step 3

Exam Tip

(3(-1)²-2(-1)-8=3+2-8=-3) है। परीक्षा में ऋण संख्या का वर्ग धनात्मक होता है।

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Question 24/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-5x+6\) का मान (x=2) पर क्या होगा?

What is the value of \(x^2-5x+6\) at (x=2)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

\(2^2-5\cdot2+6=4-10+6=0\). In exams, do square, multiplication, and addition in order.

Step 2

Why this answer is correct

The correct answer is A. (0). \(2^2-5\cdot2+6=4-10+6=0\). In exams, do square, multiplication, and addition in order.

Step 3

Exam Tip

\(2^2-5\cdot2+6=4-10+6=0\) है। परीक्षा में क्रम से वर्ग, गुणन और जोड़ करें।

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Question 25/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+ax+18\) में यदि दो स्थिर गुणनखंड (3) और (6) हैं, तो (a) क्या है?

In \(x^2+ax+18\), if the two constant factors are (3) and (6), what is (a)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

The middle coefficient will be (3+6=9). In exams, identify the form (x^-2+(p+q)x+pq).

Step 2

Why this answer is correct

The correct answer is A. (9). The middle coefficient will be (3+6=9). In exams, identify the form (x^-2+(p+q)x+pq).

Step 3

Exam Tip

मध्य गुणांक (3+6=9) होगा। परीक्षा में (x^-2+(p+q)x+pq) का रूप पहचानें।

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Question 26/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+bx-28\) के गुणनखंड (x+7) और (x-4) हैं। (b) का मान क्या है?

The factors of \(x^2+bx-28\) are (x+7) and (x-4). What is the value of (b)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

((x+7)(x-4)=x^-2+3x-28). In exams, the middle coefficient comes from the sum of constant parts.

Step 2

Why this answer is correct

The correct answer is A. (3). ((x+7)(x-4)=x^-2+3x-28). In exams, the middle coefficient comes from the sum of constant parts.

Step 3

Exam Tip

((x+7)(x-4)=x^-2+3x-28) है। परीक्षा में मध्य गुणांक स्थिर भागों के योग से मिलता है।

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Question 27/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2+kx+12\) में यदि गुणनखंड ((2x+3)(x+4)) हैं, तो (k) क्या होगा?

In \(2x^2+kx+12\), if the factors are ((2x+3)(x+4)), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

Expansion gives \(2x^2+8x+3x+12=2x^2+11x+12\). In exams, add the cross terms.

Step 2

Why this answer is correct

The correct answer is B. (11). Expansion gives \(2x^2+8x+3x+12=2x^2+11x+12\). In exams, add the cross terms.

Step 3

Exam Tip

विस्तार से \(2x^2+8x+3x+12=2x^2+11x+12\) मिलता है। परीक्षा में क्रॉस पद जोड़ें।

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Question 28/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

कौन-सा द्विघात व्यंजक पूर्ण वर्ग नहीं है?

Which quadratic expression is not a perfect square?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

For \(x^2+8x+18\), the constant should be (16) for a perfect square. In exams, check the square of half the middle coefficient.

Step 2

Why this answer is correct

The correct answer is D. \(x^2+8x+18\). For \(x^2+8x+18\), the constant should be (16) for a perfect square. In exams, check the square of half the middle coefficient.

Step 3

Exam Tip

\(x^2+8x+18\) में पूर्ण वर्ग के लिए स्थिर पद (16) चाहिए था। परीक्षा में आधे मध्य गुणांक का वर्ग जाँचें।

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Question 29/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+4x+4\) और \(x^2-4\) में क्या संबंध है?

What is the relation between \(x^2+4x+4\) and \(x^2-4\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(x^-2+4x+4=(x+2)²) and (x^-2-4=(x-2)(x+2)). In exams, check signs and the middle term.

Step 2

Why this answer is correct

The correct answer is A. पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है / First is a perfect square and second is difference of squares. (x^-2+4x+4=(x+2)²) and (x^-2-4=(x-2)(x+2)). In exams, check signs and the middle term.

Step 3

Exam Tip

(x^-2+4x+4=(x+2)²) और (x^-2-4=(x-2)(x+2)) है। परीक्षा में चिन्ह और मध्य पद देखें।

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Question 30/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+6x+5\) को ((x+3)²) से तुलना करने पर कितना अंतर है?

When \(x^2+6x+5\) is compared with ((x+3)²), what is the difference?

Explanation opens after your attempt

Correct Answer

A. (1) कम(1) less

Step 1

Concept

((x+3)²=x^-2+6x+9), so the given expression is not (1) less but (4) less. The correct comparison should be (4) less.

Step 2

Why this answer is correct

The correct answer is A. (1) कम / (1) less. ((x+3)²=x^-2+6x+9), so the given expression is not (1) less but (4) less. The correct comparison should be (4) less.

Step 3

Exam Tip

((x+3)²=x^-2+6x+9) है, इसलिए दिया व्यंजक (4) नहीं बल्कि (1) नहीं, (4) कम है। सही तुलना (4) कम होनी चाहिए।

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Question 31/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+6x+5\) को पूर्ण वर्ग पूरा करने के लिए कौन-सा पद जोड़ना होगा?

Which term must be added to complete the square for \(x^2+6x+5\)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

To make \(x^2+6x\) a perfect square, (9) is needed, and (5) is already present, so add (4). In exams, square half the middle coefficient.

Step 2

Why this answer is correct

The correct answer is B. (4). To make \(x^2+6x\) a perfect square, (9) is needed, and (5) is already present, so add (4). In exams, square half the middle coefficient.

Step 3

Exam Tip

\(x^2+6x\) को पूर्ण वर्ग बनाने के लिए (9) चाहिए और (5) पहले है, इसलिए (4) जोड़ना होगा। परीक्षा में आधे मध्य गुणांक का वर्ग लें।

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Question 32/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-8x+10\) को पूर्ण वर्ग पूरा करने के लिए कितना जोड़ना होगा?

How much must be added to \(x^2-8x+10\) to complete the square?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

For \(x^2-8x\), the perfect square constant should be (16), so add (16-10=6). In exams, subtract the current constant.

Step 2

Why this answer is correct

The correct answer is A. (6). For \(x^2-8x\), the perfect square constant should be (16), so add (16-10=6). In exams, subtract the current constant.

Step 3

Exam Tip

\(x^2-8x\) के लिए पूर्ण वर्ग स्थिर पद (16) चाहिए, इसलिए (16-10=6) जोड़ें। परीक्षा में वर्तमान स्थिर पद घटाएँ।

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Question 33/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(12x^2-18x\) का पूर्ण सामान्य गुणनखंड रूप क्या है?

What is the complete common-factor form of \(12x^2-18x\)?

Explanation opens after your attempt

Correct Answer

A. (6x(2x-3))

Step 1

Concept

The greatest common factor is (6x). In exams, take the common part of both number and variable.

Step 2

Why this answer is correct

The correct answer is A. (6x(2x-3)). The greatest common factor is (6x). In exams, take the common part of both number and variable.

Step 3

Exam Tip

महत्तम सामान्य गुणनखंड (6x) है। परीक्षा में संख्या और चर दोनों का सामान्य भाग लें।

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Question 34/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-16\) और \(x^2-8x+16\) के सही रूपों की जोड़ी कौन-सी है?

Which pair of forms is correct for \(x^2-16\) and \(x^2-8x+16\)?

Explanation opens after your attempt

Correct Answer

A. ((x-4)(x+4)) और ((x-4)²)((x-4)(x+4)) and ((x-4)²)

Step 1

Concept

The first is a difference of squares and the second is a perfect square. In exams, identify by the presence of the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((x-4)(x+4)) और ((x-4)²) / ((x-4)(x+4)) and ((x-4)²). The first is a difference of squares and the second is a perfect square. In exams, identify by the presence of the middle term.

Step 3

Exam Tip

पहला वर्गों का अंतर है और दूसरा पूर्ण वर्ग है। परीक्षा में मध्य पद की उपस्थिति से पहचान करें।

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Question 35/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+4x+3\) का मान (x=-1) पर क्या होगा?

What is the value of \(x^2+4x+3\) at (x=-1)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

((-1)²+4(-1)+3=1-4+3=0). In exams, be careful with negative numbers.

Step 2

Why this answer is correct

The correct answer is A. (0). ((-1)²+4(-1)+3=1-4+3=0). In exams, be careful with negative numbers.

Step 3

Exam Tip

((-1)²+4(-1)+3=1-4+3=0) है। परीक्षा में ऋण संख्या के साथ सावधानी रखें।

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Question 36/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

यदि \(x^2+mx+16\) पूर्ण वर्ग है और (m) ऋणात्मक है, तो (m) क्या होगा?

If \(x^2+mx+16\) is a perfect square and (m) is negative, what is (m)?

Explanation opens after your attempt

Correct Answer

A. (-8)

Step 1

Concept

\(16=4^2\), and the negative middle term is \(-2\cdot x\cdot4=-8x\). In exams, choose the coefficient according to the given sign.

Step 2

Why this answer is correct

The correct answer is A. (-8). \(16=4^2\), and the negative middle term is \(-2\cdot x\cdot4=-8x\). In exams, choose the coefficient according to the given sign.

Step 3

Exam Tip

\(16=4^2\) है और ऋणात्मक मध्य पद \(-2\cdot x\cdot4=-8x\) होगा। परीक्षा में दिए गए चिन्ह के अनुसार गुणांक चुनें।

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Question 37/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(4x^2+kx+1\) को ((2x+1)²) बनाने के लिए (k) क्या होगा?

What should (k) be to make \(4x^2+kx+1\) equal to ((2x+1)²)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

((2x+1)²=4x^-2+4x+1). In exams, check the middle term (2ab).

Step 2

Why this answer is correct

The correct answer is B. (4). ((2x+1)²=4x^-2+4x+1). In exams, check the middle term (2ab).

Step 3

Exam Tip

((2x+1)²=4x^-2+4x+1) है। परीक्षा में (2ab) वाला मध्य पद देखें।

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Question 38/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-2x-24\) के गुणनखंड कौन-से हैं?

What are the factors of \(x^2-2x-24\)?

Explanation opens after your attempt

Correct Answer

A. ((x-6)(x+4))

Step 1

Concept

(-6+4=-2) and ((-6)(4)=-24). In exams, use different signs for a negative constant term.

Step 2

Why this answer is correct

The correct answer is A. ((x-6)(x+4)). (-6+4=-2) and ((-6)(4)=-24). In exams, use different signs for a negative constant term.

Step 3

Exam Tip

(-6+4=-2) और ((-6)(4)=-24) है। परीक्षा में ऋणात्मक स्थिर पद के लिए अलग चिह्न लें।

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Question 39/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+13x+42\) के लिए सही गुणनखंड जोड़ी कौन-सी है?

Which is the correct factor pair for \(x^2+13x+42\)?

Explanation opens after your attempt

Correct Answer

A. ((x+6)(x+7))

Step 1

Concept

(6+7=13) and \(6\cdot7=42\). In exams, first check close factor pairs.

Step 2

Why this answer is correct

The correct answer is A. ((x+6)(x+7)). (6+7=13) and \(6\cdot7=42\). In exams, first check close factor pairs.

Step 3

Exam Tip

(6+7=13) और \(6\cdot7=42\) है। परीक्षा में निकट गुणनखंडों की जोड़ी पहले देखें।

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Question 40/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-15x+56\) का सही गुणनखंड रूप क्या है?

What is the correct factorised form of \(x^2-15x+56\)?

Explanation opens after your attempt

Correct Answer

A. ((x-7)(x-8))

Step 1

Concept

(-7-8=-15) and ((-7)(-8)=56). In exams, keep both factors negative.

Step 2

Why this answer is correct

The correct answer is A. ((x-7)(x-8)). (-7-8=-15) and ((-7)(-8)=56). In exams, keep both factors negative.

Step 3

Exam Tip

(-7-8=-15) और ((-7)(-8)=56) है। परीक्षा में दोनों गुणनखंड ऋणात्मक रखें।

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Question 41/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(3x^2+x-10\) का गुणनखंड रूप चुनिए।

Choose the factorised form of \(3x^2+x-10\).

Explanation opens after your attempt

Correct Answer

A. ((3x-5)(x+2))

Step 1

Concept

((3x-5)(x+2)) gives \(3x^2+6x-5x-10\). In exams, check until the middle term becomes (x).

Step 2

Why this answer is correct

The correct answer is A. ((3x-5)(x+2)). ((3x-5)(x+2)) gives \(3x^2+6x-5x-10\). In exams, check until the middle term becomes (x).

Step 3

Exam Tip

((3x-5)(x+2)) से \(3x^2+6x-5x-10\) मिलता है। परीक्षा में मध्य पद (x) बनने तक जाँचें।

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Question 42/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(4x^2-11x+6\) को गुणनखंडित कीजिए।

Factorise \(4x^2-11x+6\).

Explanation opens after your attempt

Correct Answer

A. ((4x-3)(x-2))

Step 1

Concept

((4x-3)(x-2)) gives \(4x^2-8x-3x+6\). In exams, check the middle term (-11x).

Step 2

Why this answer is correct

The correct answer is A. ((4x-3)(x-2)). ((4x-3)(x-2)) gives \(4x^2-8x-3x+6\). In exams, check the middle term (-11x).

Step 3

Exam Tip

((4x-3)(x-2)) से \(4x^2-8x-3x+6\) मिलता है। परीक्षा में मध्य पद (-11x) जाँचें।

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Question 43/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+4x-45\) का सही गुणनखंड कौन-सा है?

Which is the correct factorisation of \(x^2+4x-45\)?

Explanation opens after your attempt

Correct Answer

A. ((x+9)(x-5))

Step 1

Concept

(9-5=4) and (9\cdot(-5)=-45). In exams, keep the larger number's sign like the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((x+9)(x-5)). (9-5=4) and (9\cdot(-5)=-45). In exams, keep the larger number's sign like the middle term.

Step 3

Exam Tip

(9-5=4) और (9\cdot(-5)=-45) है। परीक्षा में बड़ी संख्या का चिह्न मध्य पद जैसा रखें।

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Question 44/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-18x+81\) का पूर्ण वर्ग रूप क्या है?

What is the perfect square form of \(x^2-18x+81\)?

Explanation opens after your attempt

Correct Answer

A. ((x-9)²)

Step 1

Concept

\(81=9^2\) and \(-18x=-2\cdot x\cdot9\). In exams, identify the subtraction square from the negative middle term.

Step 2

Why this answer is correct

The correct answer is A. ((x-9)²). \(81=9^2\) and \(-18x=-2\cdot x\cdot9\). In exams, identify the subtraction square from the negative middle term.

Step 3

Exam Tip

\(81=9^2\) और \(-18x=-2\cdot x\cdot9\) है। परीक्षा में ऋण मध्य पद से घटाव वाला वर्ग पहचानें।

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Question 45/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(16x^2+40x+25\) को किस रूप में लिखा जा सकता है?

In which form can \(16x^2+40x+25\) be written?

Explanation opens after your attempt

Correct Answer

A. ((4x+5)²)

Step 1

Concept

(16x^-2=(4x)²), \(25=5^2\), and \(40x=2\cdot4x\cdot5\). In exams, check the square roots of first and last terms.

Step 2

Why this answer is correct

The correct answer is A. ((4x+5)²). (16x^-2=(4x)²), \(25=5^2\), and \(40x=2\cdot4x\cdot5\). In exams, check the square roots of first and last terms.

Step 3

Exam Tip

(16x^-2=(4x)²), \(25=5^2\) और \(40x=2\cdot4x\cdot5\) है। परीक्षा में पहले और अंतिम पद के वर्गमूल देखें।

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Question 46/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+mx+49\) पूर्ण वर्ग है और (m) धनात्मक है। (m) का मान क्या होगा?

\(x^2+mx+49\) is a perfect square and (m) is positive. What will be the value of (m)?

Explanation opens after your attempt

Correct Answer

B. (14)

Step 1

Concept

\(49=7^2\), so the middle term is \(2\cdot x\cdot7=14x\). In exams, take the positive middle coefficient for a positive perfect square.

Step 2

Why this answer is correct

The correct answer is B. (14). \(49=7^2\), so the middle term is \(2\cdot x\cdot7=14x\). In exams, take the positive middle coefficient for a positive perfect square.

Step 3

Exam Tip

\(49=7^2\) है इसलिए मध्य पद \(2\cdot x\cdot7=14x\) होगा। परीक्षा में धनात्मक पूर्ण वर्ग के लिए धनात्मक मध्य गुणांक लें।

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Question 47/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(2x^2+px+8\) के गुणनखंड ((2x+4)(x+2)) नहीं हो सकते। सही कारण क्या है?

The factors of \(2x^2+px+8\) cannot be ((2x+4)(x+2)). What is the correct reason?

Explanation opens after your attempt

Correct Answer

A. क्योंकि विस्तार में \(2x^2+8x+8\) मिलता हैBecause expansion gives \(2x^2+8x+8\)

Step 1

Concept

Expanding ((2x+4)(x+2)) gives \(2x^2+8x+8\). In exams, verify the option by expansion.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि विस्तार में \(2x^2+8x+8\) मिलता है / Because expansion gives \(2x^2+8x+8\). Expanding ((2x+4)(x+2)) gives \(2x^2+8x+8\). In exams, verify the option by expansion.

Step 3

Exam Tip

((2x+4)(x+2)) फैलाने पर \(2x^2+8x+8\) मिलता है। परीक्षा में विकल्प को विस्तार करके सत्यापित करें।

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Question 48/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(3x^2+kx+12\) में यदि गुणनखंड ((3x+4)(x+3)) हैं, तो (k) का मान क्या है?

In \(3x^2+kx+12\), if the factors are ((3x+4)(x+3)), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

((3x+4)(x+3)=3x^-2+9x+4x+12=3x^-2+13x+12). In exams, add the cross terms.

Step 2

Why this answer is correct

The correct answer is C. (13). ((3x+4)(x+3)=3x^-2+9x+4x+12=3x^-2+13x+12). In exams, add the cross terms.

Step 3

Exam Tip

((3x+4)(x+3)=3x^-2+9x+4x+12=3x^-2+13x+12) है। परीक्षा में क्रॉस पदों को जोड़ें।

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Question 49/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2-12x+32\) का सही गुणनखंड रूप क्या है?

What is the correct factorised form of \(x^2-12x+32\)?

Explanation opens after your attempt

Correct Answer

A. ((x-4)(x-8))

Step 1

Concept

(-4-8=-12) and ((-4)(-8)=32). In exams, use both negative signs when the constant is positive and middle term is negative.

Step 2

Why this answer is correct

The correct answer is A. ((x-4)(x-8)). (-4-8=-12) and ((-4)(-8)=32). In exams, use both negative signs when the constant is positive and middle term is negative.

Step 3

Exam Tip

(-4-8=-12) और ((-4)(-8)=32) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद पर दोनों चिह्न ऋण रखें।

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Question 50/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(25x^2+mx+36\) पूर्ण वर्ग है और (m) धनात्मक है। (m) का मान क्या होगा?

\(25x^2+mx+36\) is a perfect square and (m) is positive. What will be the value of (m)?

Explanation opens after your attempt

Correct Answer

B. (60)

Step 1

Concept

(25x^-2=(5x)²) and \(36=6^2\), so the middle term is \(2\cdot5x\cdot6=60x\). In exams, multiply twice the two square roots.

Step 2

Why this answer is correct

The correct answer is B. (60). (25x^-2=(5x)²) and \(36=6^2\), so the middle term is \(2\cdot5x\cdot6=60x\). In exams, multiply twice the two square roots.

Step 3

Exam Tip

(25x^-2=(5x)²) और \(36=6^2\), इसलिए मध्य पद \(2\cdot5x\cdot6=60x\) है। परीक्षा में दोनों वर्गमूलों का दुगुना गुणन करें।

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Class 9 Mathematics Hard Quiz

\(3x^2-5x+7\) में \(x^2\) का गुणांक क्या है?

Concept

Why this answer is correct

Exam Tip

\(5x-2x^2+9\) को मानक रूप में लिखने पर कौन-सा रूप मिलेगा?

Concept

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\(2x^2+3x-4\) में (x=2) रखने पर मान क्या होगा?

Concept

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\(x^2-6x+9\) को पूर्ण वर्ग के रूप में कैसे लिखा जाएगा?

Concept

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Exam Tip

\(4x^2+12x+9\) का सही पूर्ण वर्ग रूप क्या है?

Concept

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Exam Tip

\(9x^2-24x+16\) को पूर्ण वर्ग में बदलने पर क्या मिलेगा?

Concept

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\(x^2+7x+12\) में मध्य पद विभाजन के लिए कौन-सी जोड़ी सही है?

Concept

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\(x^2-9x+20\) के मध्य पद के लिए सही विभाजन क्या है?

Concept

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\(x^2+2x-15\) का गुणनखंड रूप क्या है?

Concept

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\(x^2-4x-21\) को गुणनखंडों में लिखिए।

Concept

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\(2x^2+5x+3\) का सही गुणनखंड कौन-सा है?

Concept

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\(3x^2+14x+8\) का गुणनखंड रूप चुनिए।

Concept

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\(2x^2-7x+6\) का सही गुणनखंड क्या है?

Concept

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\(5x^2-13x+6\) के गुणनखंड कौन-से होंगे?

Concept

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\(6x^2+x-2\) को गुणनखंडित कीजिए।

Concept

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\(x^2+px+24\) में यदि एक गुणनखंड (x+6) है, तो (p) का मान क्या होगा?

Concept

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\(x^2+kx+36\) को ((x+4)(x+9)) के बराबर बनाया गया है। (k) का मान क्या है?

Concept

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\(x^2-11x+k\) के गुणनखंड (x-5) और (x-6) हैं। (k) का मान क्या होगा?

Concept

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\(x^2+8x+c\) को पूर्ण वर्ग बनाने के लिए (c) का मान क्या होना चाहिए?

Concept

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\(x^2-14x+c\) पूर्ण वर्ग हो, तो (c) का मान क्या होगा?

Concept

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\(x^2+6x+5\) को ((x+3)²) से तुलना करने पर कितना अंतर है?

\(4x^2+kx+1\) को ((2x+1)²) बनाने के लिए (k) क्या होगा?