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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

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

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

Explanation opens after your attempt

Correct Answer

A. (3)coefficient of \(x^2\)

Step 1

Concept

The number attached to \(x^2\) is (3). In exams check the sign while finding coefficients.

Step 2

Why this answer is correct

The correct answer is A. (3) / coefficient of \(x^2\). The number attached to \(x^2\) is (3). In exams check the sign while finding coefficients.

Step 3

Exam Tip

\(x^2\) के साथ लगी संख्या (3) है। परीक्षा में गुणांक निकालते समय चिन्ह भी देखें।

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Question 2/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

व्यंजक \(2y^2+9y-11\) में स्थिर पद कौन-सा है?

Which is the constant term in the expression \(2y^2+9y-11\)?

Explanation opens after your attempt

Correct Answer

C. (-11)constant term

Step 1

Concept

The term without a variable is the constant term. In exams write the constant term with its sign.

Step 2

Why this answer is correct

The correct answer is C. (-11) / constant term. The term without a variable is the constant term. In exams write the constant term with its sign.

Step 3

Exam Tip

जिस पद में चर नहीं होता वही स्थिर पद होता है। परीक्षा में चिन्ह सहित स्थिर पद लिखें।

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Question 3/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+6x+9\) को पूर्ण वर्ग के रूप में लिखें।

Write \(x^2+6x+9\) as a perfect square.

Explanation opens after your attempt

Correct Answer

A. ((x+3)²)correct perfect square

Step 1

Concept

\(9=3^2\) and \(6x=2\cdot x\cdot3\). In exams take the square root of the last term and match the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((x+3)²) / correct perfect square. \(9=3^2\) and \(6x=2\cdot x\cdot3\). In exams take the square root of the last term and match the middle term.

Step 3

Exam Tip

\(9=3^2\) और \(6x=2\cdot x\cdot3\) है। परीक्षा में अंतिम पद का वर्गमूल लेकर मध्य पद मिलाएं।

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Question 4/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(a^2-10a+25\) किस पूर्ण वर्ग के बराबर है?

Which perfect square is equal to \(a^2-10a+25\)?

Explanation opens after your attempt

Correct Answer

B. ((a-5)²)correct square

Step 1

Concept

The middle term \(-10a=-2\cdot a\cdot5\), so the sign is negative. In exams the sign of the middle term is decisive.

Step 2

Why this answer is correct

The correct answer is B. ((a-5)²) / correct square. The middle term \(-10a=-2\cdot a\cdot5\), so the sign is negative. In exams the sign of the middle term is decisive.

Step 3

Exam Tip

मध्य पद \(-10a=-2\cdot a\cdot5\) है इसलिए चिन्ह ऋणात्मक होगा। परीक्षा में मध्य पद का चिन्ह निर्णायक होता है।

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Question 5/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+8x+15\) के दो रैखिक गुणनखंड कौन-से हैं?

What are the two linear factors of \(x^2+8x+15\)?

Explanation opens after your attempt

Correct Answer

A. ((x+3)(x+5))correct factors

Step 1

Concept

(3+5=8) and \(3\cdot5=15\). In exams match the sum with the middle coefficient and the product with the constant term.

Step 2

Why this answer is correct

The correct answer is A. ((x+3)(x+5)) / correct factors. (3+5=8) and \(3\cdot5=15\). In exams match the sum with the middle coefficient and the product with the constant term.

Step 3

Exam Tip

(3+5=8) और \(3\cdot5=15\) है। परीक्षा में योग मध्य गुणांक और गुणनफल स्थिर पद से मिलाएं।

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Question 6/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-7x+12\) का गुणनखंड रूप क्या है?

What is the factorised form of \(x^2-7x+12\)?

Explanation opens after your attempt

Correct Answer

B. ((x-3)(x-4))correct factors

Step 1

Concept

(-3+(-4)=-7) and ((-3)(-4)=12). In exams use two negative signs when the constant is positive and the middle term is negative.

Step 2

Why this answer is correct

The correct answer is B. ((x-3)(x-4)) / correct factors. (-3+(-4)=-7) and ((-3)(-4)=12). In exams use two negative signs when the constant is positive and the middle term is negative.

Step 3

Exam Tip

(-3+(-4)=-7) और ((-3)(-4)=12) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद पर दोनों चिन्ह ऋणात्मक लें।

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Question 7/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+x-20\) को गुणनखंडित करें।

Factorise \(x^2+x-20\).

Explanation opens after your attempt

Correct Answer

A. ((x+5)(x-4))correct factors

Step 1

Concept

(5+(-4)=1) and (5\cdot(-4)=-20). In exams look for opposite signs when the constant is negative.

Step 2

Why this answer is correct

The correct answer is A. ((x+5)(x-4)) / correct factors. (5+(-4)=1) and (5\cdot(-4)=-20). In exams look for opposite signs when the constant is negative.

Step 3

Exam Tip

(5+(-4)=1) और (5\cdot(-4)=-20) है। परीक्षा में ऋणात्मक स्थिर पद के लिए विपरीत चिन्ह खोजें।

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Question 8/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(3x^2+10x+8\) का सही गुणनखंड रूप चुनें।

Choose the correct factorised form of \(3x^2+10x+8\).

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

In ((3x+4)(x+2)), the cross terms are (6x) and (4x). In exams their sum should be the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((3x+4)(x+2)) / correct factors. In ((3x+4)(x+2)), the cross terms are (6x) and (4x). In exams their sum should be the middle term.

Step 3

Exam Tip

((3x+4)(x+2)) में क्रॉस पद (6x) और (4x) हैं। परीक्षा में क्रॉस पदों का योग मध्य पद होना चाहिए।

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Question 9/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(4x^2-9\) को द्विघात पहचान से लिखें।

Write \(4x^2-9\) using a quadratic identity.

Explanation opens after your attempt

Correct Answer

B. ((2x-3)(2x+3))difference of squares

Step 1

Concept

(4x^-2=(2x)²) and \(9=3^2\). In exams write difference of squares as ((a-b)(a+b)).

Step 2

Why this answer is correct

The correct answer is B. ((2x-3)(2x+3)) / difference of squares. (4x^-2=(2x)²) and \(9=3^2\). In exams write difference of squares as ((a-b)(a+b)).

Step 3

Exam Tip

(4x^-2=(2x)²) और \(9=3^2\) है। परीक्षा में वर्गों के अंतर को ((a-b)(a+b)) लिखें।

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Question 10/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(9y^2-24y+16\) किसके बराबर है?

What is \(9y^2-24y+16\) equal to?

Explanation opens after your attempt

Correct Answer

B. ((3y-4)²)correct perfect square

Step 1

Concept

(9y^-2=(3y)²), \(16=4^2\), and the middle term is (-24y). In exams match both square terms and the middle term.

Step 2

Why this answer is correct

The correct answer is B. ((3y-4)²) / correct perfect square. (9y^-2=(3y)²), \(16=4^2\), and the middle term is (-24y). In exams match both square terms and the middle term.

Step 3

Exam Tip

(9y^-2=(3y)²), \(16=4^2\), और मध्य पद (-24y) है। परीक्षा में दोनों वर्ग पद और मध्य पद मिलाएं।

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Question 11/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

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

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

Explanation opens after your attempt

Correct Answer

A. (0)correct value

Step 1

Concept

Substitution gives \(2^2-5\cdot2+6=0\). In exams do powers first, then multiplication, then addition or subtraction.

Step 2

Why this answer is correct

The correct answer is A. (0) / correct value. Substitution gives \(2^2-5\cdot2+6=0\). In exams do powers first, then multiplication, then addition or subtraction.

Step 3

Exam Tip

मान रखने पर \(2^2-5\cdot2+6=0\) मिलता है। परीक्षा में पहले घात फिर गुणा और फिर जोड़-घटाव करें।

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Question 12/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

(t=-1) पर \(2t^2+3t-5\) का मान क्या है?

What is the value of \(2t^2+3t-5\) at (t=-1)?

Explanation opens after your attempt

Correct Answer

A. (-6)correct value

Step 1

Concept

(2(-1)²+3(-1)-5=2-3-5=-6). In exams the square of a negative number is positive.

Step 2

Why this answer is correct

The correct answer is A. (-6) / correct value. (2(-1)²+3(-1)-5=2-3-5=-6). In exams the square of a negative number is positive.

Step 3

Exam Tip

(2(-1)²+3(-1)-5=2-3-5=-6) है। परीक्षा में ऋणात्मक संख्या का वर्ग धनात्मक होता है।

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Question 13/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+kx+16\) पूर्ण वर्ग हो और (k) धनात्मक हो तो (k) का मान क्या है?

If \(x^2+kx+16\) is a perfect square and (k) is positive, what is the value of (k)?

Explanation opens after your attempt

Correct Answer

B. (8)correct middle coefficient

Step 1

Concept

\(16=4^2\), and in a perfect square the middle term is \(2\cdot x\cdot4=8x\). In exams double the root of the constant term.

Step 2

Why this answer is correct

The correct answer is B. (8) / correct middle coefficient. \(16=4^2\), and in a perfect square the middle term is \(2\cdot x\cdot4=8x\). In exams double the root of the constant term.

Step 3

Exam Tip

\(16=4^2\) और पूर्ण वर्ग में मध्य पद \(2\cdot x\cdot4=8x\) होगा। परीक्षा में स्थिर पद की जड़ को दोगुना करें।

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Question 14/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

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

If \(x^2-14x+c\) is a perfect square, what is (c)?

Explanation opens after your attempt

Correct Answer

C. (49)square of half coefficient

Step 1

Concept

\(-14x=-2\cdot x\cdot7\), so \(c=7^2=49\). In exams take half of the middle coefficient and square it.

Step 2

Why this answer is correct

The correct answer is C. (49) / square of half coefficient. \(-14x=-2\cdot x\cdot7\), so \(c=7^2=49\). In exams take half of the middle coefficient and square it.

Step 3

Exam Tip

\(-14x=-2\cdot x\cdot7\), इसलिए \(c=7^2=49\) है। परीक्षा में मध्य गुणांक का आधा लेकर उसका वर्ग करें।

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Question 15/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+px+21\) के गुणनखंड ((x+3)(x+7)) हैं। (p) का मान क्या है?

The factors of \(x^2+px+21\) are ((x+3)(x+7)). What is the value of (p)?

Explanation opens after your attempt

Correct Answer

C. (10)sum of constants

Step 1

Concept

((x+3)(x+7)=x^-2+10x+21), so (p=10). In exams the middle term comes from the sum of the constants.

Step 2

Why this answer is correct

The correct answer is C. (10) / sum of constants. ((x+3)(x+7)=x^-2+10x+21), so (p=10). In exams the middle term comes from the sum of the constants.

Step 3

Exam Tip

((x+3)(x+7)=x^-2+10x+21), इसलिए (p=10) है। परीक्षा में मध्य पद स्थिर संख्याओं के योग से बनता है।

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Question 16/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-11x+30\) के शून्य बनाने वाले गुणनखंड कौन-से हैं?

Which factors make \(x^2-11x+30\) zero?

Explanation opens after your attempt

Correct Answer

A. ((x-5)(x-6))correct factors

Step 1

Concept

(-5+(-6)=-11) and ((-5)(-6)=30). In exams verify by expanding the factors.

Step 2

Why this answer is correct

The correct answer is A. ((x-5)(x-6)) / correct factors. (-5+(-6)=-11) and ((-5)(-6)=30). In exams verify by expanding the factors.

Step 3

Exam Tip

(-5+(-6)=-11) और ((-5)(-6)=30) है। परीक्षा में गुणनखंड फैलाकर सत्यापन करें।

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Question 17/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

कौन-सा द्विघात व्यंजक ((x-4)(x+2)) से प्राप्त होता है?

Which quadratic expression is obtained from ((x-4)(x+2))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-2x-8\)correct expansion

Step 1

Concept

The cross terms (2x) and (-4x) combine to (-2x). In exams add outer and inner terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-8\) / correct expansion. The cross terms (2x) and (-4x) combine to (-2x). In exams add outer and inner terms.

Step 3

Exam Tip

क्रॉस पद (2x) और (-4x) मिलकर (-2x) देते हैं। परीक्षा में बाहरी और अंदरूनी पद जोड़ें।

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Question 18/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

((2x-3)(x+5)) का विस्तार क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(2x^2+7x-15\)correct expansion

Step 1

Concept

\(2x\cdot5=10x\) and \(-3\cdot x=-3x\), so the middle term is (7x). In exams write all four products.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+7x-15\) / correct expansion. \(2x\cdot5=10x\) and \(-3\cdot x=-3x\), so the middle term is (7x). In exams write all four products.

Step 3

Exam Tip

\(2x\cdot5=10x\) और \(-3\cdot x=-3x\), इसलिए मध्य पद (7x) है। परीक्षा में चारों गुणनफल लिखें।

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Question 19/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(5x^2-20x+20\) में समान गुणनखंड निकालने के बाद अंदर कौन-सा द्विघात व्यंजक बचेगा?

After taking the common factor from \(5x^2-20x+20\), which quadratic expression remains inside?

Explanation opens after your attempt

Correct Answer

A. \(x^2-4x+4\)correct inside expression

Step 1

Concept

Taking common (5) gives (5\(x^2-4x+4\)). In exams first take the common factor and then apply identities.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+4\) / correct inside expression. Taking common (5) gives (5\(x^2-4x+4\)). In exams first take the common factor and then apply identities.

Step 3

Exam Tip

समान गुणनखंड (5) निकालने पर (5\(x^2-4x+4\)) मिलता है। परीक्षा में पहले समान गुणनखंड निकालें फिर पहचान लगाएं।

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Question 20/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(3x^2-27\) का पूर्ण गुणनखंड रूप क्या है?

What is the complete factorised form of \(3x^2-27\)?

Explanation opens after your attempt

Correct Answer

A. (3(x-3)(x+3))correct complete form

Step 1

Concept

First take out (3), and \(x^2-9\) is a difference of squares. In exams factorise the inside expression too.

Step 2

Why this answer is correct

The correct answer is A. (3(x-3)(x+3)) / correct complete form. First take out (3), and \(x^2-9\) is a difference of squares. In exams factorise the inside expression too.

Step 3

Exam Tip

पहले (3) निकालें और \(x^2-9\) वर्गों का अंतर है। परीक्षा में अंदर की अभिव्यक्ति को भी गुणनखंडित करें।

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Question 21/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(4x^2+12x+k\) पूर्ण वर्ग हो तो (k) क्या होगा?

If \(4x^2+12x+k\) is a perfect square, what is (k)?

Explanation opens after your attempt

Correct Answer

B. (9)correct constant

Step 1

Concept

(4x^-2=(2x)²) and \(12x=2\cdot2x\cdot3\), so (k=9). In exams identify the second part using (2ab).

Step 2

Why this answer is correct

The correct answer is B. (9) / correct constant. (4x^-2=(2x)²) and \(12x=2\cdot2x\cdot3\), so (k=9). In exams identify the second part using (2ab).

Step 3

Exam Tip

(4x^-2=(2x)²) और \(12x=2\cdot2x\cdot3\), इसलिए (k=9) है। परीक्षा में (2ab) से दूसरा भाग पहचानें।

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Question 22/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(9x^2+kx+25\) पूर्ण वर्ग हो और (k) ऋणात्मक हो तो (k) क्या है?

If \(9x^2+kx+25\) is a perfect square and (k) is negative, what is (k)?

Explanation opens after your attempt

Correct Answer

B. (-30)correct middle

Step 1

Concept

(9x^-2=(3x)²), \(25=5^2\), so the middle term is \(-2\cdot3x\cdot5=-30x\). In exams follow the given sign.

Step 2

Why this answer is correct

The correct answer is B. (-30) / correct middle. (9x^-2=(3x)²), \(25=5^2\), so the middle term is \(-2\cdot3x\cdot5=-30x\). In exams follow the given sign.

Step 3

Exam Tip

(9x^-2=(3x)²), \(25=5^2\), इसलिए मध्य पद \(-2\cdot3x\cdot5=-30x\) है। परीक्षा में दिए गए चिन्ह का पालन करें।

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Question 23/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+2xy-15y^2\) का गुणनखंड रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

A. ((x+5y)(x-3y))correct factors

Step 1

Concept

(5y+(-3y)=2y) and (5y\cdot(-3y)=-15y^-2). In exams add the factors along with variables.

Step 2

Why this answer is correct

The correct answer is A. ((x+5y)(x-3y)) / correct factors. (5y+(-3y)=2y) and (5y\cdot(-3y)=-15y^-2). In exams add the factors along with variables.

Step 3

Exam Tip

(5y+(-3y)=2y) और (5y\cdot(-3y)=-15y^-2) है। परीक्षा में चर सहित गुणनखंडों का योग करें।

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Question 24/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(2a^2+ab-6b^2\) के गुणनखंड कौन-से हैं?

What are the factors of \(2a^2+ab-6b^2\)?

Explanation opens after your attempt

Correct Answer

A. ((2a-3b)(a+2b))correct factors

Step 1

Concept

((2a-3b)(a+2b)=2a^-2+ab-6b^-2). In exams add cross terms to check the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((2a-3b)(a+2b)) / correct factors. ((2a-3b)(a+2b)=2a^-2+ab-6b^-2). In exams add cross terms to check the middle term.

Step 3

Exam Tip

((2a-3b)(a+2b)=2a^-2+ab-6b^-2) है। परीक्षा में क्रॉस पदों को जोड़कर मध्य पद जांचें।

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Question 25/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(6p^2+5pq-q^2\) का सही गुणनखंड रूप चुनें।

Choose the correct factorised form of \(6p^2+5pq-q^2\).

Explanation opens after your attempt

Correct Answer

A. ((3p-q)(2p+q))correct factors

Step 1

Concept

Actually ((3p-q)(2p+q)) gives \(6p^2+pq-q^2\). Check the cross terms carefully in exams.

Step 2

Why this answer is correct

The correct answer is A. ((3p-q)(2p+q)) / correct factors. Actually ((3p-q)(2p+q)) gives \(6p^2+pq-q^2\). Check the cross terms carefully in exams.

Step 3

Exam Tip

क्रॉस पद (3pq) और (-2pq) नहीं, सही रूप में \(3p\cdot q=3pq\) और \(-q\cdot2p=-2pq\) से (pq) मिलता है?

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Question 26/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(6p^2+5pq-q^2\) का सही गुणनखंड रूप कौन-सा है?

Which is the correct factorised form of \(6p^2+5pq-q^2\)?

Explanation opens after your attempt

Correct Answer

A. ((6p-q)(p+q))correct factors

Step 1

Concept

((6p-q)(p+q)=6p^-2+5pq-q^-2). In exams always expand the option and check cross terms.

Step 2

Why this answer is correct

The correct answer is A. ((6p-q)(p+q)) / correct factors. ((6p-q)(p+q)=6p^-2+5pq-q^-2). In exams always expand the option and check cross terms.

Step 3

Exam Tip

((6p-q)(p+q)=6p^-2+5pq-q^-2) है। परीक्षा में विकल्प को फैलाकर क्रॉस पद जरूर जांचें।

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Question 27/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+4x+4-y^2\) का पूर्ण गुणनखंड रूप क्या है?

What is the complete factorised form of \(x^2+4x+4-y^2\)?

Explanation opens after your attempt

Correct Answer

A. ((x+2-y)(x+2+y))correct form

Step 1

Concept

First (x^-2+4x+4=(x+2)²), then apply difference of squares. In exams do not stop at the partial form.

Step 2

Why this answer is correct

The correct answer is A. ((x+2-y)(x+2+y)) / correct form. First (x^-2+4x+4=(x+2)²), then apply difference of squares. In exams do not stop at the partial form.

Step 3

Exam Tip

पहले (x^-2+4x+4=(x+2)²), फिर वर्गों का अंतर लगाएं। परीक्षा में आंशिक रूप पर न रुकें।

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Question 28/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-6x+9-z^2\) को गुणनखंडित करें।

Factorise \(x^2-6x+9-z^2\).

Explanation opens after your attempt

Correct Answer

A. ((x-3-z)(x-3+z))correct form

Step 1

Concept

First (x^-2-6x+9=(x-3)²), then use the \(a^2-b^2\) identity. In exams identify the perfect-square group.

Step 2

Why this answer is correct

The correct answer is A. ((x-3-z)(x-3+z)) / correct form. First (x^-2-6x+9=(x-3)²), then use the \(a^2-b^2\) identity. In exams identify the perfect-square group.

Step 3

Exam Tip

पहले (x^-2-6x+9=(x-3)²), फिर (\(a^2-b^2\)) पहचान लगती है। परीक्षा में पूर्ण वर्ग समूह पहचानें।

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Question 29/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+ax+24\) का एक गुणनखंड (x+6) है। दूसरा गुणनखंड (x+4) हो तो (a) क्या है?

One factor of \(x^2+ax+24\) is (x+6). If the other factor is (x+4), what is (a)?

Explanation opens after your attempt

Correct Answer

A. (10)correct coefficient

Step 1

Concept

((x+6)(x+4)=x^-2+10x+24), so (a=10). In exams add the constant parts of the factors.

Step 2

Why this answer is correct

The correct answer is A. (10) / correct coefficient. ((x+6)(x+4)=x^-2+10x+24), so (a=10). In exams add the constant parts of the factors.

Step 3

Exam Tip

((x+6)(x+4)=x^-2+10x+24), इसलिए (a=10) है। परीक्षा में गुणनखंडों के स्थिर भाग जोड़ें।

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Question 30/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-bx+18\) के गुणनखंड ((x-3)(x-6)) हैं। (b) क्या है?

The factors of \(x^2-bx+18\) are ((x-3)(x-6)). What is (b)?

Explanation opens after your attempt

Correct Answer

C. (9)correct value

Step 1

Concept

((x-3)(x-6)=x^-2-9x+18), so (b=9). In exams (b) remains positive because the expression has (-bx).

Step 2

Why this answer is correct

The correct answer is C. (9) / correct value. ((x-3)(x-6)=x^-2-9x+18), so (b=9). In exams (b) remains positive because the expression has (-bx).

Step 3

Exam Tip

((x-3)(x-6)=x^-2-9x+18), इसलिए (b=9) है। परीक्षा में ऋण चिन्ह के कारण (b) धनात्मक रहता है।

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Question 31/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(2x^2+mx+10\) का गुणनखंड रूप ((2x+5)(x+2)) है। (m) क्या होगा?

The factorised form of \(2x^2+mx+10\) is ((2x+5)(x+2)). What is (m)?

Explanation opens after your attempt

Correct Answer

C. (9)correct middle coefficient

Step 1

Concept

The cross terms are (4x) and (5x), whose sum is (9x). In exams add both cross terms.

Step 2

Why this answer is correct

The correct answer is C. (9) / correct middle coefficient. The cross terms are (4x) and (5x), whose sum is (9x). In exams add both cross terms.

Step 3

Exam Tip

क्रॉस पद (4x) और (5x) हैं, जिनका योग (9x) है। परीक्षा में दोनों क्रॉस पद जोड़ें।

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Question 32/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

कौन-सा (k), \(x^2+kx+81\) को पूर्ण वर्ग बनाएगा और (k) ऋणात्मक है?

Which (k) makes \(x^2+kx+81\) a perfect square and (k) is negative?

Explanation opens after your attempt

Correct Answer

B. (-18)correct middle

Step 1

Concept

\(81=9^2\), so the negative middle term is \(-2\cdot x\cdot9=-18x\). In exams do not forget the given sign.

Step 2

Why this answer is correct

The correct answer is B. (-18) / correct middle. \(81=9^2\), so the negative middle term is \(-2\cdot x\cdot9=-18x\). In exams do not forget the given sign.

Step 3

Exam Tip

\(81=9^2\), इसलिए ऋणात्मक मध्य पद \(-2\cdot x\cdot9=-18x\) होगा। परीक्षा में दिए गए चिन्ह को न भूलें।

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Question 33/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-4x+5\) को पूर्ण वर्ग जोड़कर किस रूप में लिखा जा सकता है?

How can \(x^2-4x+5\) be written by completing the square?

Explanation opens after your attempt

Correct Answer

A. ((x-2)²+1)correct form

Step 1

Concept

(x^-2-4x+4=(x-2)²), so write (5) as (4+1). In exams take half of the middle coefficient.

Step 2

Why this answer is correct

The correct answer is A. ((x-2)²+1) / correct form. (x^-2-4x+4=(x-2)²), so write (5) as (4+1). In exams take half of the middle coefficient.

Step 3

Exam Tip

(x^-2-4x+4=(x-2)²), इसलिए (5) को (4+1) लिखते हैं। परीक्षा में मध्य गुणांक का आधा लें।

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Question 34/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+6x+11\) को पूर्ण वर्ग रूप में लिखें।

Write \(x^2+6x+11\) in completed square form.

Explanation opens after your attempt

Correct Answer

A. ((x+3)²+2)correct form

Step 1

Concept

(x^-2+6x+9=(x+3)²), so (11=9+2). In exams form the needed square and keep the remainder separate.

Step 2

Why this answer is correct

The correct answer is A. ((x+3)²+2) / correct form. (x^-2+6x+9=(x+3)²), so (11=9+2). In exams form the needed square and keep the remainder separate.

Step 3

Exam Tip

(x^-2+6x+9=(x+3)²), इसलिए (11=9+2) है। परीक्षा में आवश्यक वर्ग जोड़कर शेष अलग रखें।

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Question 35/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-8x+13\) का पूर्ण वर्ग रूप कौन-सा है?

Which is the completed square form of \(x^2-8x+13\)?

Explanation opens after your attempt

Correct Answer

A. ((x-4)²-3)correct form

Step 1

Concept

(x^-2-8x+16=(x-4)²) and (13=16-3). In exams balance the square that was added.

Step 2

Why this answer is correct

The correct answer is A. ((x-4)²-3) / correct form. (x^-2-8x+16=(x-4)²) and (13=16-3). In exams balance the square that was added.

Step 3

Exam Tip

(x^-2-8x+16=(x-4)²) और (13=16-3) है। परीक्षा में जो वर्ग जोड़ा गया है उसे संतुलित करें।

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Question 36/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (x+y=7) और (xy=10), तो \(x^2+y^2\) का मान क्या है?

If (x+y=7) and (xy=10), what is the value of \(x^2+y^2\)?

Explanation opens after your attempt

Correct Answer

A. (29)correct value

Step 1

Concept

(x^-2+y^-2=(x+y)²-2xy=49-20=29). In exams use the square of sum identity.

Step 2

Why this answer is correct

The correct answer is A. (29) / correct value. (x^-2+y^-2=(x+y)²-2xy=49-20=29). In exams use the square of sum identity.

Step 3

Exam Tip

(x^-2+y^-2=(x+y)²-2xy=49-20=29) है। परीक्षा में योग के वर्ग की पहचान उपयोग करें।

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Question 37/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (a-b=5) और (ab=6), तो \(a^2+b^2\) क्या होगा?

If (a-b=5) and (ab=6), what is \(a^2+b^2\)?

Explanation opens after your attempt

Correct Answer

C. (37)correct value

Step 1

Concept

(a^-2+b^-2=(a-b)²+2ab=25+12=37). In exams add (2ab) when using the square of difference identity.

Step 2

Why this answer is correct

The correct answer is C. (37) / correct value. (a^-2+b^-2=(a-b)²+2ab=25+12=37). In exams add (2ab) when using the square of difference identity.

Step 3

Exam Tip

(a^-2+b^-2=(a-b)²+2ab=25+12=37) है। परीक्षा में अंतर के वर्ग की पहचान में (+2ab) जोड़ें।

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Question 38/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (p+q=9) और \(p^2+q^2=41\), तो (pq) क्या है?

If (p+q=9) and \(p^2+q^2=41\), what is (pq)?

Explanation opens after your attempt

Correct Answer

A. (20)correct value

Step 1

Concept

((p+q)²=p^-2+q^-2+2pq), so (81=41+2pq) and (pq=20). In exams find (2pq) first.

Step 2

Why this answer is correct

The correct answer is A. (20) / correct value. ((p+q)²=p^-2+q^-2+2pq), so (81=41+2pq) and (pq=20). In exams find (2pq) first.

Step 3

Exam Tip

((p+q)²=p^-2+q^-2+2pq), इसलिए (81=41+2pq) और (pq=20) है। परीक्षा में (2pq) पहले निकालें।

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Question 39/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (m-n=4) और \(m^2+n^2=34\), तो (mn) क्या है?

If (m-n=4) and \(m^2+n^2=34\), what is (mn)?

Explanation opens after your attempt

Correct Answer

A. (9)correct value

Step 1

Concept

((m-n)²=m^-2+n^-2-2mn), so (16=34-2mn) and (mn=9). In exams pay attention to the sign.

Step 2

Why this answer is correct

The correct answer is A. (9) / correct value. ((m-n)²=m^-2+n^-2-2mn), so (16=34-2mn) and (mn=9). In exams pay attention to the sign.

Step 3

Exam Tip

((m-n)²=m^-2+n^-2-2mn), इसलिए (16=34-2mn) और (mn=9) है। परीक्षा में चिन्ह पर ध्यान दें।

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Question 40/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(2x^2-3x-2\) का गुणनखंड रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

A. ((2x+1)(x-2))correct factors

Step 1

Concept

((2x+1)(x-2)=2x^-2-3x-2). In exams check opposite signs when the constant term is negative.

Step 2

Why this answer is correct

The correct answer is A. ((2x+1)(x-2)) / correct factors. ((2x+1)(x-2)=2x^-2-3x-2). In exams check opposite signs when the constant term is negative.

Step 3

Exam Tip

((2x+1)(x-2)=2x^-2-3x-2) है। परीक्षा में ऋणात्मक स्थिर पद पर विपरीत चिन्हों को जांचें।

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Question 41/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(5x^2+13x+6\) के गुणनखंड कौन-से हैं?

What are the factors of \(5x^2+13x+6\)?

Explanation opens after your attempt

Correct Answer

A. ((5x+3)(x+2))correct factors

Step 1

Concept

The cross terms (10x) and (3x) combine to (13x). In exams check options using both leading coefficient and constant term.

Step 2

Why this answer is correct

The correct answer is A. ((5x+3)(x+2)) / correct factors. The cross terms (10x) and (3x) combine to (13x). In exams check options using both leading coefficient and constant term.

Step 3

Exam Tip

क्रॉस पद (10x) और (3x) मिलकर (13x) देते हैं। परीक्षा में अग्र गुणांक और स्थिर पद दोनों से विकल्प जांचें।

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Question 42/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(6x^2-x-2\) का सही गुणनखंड रूप चुनें।

Choose the correct factorised form of \(6x^2-x-2\).

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((3x-2)(2x+1)=6x^-2-x-2). In exams add cross terms (3x) and (-4x).

Step 2

Why this answer is correct

The correct answer is A. ((3x-2)(2x+1)) / correct factors. ((3x-2)(2x+1)=6x^-2-x-2). In exams add cross terms (3x) and (-4x).

Step 3

Exam Tip

((3x-2)(2x+1)=6x^-2-x-2) है। परीक्षा में क्रॉस पद (3x) और (-4x) जोड़ें।

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Question 43/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(12x^2+7x-12\) का गुणनखंड रूप क्या है?

What is the factorised form of \(12x^2+7x-12\)?

Explanation opens after your attempt

Correct Answer

A. ((3x+4)(4x-3))correct factors

Step 1

Concept

((3x+4)(4x-3)=12x^-2+7x-12). In exams check that (16x-9x=7x).

Step 2

Why this answer is correct

The correct answer is A. ((3x+4)(4x-3)) / correct factors. ((3x+4)(4x-3)=12x^-2+7x-12). In exams check that (16x-9x=7x).

Step 3

Exam Tip

((3x+4)(4x-3)=12x^-2+7x-12) है। परीक्षा में (16x-9x=7x) जांचें।

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Question 44/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(7-4x+2x^2\) को मानक द्विघात रूप में लिखें।

Write \(7-4x+2x^2\) in standard quadratic form.

Explanation opens after your attempt

Correct Answer

A. \(2x^2-4x+7\)correct standard form

Step 1

Concept

In standard form, the \(x^2\) term comes first, then the (x) term, then the constant term. In exams arrange terms in descending powers.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-4x+7\) / correct standard form. In standard form, the \(x^2\) term comes first, then the (x) term, then the constant term. In exams arrange terms in descending powers.

Step 3

Exam Tip

मानक रूप में \(x^2\) वाला पद पहले, फिर (x) वाला पद और फिर स्थिर पद आता है। परीक्षा में पदों को घात के घटते क्रम में रखें।

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Question 45/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2+10x+24\) को ((x+a)(x+b)) रूप में लिखने पर (a+b) क्या होगा?

When \(x^2+10x+24\) is written as ((x+a)(x+b)), what is (a+b)?

Explanation opens after your attempt

Correct Answer

A. (10)correct sum

Step 1

Concept

((x+a)(x+b)=x^-2+(a+b)x+ab), so (a+b=10). In exams treat the middle coefficient as (a+b).

Step 2

Why this answer is correct

The correct answer is A. (10) / correct sum. ((x+a)(x+b)=x^-2+(a+b)x+ab), so (a+b=10). In exams treat the middle coefficient as (a+b).

Step 3

Exam Tip

((x+a)(x+b)=x^-2+(a+b)x+ab), इसलिए (a+b=10) है। परीक्षा में मध्य गुणांक को (a+b) मानें।

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Question 46/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (x^-2+sx+35=(x+5)(x+7)), तो (s) क्या है?

If (x^-2+sx+35=(x+5)(x+7)), what is (s)?

Explanation opens after your attempt

Correct Answer

C. (12)correct sum

Step 1

Concept

((x+5)(x+7)=x^-2+12x+35), so (s=12). In exams the sum of constant parts is the middle coefficient.

Step 2

Why this answer is correct

The correct answer is C. (12) / correct sum. ((x+5)(x+7)=x^-2+12x+35), so (s=12). In exams the sum of constant parts is the middle coefficient.

Step 3

Exam Tip

((x+5)(x+7)=x^-2+12x+35), इसलिए (s=12) है। परीक्षा में स्थिर भागों का योग मध्य गुणांक होता है।

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Question 47/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-16x+64\) के लिए सही कथन कौन-सा है?

Which statement is correct for \(x^2-16x+64\)?

Explanation opens after your attempt

Correct Answer

A. यह ((x-8)²) हैit is ((x-8)²)

Step 1

Concept

\(64=8^2\) and \(-16x=-2\cdot x\cdot8\). In exams check both the last term and the middle term in a perfect square.

Step 2

Why this answer is correct

The correct answer is A. यह ((x-8)²) है / it is ((x-8)²). \(64=8^2\) and \(-16x=-2\cdot x\cdot8\). In exams check both the last term and the middle term in a perfect square.

Step 3

Exam Tip

\(64=8^2\) और \(-16x=-2\cdot x\cdot8\) है। परीक्षा में पूर्ण वर्ग में अंतिम पद और मध्य पद दोनों जांचें।

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Question 48/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(3x^2+14x+8\) का सही गुणनखंड रूप क्या है?

What is the correct factorised form of \(3x^2+14x+8\)?

Explanation opens after your attempt

Correct Answer

A. ((3x+2)(x+4))सही गुणनखंड

Step 1

Concept

((3x+2)(x+4)=3x^-2+14x+8). In exams check by adding the cross terms (12x) and (2x).

Step 2

Why this answer is correct

The correct answer is A. ((3x+2)(x+4)) / सही गुणनखंड. ((3x+2)(x+4)=3x^-2+14x+8). In exams check by adding the cross terms (12x) and (2x).

Step 3

Exam Tip

((3x+2)(x+4)=3x^-2+14x+8) है। परीक्षा में क्रॉस पदों (12x) और (2x) को जोड़कर जांचें।

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Question 49/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

\(x^2-12x+20\) को पूर्ण वर्ग रूप में लिखें।

Write \(x^2-12x+20\) in completed square form.

Explanation opens after your attempt

Correct Answer

A. ((x-6)²-16)सही रूप

Step 1

Concept

(x^-2-12x+36=(x-6)²) and (20=36-16). In exams take half of the middle coefficient and form its square.

Step 2

Why this answer is correct

The correct answer is A. ((x-6)²-16) / सही रूप. (x^-2-12x+36=(x-6)²) and (20=36-16). In exams take half of the middle coefficient and form its square.

Step 3

Exam Tip

(x^-2-12x+36=(x-6)²) और (20=36-16) है। परीक्षा में मध्य गुणांक का आधा लेकर उसका वर्ग बनाएं।

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Question 50/50 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 72

यदि (u+v=11) और (uv=28), तो \(u^2+v^2\) का मान क्या होगा?

If (u+v=11) and (uv=28), what is the value of \(u^2+v^2\)?

Explanation opens after your attempt

Correct Answer

A. (65)सही मान

Step 1

Concept

(u^-2+v^-2=(u+v)²-2uv=121-56=65). In exams subtract (2uv) from the square of the sum.

Step 2

Why this answer is correct

The correct answer is A. (65) / सही मान. (u^-2+v^-2=(u+v)²-2uv=121-56=65). In exams subtract (2uv) from the square of the sum.

Step 3

Exam Tip

(u^-2+v^-2=(u+v)²-2uv=121-56=65) है। परीक्षा में योग के वर्ग से (2uv) घटाएं।

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Class 9 Mathematics - Exploring Algebraic Identities - Quadratic expressions Hard Quiz

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

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व्यंजक \(2y^2+9y-11\) में स्थिर पद कौन-सा है?

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\(x^2+6x+9\) को पूर्ण वर्ग के रूप में लिखें।

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\(a^2-10a+25\) किस पूर्ण वर्ग के बराबर है?

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\(x^2+8x+15\) के दो रैखिक गुणनखंड कौन-से हैं?

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\(x^2-7x+12\) का गुणनखंड रूप क्या है?

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\(x^2+x-20\) को गुणनखंडित करें।

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\(3x^2+10x+8\) का सही गुणनखंड रूप चुनें।

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\(4x^2-9\) को द्विघात पहचान से लिखें।

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\(9y^2-24y+16\) किसके बराबर है?

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

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(t=-1) पर \(2t^2+3t-5\) का मान क्या है?

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\(x^2+kx+16\) पूर्ण वर्ग हो और (k) धनात्मक हो तो (k) का मान क्या है?

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

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\(x^2+px+21\) के गुणनखंड ((x+3)(x+7)) हैं। (p) का मान क्या है?

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\(x^2-11x+30\) के शून्य बनाने वाले गुणनखंड कौन-से हैं?

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कौन-सा द्विघात व्यंजक ((x-4)(x+2)) से प्राप्त होता है?

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((2x-3)(x+5)) का विस्तार क्या है?

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\(5x^2-20x+20\) में समान गुणनखंड निकालने के बाद अंदर कौन-सा द्विघात व्यंजक बचेगा?

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\(3x^2-27\) का पूर्ण गुणनखंड रूप क्या है?

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