किसी द्विघात अभिव्यक्ति में चर की सबसे बड़ी घात कितनी होती है?
What is the highest power of the variable in a quadratic expression?
#quadratic expressions
#degree
#algebra
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A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
A quadratic expression has highest power (2). Exam tip: identify the type by checking the power.
Step 2
Why this answer is correct
The correct answer is B. (2). A quadratic expression has highest power (2). Exam tip: identify the type by checking the power.
Step 3
Exam Tip
द्विघात अभिव्यक्ति में चर की सबसे बड़ी घात (2) होती है। परीक्षा में घात देखकर प्रकार पहचानें।
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\(3x^2+5x-7\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(3x^2+5x-7\)?
#quadratic expressions
#coefficient
#standard form
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A (3)
B (5)
C (-7)
D (1)
Explanation opens after your attempt
Step 1
Concept
The number multiplying \(x^2\) is (3). Exam tip: check the coefficient just before the term.
Step 2
Why this answer is correct
The correct answer is A. (3). The number multiplying \(x^2\) is (3). Exam tip: check the coefficient just before the term.
Step 3
Exam Tip
\(x^2\) के साथ गुणा हो रही संख्या (3) है। परीक्षा में पद के ठीक पहले का गुणांक देखें।
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\(x^2-9x+14\) में रैखिक पद कौन सा है?
Which is the linear term in \(x^2-9x+14\)?
#quadratic expressions
#linear term
#terms
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A \(x^2\)
B (14)
C (-9x)
D \(9x^2\)
Explanation opens after your attempt
Step 1
Concept
The linear term has power (1). Exam tip: treat the (x)-term as the linear term.
Step 2
Why this answer is correct
The correct answer is C. (-9x). The linear term has power (1). Exam tip: treat the (x)-term as the linear term.
Step 3
Exam Tip
रैखिक पद में चर की घात (1) होती है। परीक्षा में (x) वाला पद रैखिक पद मानें।
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\(2x^2-3x+8\) में स्थिर पद क्या है?
What is the constant term in \(2x^2-3x+8\)?
#quadratic expressions
#constant term
#standard form
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A \(2x^2\)
B (-3x)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The term without a variable is the constant term. Exam tip: identify the term without (x).
Step 2
Why this answer is correct
The correct answer is D. (8). The term without a variable is the constant term. Exam tip: identify the term without (x).
Step 3
Exam Tip
जिस पद में कोई चर नहीं है वह स्थिर पद होता है। परीक्षा में बिना (x) वाला पद अलग पहचानें।
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((x+4)2 ) का विस्तार कौन सा है?
Which is the expansion of ((x+4)2 )?
#quadratic expressions
#expansion
#identity
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A \(x^2+8x+16\)
B \(x^2+4x+16\)
C \(x^2+16x+8\)
D \(x^2-8x+16\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+16\)
Step 1
Concept
((x+4)2 =x-2 +2\cdot x\cdot4+16). Exam tip: the middle term is twice the product.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+8x+16\). ((x+4)2 =x-2 +2\cdot x\cdot4+16). Exam tip: the middle term is twice the product.
Step 3
Exam Tip
((x+4)2 =x-2 +2\cdot x\cdot4+16) होता है। परीक्षा में बीच का पद दोगुना गुणन होता है।
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((x-5)2 ) का सही विस्तार क्या है?
What is the correct expansion of ((x-5)2 )?
#quadratic expressions
#minus square
#expansion
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A \(x^2-5x+25\)
B \(x^2-10x+25\)
C \(x^2+10x+25\)
D \(x^2-25\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-10x+25\)
Step 1
Concept
((x-5)2 =x-2 -2\cdot x\cdot5+25). Exam tip: note both the negative sign and (2ab).
Step 2
Why this answer is correct
The correct answer is B. \(x^2-10x+25\). ((x-5)2 =x-2 -2\cdot x\cdot5+25). Exam tip: note both the negative sign and (2ab).
Step 3
Exam Tip
((x-5)2 =x-2 -2\cdot x\cdot5+25) है। परीक्षा में ऋण चिन्ह और (2ab) दोनों ध्यान रखें।
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\(x^2+12x+36\) किस पूर्ण वर्ग के बराबर है?
Which perfect square equals \(x^2+12x+36\)?
#quadratic expressions
#perfect square
#identity
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A ((x+12)2 )
B ((x-6)2 )
C ((x+6)2 )
D ((x+3)2 )
Explanation opens after your attempt
Correct Answer
C. ((x+6)2 )
Step 1
Concept
Here \(36=6^2\) and \(12x=2\cdot6\cdot x\). Exam tip: confirm using the square root of the last term.
Step 2
Why this answer is correct
The correct answer is C. ((x+6)2 ). Here \(36=6^2\) and \(12x=2\cdot6\cdot x\). Exam tip: confirm using the square root of the last term.
Step 3
Exam Tip
\(36=6^2\) और \(12x=2\cdot6\cdot x\) है। परीक्षा में अंतिम पद की वर्गमूल से पुष्टि करें।
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\(x^2-14x+49\) किस पूर्ण वर्ग के बराबर है?
Which perfect square equals \(x^2-14x+49\)?
#quadratic expressions
#perfect square
#minus square
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A ((x+7)2 )
B ((x-14)2 )
C ((x+14)2 )
D ((x-7)2 )
Explanation opens after your attempt
Correct Answer
D. ((x-7)2 )
Step 1
Concept
Here \(49=7^2\) and \(-14x=-2\cdot7\cdot x\). Exam tip: identify ((x-7)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is D. ((x-7)2 ). Here \(49=7^2\) and \(-14x=-2\cdot7\cdot x\). Exam tip: identify ((x-7)2 ) from the negative middle term.
Step 3
Exam Tip
\(49=7^2\) और \(-14x=-2\cdot7\cdot x\) है। परीक्षा में ऋणात्मक मध्य पद से ((x-7)2 ) पहचानें।
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\(2x^2+7x+3\) में द्विघात पद कौन सा है?
Which is the quadratic term in \(2x^2+7x+3\)?
#quadratic expressions
#quadratic term
#terms
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A \(2x^2\)
B (7x)
C (3)
D (2x)
Explanation opens after your attempt
Correct Answer
A. \(2x^2\)
Step 1
Concept
The quadratic term has variable power (2). Exam tip: identify the \(x^2\)-term first.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2\). The quadratic term has variable power (2). Exam tip: identify the \(x^2\)-term first.
Step 3
Exam Tip
द्विघात पद में चर की घात (2) होती है। परीक्षा में \(x^2\) वाला पद पहले पहचानें।
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\(5x^2-2x+1\) को मानक रूप \(ax^2+bx+c\) में (b) का मान क्या है?
In the standard form \(ax^2+bx+c\), what is (b) for \(5x^2-2x+1\)?
#quadratic expressions
#standard form
#coefficient
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A (5)
B (1)
C (-2)
D (2)
Explanation opens after your attempt
Step 1
Concept
(b) is the coefficient of the linear term (x). Exam tip: write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is C. (-2). (b) is the coefficient of the linear term (x). Exam tip: write the coefficient with its sign.
Step 3
Exam Tip
(b) रैखिक पद (x) का गुणांक है। परीक्षा में चिन्ह सहित गुणांक लिखें।
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\(4x^2+0x-9\) में रैखिक गुणांक क्या है?
What is the linear coefficient in \(4x^2+0x-9\)?
#quadratic expressions
#zero coefficient
#standard form
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A (4)
B (-9)
C (9)
D (0)
Explanation opens after your attempt
Step 1
Concept
The linear term is (0x), so its coefficient is (0). Exam tip: take the missing (x)-term coefficient as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). The linear term is (0x), so its coefficient is (0). Exam tip: take the missing (x)-term coefficient as (0).
Step 3
Exam Tip
रैखिक पद (0x) है इसलिए उसका गुणांक (0) है। परीक्षा में अनुपस्थित (x) पद का गुणांक (0) मानें।
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\(x^2+7x+10\) में ऐसे दो संख्याएं कौन सी हैं जिनका योग (7) और गुणनफल (10) है?
Which two numbers have sum (7) and product (10) for \(x^2+7x+10\)?
#quadratic expressions
#sum product
#factor pair
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A (2) और (5) / (2) and (5)
B (1) और (10) / (1) and (10)
C (3) और (4) / (3) and (4)
D (7) और (10) / (7) and (10)
Explanation opens after your attempt
Correct Answer
A. (2) और (5) / (2) and (5)
Step 1
Concept
(2+5=7) and \(2\cdot5=10\). Exam tip: check the pair using both the middle and constant terms.
Step 2
Why this answer is correct
The correct answer is A. (2) और (5) / (2) and (5). (2+5=7) and \(2\cdot5=10\). Exam tip: check the pair using both the middle and constant terms.
Step 3
Exam Tip
(2+5=7) और \(2\cdot5=10\) है। परीक्षा में मध्य पद और स्थिर पद दोनों से जोड़ी जांचें।
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\(x^2-3x-18\) के लिए कौन सी संख्या जोड़ी सही है?
Which number pair is correct for \(x^2-3x-18\)?
#quadratic expressions
#signs
#sum product
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A (3) और (-6) / (3) and (-6)
B (6) और (-3) / (6) and (-3)
C (-6) और (3) / (-6) and (3)
D (9) और (-2) / (9) and (-2)
Explanation opens after your attempt
Correct Answer
C. (-6) और (3) / (-6) and (3)
Step 1
Concept
(-6+3=-3) and \(-6\cdot3=-18\). Exam tip: choose opposite signs for a negative product.
Step 2
Why this answer is correct
The correct answer is C. (-6) और (3) / (-6) and (3). (-6+3=-3) and \(-6\cdot3=-18\). Exam tip: choose opposite signs for a negative product.
Step 3
Exam Tip
(-6+3=-3) और \(-6\cdot3=-18\) है। परीक्षा में ऋणात्मक गुणनफल के लिए विपरीत चिन्ह चुनें।
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(x=2) रखने पर \(x^2+3x+4\) का मान क्या होगा?
What is the value of \(x^2+3x+4\) when (x=2)?
#quadratic expressions
#value
#substitution
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
The value is \(2^2+3\cdot2+4=14\). Exam tip: do square first and then multiplication.
Step 2
Why this answer is correct
The correct answer is C. (14). The value is \(2^2+3\cdot2+4=14\). Exam tip: do square first and then multiplication.
Step 3
Exam Tip
मान \(2^2+3\cdot2+4=14\) है। परीक्षा में पहले वर्ग फिर गुणन करें।
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(x=-1) रखने पर \(2x^2-5x+1\) का मान क्या है?
What is the value of \(2x^2-5x+1\) when (x=-1)?
#quadratic expressions
#substitution
#negative value
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A (8)
B (6)
C (4)
D (2)
Explanation opens after your attempt
Step 1
Concept
(2(-1)2 -5(-1)+1=2+5+1=8). Exam tip: put negative values in brackets.
Step 2
Why this answer is correct
The correct answer is A. (8). (2(-1)2 -5(-1)+1=2+5+1=8). Exam tip: put negative values in brackets.
Step 3
Exam Tip
(2(-1)2 -5(-1)+1=2+5+1=8) है। परीक्षा में ऋणात्मक मान को कोष्ठक में रखें।
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\(3x^2-12\) को (3) बाहर निकालकर कैसे लिखा जाएगा?
How is \(3x^2-12\) written by taking (3) outside?
#quadratic expressions
#common factor
#simplification
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A (3\(x^2-12\))
B (3\(x^2-4\))
C (3(x-4))
D (3x(x-4))
Explanation opens after your attempt
Correct Answer
B. (3\(x^2-4\))
Step 1
Concept
The common factor is (3), and \(12\div3=4\). Exam tip: check inner terms after taking out the factor.
Step 2
Why this answer is correct
The correct answer is B. (3\(x^2-4\)). The common factor is (3), and \(12\div3=4\). Exam tip: check inner terms after taking out the factor.
Step 3
Exam Tip
दोनों पदों में (3) सामान्य है और \(12\div3=4\) है। परीक्षा में बाहर निकाले गुणनखंड से अंदर के पद जांचें।
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\(x^2-25\) किस पहचान का उदाहरण है?
Which identity is exemplified by \(x^2-25\)?
#quadratic expressions
#difference of squares
#identity
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A पूर्ण वर्ग त्रिपद / Perfect square trinomial
B दो वर्गों का अंतर / Difference of two squares
C दो घनों का योग / Sum of two cubes
D रैखिक अभिव्यक्ति / Linear expression
Explanation opens after your attempt
Correct Answer
B. दो वर्गों का अंतर / Difference of two squares
Step 1
Concept
Since \(25=5^2\), \(x^2-25\) is a difference of two squares. Exam tip: identify square numbers.
Step 2
Why this answer is correct
The correct answer is B. दो वर्गों का अंतर / Difference of two squares. Since \(25=5^2\), \(x^2-25\) is a difference of two squares. Exam tip: identify square numbers.
Step 3
Exam Tip
\(25=5^2\), इसलिए \(x^2-25\) दो वर्गों का अंतर है। परीक्षा में वर्ग संख्या पहचानें।
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\(2x^2+5x\) में सामान्य गुणनखंड क्या है?
What is the common factor in \(2x^2+5x\)?
#quadratic expressions
#common factor
#terms
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A (x)
B (2x)
C (5x)
D (10x)
Explanation opens after your attempt
Step 1
Concept
Only (x) is common in both terms. Exam tip: check common numerical and variable parts separately.
Step 2
Why this answer is correct
The correct answer is A. (x). Only (x) is common in both terms. Exam tip: check common numerical and variable parts separately.
Step 3
Exam Tip
दोनों पदों में केवल (x) सामान्य है। परीक्षा में संख्या और चर दोनों का सामान्य भाग अलग देखें।
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\(x^2+6x+k\) को पूर्ण वर्ग बनाने के लिए (k) का मान क्या होना चाहिए?
What should be the value of (k) to make \(x^2+6x+k\) a perfect square?
#quadratic expressions
#completing square
#perfect square
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A (6)
B (9)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
Half of (6) is (3), so the constant term should be \(3^2=9\). Exam tip: square half the coefficient of (x).
Step 2
Why this answer is correct
The correct answer is B. (9). Half of (6) is (3), so the constant term should be \(3^2=9\). Exam tip: square half the coefficient of (x).
Step 3
Exam Tip
(6x) का आधा (3x) है इसलिए स्थिर पद \(3^2=9\) चाहिए। परीक्षा में (x) के गुणांक का आधा करके वर्ग करें।
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\(x^2-8x+k\) को पूर्ण वर्ग बनाने के लिए (k) क्या होगा?
What is (k) to make \(x^2-8x+k\) a perfect square?
#quadratic expressions
#completing square
#minus term
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A (4)
B (8)
C (16)
D (64)
Explanation opens after your attempt
Step 1
Concept
Half of (-8) is (-4), and ((-4)2 =16). Exam tip: the square of half the coefficient is positive.
Step 2
Why this answer is correct
The correct answer is C. (16). Half of (-8) is (-4), and ((-4)2 =16). Exam tip: the square of half the coefficient is positive.
Step 3
Exam Tip
(-8) का आधा (-4) है और ((-4)2 =16) है। परीक्षा में आधे गुणांक का वर्ग हमेशा धनात्मक होता है।
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\(x^2+10x+21\) में मध्य पद को किन दो पदों में तोड़ा जा सकता है?
Into which two terms can the middle term of \(x^2+10x+21\) be split?
#quadratic expressions
#middle term
#splitting
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A (3x) और (7x) / (3x) and (7x)
B (4x) और (6x) / (4x) and (6x)
C (5x) और (5x) / (5x) and (5x)
D (2x) और (8x) / (2x) and (8x)
Explanation opens after your attempt
Correct Answer
A. (3x) और (7x) / (3x) and (7x)
Step 1
Concept
(3+7=10) and \(3\cdot7=21\). Exam tip: check the sum of factors of the constant term.
Step 2
Why this answer is correct
The correct answer is A. (3x) और (7x) / (3x) and (7x). (3+7=10) and \(3\cdot7=21\). Exam tip: check the sum of factors of the constant term.
Step 3
Exam Tip
(3+7=10) और \(3\cdot7=21\) है। परीक्षा में स्थिर पद के गुणनखंडों का योग देखें।
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\(x^2-x-20\) में मध्य पद के लिए सही विभाजन कौन सा है?
Which is the correct split for the middle term in \(x^2-x-20\)?
#quadratic expressions
#middle term
#signs
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A (4x-5x)
B (5x-4x)
C (-4x+5x)
D (-2x+x)
Explanation opens after your attempt
Correct Answer
A. (4x-5x)
Step 1
Concept
(4+(-5)=-1) and (4\cdot(-5)=-20). Exam tip: signs change the sum.
Step 2
Why this answer is correct
The correct answer is A. (4x-5x). (4+(-5)=-1) and (4\cdot(-5)=-20). Exam tip: signs change the sum.
Step 3
Exam Tip
(4+(-5)=-1) और (4\cdot(-5)=-20) है। परीक्षा में चिन्हों के कारण योग बदलता है।
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\(2x^2+3x+1\) को फैलाने वाले गुणनखंड कौन से हो सकते हैं?
Which factors can expand to \(2x^2+3x+1\)?
#quadratic expressions
#expansion
#factors
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A ((2x+1)(x+1))
B ((2x+3)(x+1))
C ((x+1)(x+1))
D ((2x-1)(x-1))
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x+1))
Step 1
Concept
((2x+1)(x+1)=2x-2 +2x+x+1). Exam tip: expand and match the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x+1)). ((2x+1)(x+1)=2x-2 +2x+x+1). Exam tip: expand and match the middle term.
Step 3
Exam Tip
((2x+1)(x+1)=2x-2 +2x+x+1) है। परीक्षा में फैलाकर मध्य पद मिलाएं।
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\(3x^2+8x+4\) के लिए सही गुणनखंड कौन से हैं?
Which are the correct factors for \(3x^2+8x+4\)?
#quadratic expressions
#factorisation
#checking
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A ((3x+4)(x+1))
B ((3x+2)(x+2))
C ((x+4)(3x+1))
D ((3x-2)(x-2))
Explanation opens after your attempt
Correct Answer
B. ((3x+2)(x+2))
Step 1
Concept
((3x+2)(x+2)) gives \(3x^2+6x+2x+4\). Exam tip: check that (8x) is formed.
Step 2
Why this answer is correct
The correct answer is B. ((3x+2)(x+2)). ((3x+2)(x+2)) gives \(3x^2+6x+2x+4\). Exam tip: check that (8x) is formed.
Step 3
Exam Tip
((3x+2)(x+2)) से \(3x^2+6x+2x+4\) मिलता है। परीक्षा में (8x) बनने की जांच करें।
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\(7x^2\) किस प्रकार का पद है?
What type of term is \(7x^2\)?
#quadratic expressions
#quadratic term
#degree
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A रैखिक पद / Linear term
B स्थिर पद / Constant term
C द्विघात पद / Quadratic term
D घन पद / Cubic term
Explanation opens after your attempt
Correct Answer
C. द्विघात पद / Quadratic term
Step 1
Concept
In \(7x^2\), the power of the variable is (2). Exam tip: call a term with power (2) a quadratic term.
Step 2
Why this answer is correct
The correct answer is C. द्विघात पद / Quadratic term. In \(7x^2\), the power of the variable is (2). Exam tip: call a term with power (2) a quadratic term.
Step 3
Exam Tip
\(7x^2\) में चर की घात (2) है। परीक्षा में घात (2) वाले पद को द्विघात पद कहें।
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\(4x^2-12x+9\) का पूर्ण वर्ग रूप क्या है?
What is the perfect square form of \(4x^2-12x+9\)?
#quadratic expressions
#perfect square
#coefficient
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A ((2x+3)2 )
B ((4x-3)2 )
C ((2x-3)2 )
D ((x-3)2 )
Explanation opens after your attempt
Correct Answer
C. ((2x-3)2 )
Step 1
Concept
(4x-2 =(2x)2 ), \(9=3^2\), and the middle term is (-12x). Exam tip: take square roots with coefficients.
Step 2
Why this answer is correct
The correct answer is C. ((2x-3)2 ). (4x-2 =(2x)2 ), \(9=3^2\), and the middle term is (-12x). Exam tip: take square roots with coefficients.
Step 3
Exam Tip
(4x-2 =(2x)2 ), \(9=3^2\) और बीच का पद (-12x) है। परीक्षा में गुणांक सहित वर्गमूल लें।
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\(9x^2+24x+16\) किसके बराबर है?
What is \(9x^2+24x+16\) equal to?
#quadratic expressions
#perfect square
#identity
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A ((3x+4)2 )
B ((9x+4)2 )
C ((3x-4)2 )
D ((x+4)2 )
Explanation opens after your attempt
Correct Answer
A. ((3x+4)2 )
Step 1
Concept
(9x-2 =(3x)2 ), \(16=4^2\), and \(24x=2\cdot3x\cdot4\). Exam tip: look for all three perfect square clues.
Step 2
Why this answer is correct
The correct answer is A. ((3x+4)2 ). (9x-2 =(3x)2 ), \(16=4^2\), and \(24x=2\cdot3x\cdot4\). Exam tip: look for all three perfect square clues.
Step 3
Exam Tip
(9x-2 =(3x)2 ), \(16=4^2\) और \(24x=2\cdot3x\cdot4\) है। परीक्षा में पूर्ण वर्ग के तीन संकेत देखें।
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\(x^2+2xy+y^2\) को किस द्विघात रूप में देखा जा सकता है?
In which quadratic form can \(x^2+2xy+y^2\) be seen?
#quadratic expressions
#two variables
#perfect square
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A ((x+y)2 )
B ((x-y)2 )
C ((x+y)(x-y))
D \(x^2-y^2\)
Explanation opens after your attempt
Correct Answer
A. ((x+y)2 )
Step 1
Concept
This is a perfect square trinomial in two variables. Exam tip: treat (2xy) as the middle double product.
Step 2
Why this answer is correct
The correct answer is A. ((x+y)2 ). This is a perfect square trinomial in two variables. Exam tip: treat (2xy) as the middle double product.
Step 3
Exam Tip
यह दो चरों वाला पूर्ण वर्ग त्रिपद है। परीक्षा में (2xy) को बीच का दोगुना गुणन मानें।
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\(x^2-y^2\) को द्विघात अभिव्यक्ति के रूप में किस पहचान से जोड़ा जाता है?
With which identity is \(x^2-y^2\) linked as a quadratic expression?
#quadratic expressions
#difference of squares
#identity
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A दो वर्गों का अंतर / Difference of two squares
B दो वर्गों का योग / Sum of two squares
C पूर्ण वर्ग योग / Perfect square sum
D घन का अंतर / Difference of cubes
Explanation opens after your attempt
Correct Answer
A. दो वर्गों का अंतर / Difference of two squares
Step 1
Concept
\(x^2-y^2\) is a difference of two squares. Exam tip: connect it with ((x-y)(x+y)).
Step 2
Why this answer is correct
The correct answer is A. दो वर्गों का अंतर / Difference of two squares. \(x^2-y^2\) is a difference of two squares. Exam tip: connect it with ((x-y)(x+y)).
Step 3
Exam Tip
\(x^2-y^2\) में दो वर्गों का अंतर है। परीक्षा में इसे ((x-y)(x+y)) से जोड़ें।
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\(x^2+0x+16\) में स्थिर पद और रैखिक गुणांक क्रमशः क्या हैं?
What are the constant term and linear coefficient respectively in \(x^2+0x+16\)?
#quadratic expressions
#constant term
#linear coefficient
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A (16) और (0) / (16) and (0)
B (0) और (16) / (0) and (16)
C (1) और (16) / (1) and (16)
D (16) और (1) / (16) and (1)
Explanation opens after your attempt
Correct Answer
A. (16) और (0) / (16) and (0)
Step 1
Concept
The constant term is (16), and the coefficient of (x) is (0). Exam tip: read the order word carefully.
Step 2
Why this answer is correct
The correct answer is A. (16) और (0) / (16) and (0). The constant term is (16), and the coefficient of (x) is (0). Exam tip: read the order word carefully.
Step 3
Exam Tip
स्थिर पद (16) और (x) का गुणांक (0) है। परीक्षा में क्रम शब्द को ध्यान से पढ़ें।
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कौन सी अभिव्यक्ति द्विघात नहीं है?
Which expression is not quadratic?
#quadratic expressions
#non quadratic
#degree
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A \(x^2+2x+1\)
B \(3x^2-5\)
C \(x^3+x+1\)
D \(5x^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^3+x+1\)
Step 1
Concept
The highest power in \(x^3+x+1\) is (3). Exam tip: for a quadratic, the highest power must be (2).
Step 2
Why this answer is correct
The correct answer is C. \(x^3+x+1\). The highest power in \(x^3+x+1\) is (3). Exam tip: for a quadratic, the highest power must be (2).
Step 3
Exam Tip
\(x^3+x+1\) में सबसे बड़ी घात (3) है। परीक्षा में द्विघात के लिए सबसे बड़ी घात (2) होनी चाहिए।
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कौन सी अभिव्यक्ति द्विघात एकपद है?
Which expression is a quadratic monomial?
#quadratic expressions
#monomial
#degree
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A \(7x^2\)
B \(x^2+7\)
C \(x^2+7x+1\)
D (7x+2)
Explanation opens after your attempt
Correct Answer
A. \(7x^2\)
Step 1
Concept
\(7x^2\) has only one term and power (2). Exam tip: check both number of terms and degree.
Step 2
Why this answer is correct
The correct answer is A. \(7x^2\). \(7x^2\) has only one term and power (2). Exam tip: check both number of terms and degree.
Step 3
Exam Tip
\(7x^2\) में केवल एक पद है और घात (2) है। परीक्षा में पदों की संख्या और घात दोनों देखें।
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कौन सी अभिव्यक्ति द्विघात द्विपद है?
Which expression is a quadratic binomial?
#quadratic expressions
#binomial
#terms
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A \(x^2+3x+2\)
B \(x^2-9\)
C (x+9)
D \(x^3-9\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-9\)
Step 1
Concept
\(x^2-9\) has two terms and highest power (2). Exam tip: count two terms for a binomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-9\). \(x^2-9\) has two terms and highest power (2). Exam tip: count two terms for a binomial.
Step 3
Exam Tip
\(x^2-9\) में दो पद हैं और सबसे बड़ी घात (2) है। परीक्षा में द्विपद के लिए दो पद गिनें।
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कौन सी अभिव्यक्ति द्विघात त्रिपद है?
Which expression is a quadratic trinomial?
#quadratic expressions
#trinomial
#classification
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A \(x^2+5\)
B \(x^3+x+1\)
C \(x^2+4x+4\)
D (4x+4)
Explanation opens after your attempt
Correct Answer
C. \(x^2+4x+4\)
Step 1
Concept
\(x^2+4x+4\) has three terms and degree (2). Exam tip: a trinomial must have three terms.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+4x+4\). \(x^2+4x+4\) has three terms and degree (2). Exam tip: a trinomial must have three terms.
Step 3
Exam Tip
\(x^2+4x+4\) में तीन पद हैं और घात (2) है। परीक्षा में त्रिपद के लिए तीन पद होने चाहिए।
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\(2x^2+7x+6\) में (a), (b), (c) के मान क्रमशः क्या हैं?
What are the values of (a), (b), and (c) respectively in \(2x^2+7x+6\)?
#quadratic expressions
#standard form
#abc
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A (2), (7), (6)
B (7), (2), (6)
C (6), (7), (2)
D (2), (6), (7)
Explanation opens after your attempt
Correct Answer
A. (2), (7), (6)
Step 1
Concept
From standard form \(ax^2+bx+c\), (a=2), (b=7), (c=6). Exam tip: do not change the order of terms.
Step 2
Why this answer is correct
The correct answer is A. (2), (7), (6). From standard form \(ax^2+bx+c\), (a=2), (b=7), (c=6). Exam tip: do not change the order of terms.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c\) से (a=2), (b=7), (c=6) हैं। परीक्षा में पदों का क्रम न बदलें।
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\(-x^2+4x+5\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(-x^2+4x+5\)?
#quadratic expressions
#coefficient
#negative coefficient
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A (1)
B (-1)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(-x^2\) means \(-1\cdot x^2\). Exam tip: remember the sign of the hidden (1).
Step 2
Why this answer is correct
The correct answer is B. (-1). \(-x^2\) means \(-1\cdot x^2\). Exam tip: remember the sign of the hidden (1).
Step 3
Exam Tip
\(-x^2\) का अर्थ \(-1\cdot x^2\) है। परीक्षा में छिपे हुए (1) का चिन्ह याद रखें।
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(x=3) पर \(x^2-4x+7\) का मान क्या है?
What is the value of \(x^2-4x+7\) at (x=3)?
#quadratic expressions
#value
#substitution
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(3^2-4\cdot3+7=9-12+7=4\). Exam tip: calculate stepwise with signs.
Step 2
Why this answer is correct
The correct answer is B. (4). \(3^2-4\cdot3+7=9-12+7=4\). Exam tip: calculate stepwise with signs.
Step 3
Exam Tip
\(3^2-4\cdot3+7=9-12+7=4\) है। परीक्षा में चिन्हों के साथ चरणबद्ध गणना करें।
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(x=-2) पर \(x^2+2x-3\) का मान क्या है?
What is the value of \(x^2+2x-3\) at (x=-2)?
#quadratic expressions
#negative substitution
#value
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A (-3)
B (3)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
((-2)2 +2(-2)-3=4-4-3=-3). Exam tip: keep the square of a negative number positive.
Step 2
Why this answer is correct
The correct answer is A. (-3). ((-2)2 +2(-2)-3=4-4-3=-3). Exam tip: keep the square of a negative number positive.
Step 3
Exam Tip
((-2)2 +2(-2)-3=4-4-3=-3) है। परीक्षा में ऋणात्मक संख्या का वर्ग धनात्मक रखें।
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\(x^2+bx+16\) पूर्ण वर्ग हो और (b) धनात्मक हो, तो (b) क्या होगा?
If \(x^2+bx+16\) is a perfect square and (b) is positive, what is (b)?
#quadratic expressions
#perfect square
#missing coefficient
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
Since \(16=4^2\), the middle term is \(2\cdot4\cdot x=8x\). Exam tip: \(b=2\sqrt{c}\) is useful here.
Step 2
Why this answer is correct
The correct answer is B. (8). Since \(16=4^2\), the middle term is \(2\cdot4\cdot x=8x\). Exam tip: \(b=2\sqrt{c}\) is useful here.
Step 3
Exam Tip
\(16=4^2\), इसलिए बीच का पद \(2\cdot4\cdot x=8x\) होगा। परीक्षा में \(b=2\sqrt{c}\) यहां उपयोगी है।
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\(x^2+bx+25\) पूर्ण वर्ग हो और (b) ऋणात्मक हो, तो (b) क्या होगा?
If \(x^2+bx+25\) is a perfect square and (b) is negative, what is (b)?
#quadratic expressions
#missing coefficient
#minus square
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A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Since \(25=5^2\), for the negative perfect square \(b=-2\cdot5=-10\). Exam tip: read the sign condition carefully.
Step 2
Why this answer is correct
The correct answer is B. (-10). Since \(25=5^2\), for the negative perfect square \(b=-2\cdot5=-10\). Exam tip: read the sign condition carefully.
Step 3
Exam Tip
\(25=5^2\), इसलिए ऋणात्मक पूर्ण वर्ग में \(b=-2\cdot5=-10\) है। परीक्षा में संकेत शर्त जरूर पढ़ें।
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\(2x^2+5x+2\) में मध्य पद को कैसे विभाजित करेंगे?
How will you split the middle term in \(2x^2+5x+2\)?
#quadratic expressions
#middle term
#splitting
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A (2x+3x)
B (x+4x)
C (5x+0x)
D (-2x+7x)
Explanation opens after your attempt
Step 1
Concept
Here \(2\cdot2=4\), and (1+4=5), so (x+4x) works. Exam tip: check the relation of (ac) and (b).
Step 2
Why this answer is correct
The correct answer is B. (x+4x). Here \(2\cdot2=4\), and (1+4=5), so (x+4x) works. Exam tip: check the relation of (ac) and (b).
Step 3
Exam Tip
\(2\cdot2=4\) और (1+4=5), इसलिए (x+4x) उपयुक्त है। परीक्षा में (ac) और (b) का संबंध देखें।
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\(3x^2+10x+8\) में मध्य पद को किस तरह तोड़ना सही है?
How should the middle term be split in \(3x^2+10x+8\)?
#quadratic expressions
#splitting middle term
#ac method
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A (4x+6x)
B (3x+7x)
C (2x+8x)
D (5x+5x)
Explanation opens after your attempt
Correct Answer
A. (4x+6x)
Step 1
Concept
\(3\cdot8=24\), and (4+6=10), \(4\cdot6=24\). Exam tip: factors of (ac) must add to (b).
Step 2
Why this answer is correct
The correct answer is A. (4x+6x). \(3\cdot8=24\), and (4+6=10), \(4\cdot6=24\). Exam tip: factors of (ac) must add to (b).
Step 3
Exam Tip
\(3\cdot8=24\) और (4+6=10), \(4\cdot6=24\) है। परीक्षा में (ac) के गुणनखंडों का योग (b) होना चाहिए।
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\(5x^2+16x+3\) में (ac) विधि के लिए (ac) का मान क्या है?
What is the value of (ac) for the (ac) method in \(5x^2+16x+3\)?
#quadratic expressions
#ac method
#coefficients
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A (5)
B (8)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
Here (a=5) and (c=3), so (ac=15). Exam tip: identify (a) and (c) clearly first.
Step 2
Why this answer is correct
The correct answer is C. (15). Here (a=5) and (c=3), so (ac=15). Exam tip: identify (a) and (c) clearly first.
Step 3
Exam Tip
यहां (a=5) और (c=3), इसलिए (ac=15) है। परीक्षा में पहले (a) और (c) साफ पहचानें।
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\(5x^2+16x+3\) के लिए मध्य पद की सही जोड़ी कौन सी है?
Which is the correct middle-term pair for \(5x^2+16x+3\)?
#quadratic expressions
#middle term
#ac method
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A (5x) और (11x) / (5x) and (11x)
B (15x) और (x) / (15x) and (x)
C (10x) और (6x) / (10x) and (6x)
D (3x) और (13x) / (3x) and (13x)
Explanation opens after your attempt
Correct Answer
B. (15x) और (x) / (15x) and (x)
Step 1
Concept
(15+1=16) and \(15\cdot1=15\). Exam tip: check both product (ac) and sum (b).
Step 2
Why this answer is correct
The correct answer is B. (15x) और (x) / (15x) and (x). (15+1=16) and \(15\cdot1=15\). Exam tip: check both product (ac) and sum (b).
Step 3
Exam Tip
(15+1=16) और \(15\cdot1=15\) है। परीक्षा में (ac) के गुणनफल और (b) के योग दोनों जांचें।
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\(4x^2-1\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(4x^2-1\)?
#quadratic expressions
#difference of squares
#coefficient
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A ((4x-1)(4x+1))
B ((2x-1)(2x+1))
C ((2x-1)2 )
D ((x-1)(x+1))
Explanation opens after your attempt
Correct Answer
B. ((2x-1)(2x+1))
Step 1
Concept
(4x-2 =(2x)2 ) and \(1=1^2\). Exam tip: take square roots with coefficients.
Step 2
Why this answer is correct
The correct answer is B. ((2x-1)(2x+1)). (4x-2 =(2x)2 ) and \(1=1^2\). Exam tip: take square roots with coefficients.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(1=1^2\) है। परीक्षा में गुणांक सहित वर्गमूल निकालें।
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\(x^2+9\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(x^2+9\)?
#quadratic expressions
#sum of squares
#concept
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A यह वास्तविक रैखिक गुणनखंडों में तुरंत टूटता है / It directly splits into real linear factors
B यह दो वर्गों का योग है / It is a sum of two squares
C यह ((x+3)2 ) है / It is ((x+3)2 )
D यह रैखिक अभिव्यक्ति है / It is a linear expression
Explanation opens after your attempt
Correct Answer
B. यह दो वर्गों का योग है / It is a sum of two squares
Step 1
Concept
\(x^2+9\) is a sum of two squares, not a difference. Exam tip: do not write \(x^2+9\) as ((x+3)2 ).
Step 2
Why this answer is correct
The correct answer is B. यह दो वर्गों का योग है / It is a sum of two squares. \(x^2+9\) is a sum of two squares, not a difference. Exam tip: do not write \(x^2+9\) as ((x+3)2 ).
Step 3
Exam Tip
\(x^2+9\) दो वर्गों का योग है, अंतर नहीं। परीक्षा में \(x^2+9\) को ((x+3)2 ) न लिखें।
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\(x^2+6x+9\) और \(x^2+9\) में मुख्य अंतर क्या है?
What is the main difference between \(x^2+6x+9\) and \(x^2+9\)?
#quadratic expressions
#perfect square
#comparison
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A पहली में मध्य पद (6x) है / The first has middle term (6x)
B दूसरी द्विघात नहीं है / The second is not quadratic
C पहली में \(x^2\) नहीं है / The first has no \(x^2\)
D दोनों समान हैं / Both are the same
Explanation opens after your attempt
Correct Answer
A. पहली में मध्य पद (6x) है / The first has middle term (6x)
Step 1
Concept
\(x^2+6x+9\) is a perfect square, but \(x^2+9\) lacks the middle term. Exam tip: check whether the middle term is present.
Step 2
Why this answer is correct
The correct answer is A. पहली में मध्य पद (6x) है / The first has middle term (6x). \(x^2+6x+9\) is a perfect square, but \(x^2+9\) lacks the middle term. Exam tip: check whether the middle term is present.
Step 3
Exam Tip
\(x^2+6x+9\) पूर्ण वर्ग है लेकिन \(x^2+9\) में मध्य पद नहीं है। परीक्षा में मध्य पद की उपस्थिति जांचें।
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\(x^2-5x+6\) में मध्य पद को किस प्रकार विभाजित करना सही होगा?
How should the middle term be split in \(x^2-5x+6\)?
#quadratic expressions
#middle term
#splitting
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A (-2x-3x)
B (2x+3x)
C (-1x-6x)
D (x-6x)
Explanation opens after your attempt
Correct Answer
A. (-2x-3x)
Step 1
Concept
Here (-2-3=-5) and ((-2)(-3)=6). Exam tip: for a positive constant and negative middle term, take both numbers negative.
Step 2
Why this answer is correct
The correct answer is A. (-2x-3x). Here (-2-3=-5) and ((-2)(-3)=6). Exam tip: for a positive constant and negative middle term, take both numbers negative.
Step 3
Exam Tip
(-2-3=-5) और ((-2)(-3)=6) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद के लिए दोनों संख्याएं ऋणात्मक लें।
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\(2x^2-7x+3\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(2x^2-7x+3\)?
#quadratic expressions
#factorisation
#checking
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A ((2x-1)(x-3))
B ((2x+1)(x-3))
C ((2x-3)(x-1))
D ((x-1)(x-3))
Explanation opens after your attempt
Correct Answer
A. ((2x-1)(x-3))
Step 1
Concept
Expanding ((2x-1)(x-3)) gives \(2x^2-6x-x+3\). Exam tip: verify the middle term by expansion.
Step 2
Why this answer is correct
The correct answer is A. ((2x-1)(x-3)). Expanding ((2x-1)(x-3)) gives \(2x^2-6x-x+3\). Exam tip: verify the middle term by expansion.
Step 3
Exam Tip
((2x-1)(x-3)) फैलाने पर \(2x^2-6x-x+3\) मिलता है। परीक्षा में फैलाकर मध्य पद की पुष्टि करें।
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यदि \(x^2+px+36\) पूर्ण वर्ग हो और (p) धनात्मक हो, तो (p) का मान क्या होगा?
If \(x^2+px+36\) is a perfect square and (p) is positive, what is the value of (p)?
#quadratic expressions
#perfect square
#missing coefficient
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A (6)
B (9)
C (12)
D (18)
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Step 1
Concept
Since \(36=6^2\), the middle term will be \(2\cdot6\cdot x=12x\). Exam tip: double the square root of the constant term.
Step 2
Why this answer is correct
The correct answer is C. (12). Since \(36=6^2\), the middle term will be \(2\cdot6\cdot x=12x\). Exam tip: double the square root of the constant term.
Step 3
Exam Tip
\(36=6^2\) है इसलिए मध्य पद \(2\cdot6\cdot x=12x\) होगा। परीक्षा में अंतिम पद की वर्गमूल को दोगुना करें।
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