कौन सा व्यंजक (x) में द्विघात व्यंजक है?
Which expression is a quadratic expression in (x)?
#quadratic expression
#degree
#identification
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A (3x+5)
B \(x^2-4x+7\)
C \(x^3+2x\)
D \(\frac{2}{x}+1\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-4x+7\)
Step 1
Concept
A quadratic expression has the highest power (2). Exam tip: identify it by checking the highest power.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-4x+7\). A quadratic expression has the highest power (2). Exam tip: identify it by checking the highest power.
Step 3
Exam Tip
द्विघात व्यंजक में चर की अधिकतम घात (2) होती है। परीक्षा में सबसे बड़ी घात देखकर पहचान करें।
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\(5x^2-3x+9\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(5x^2-3x+9\)?
#coefficient
#quadratic expression
#x square
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A (-3)
B (9)
C (1)
D (5)
Explanation opens after your attempt
Step 1
Concept
The number attached to \(x^2\) is (5). Exam tip: identify the term and its coefficient separately.
Step 2
Why this answer is correct
The correct answer is D. (5). The number attached to \(x^2\) is (5). Exam tip: identify the term and its coefficient separately.
Step 3
Exam Tip
\(x^2\) के साथ लगा हुआ संख्या गुणांक (5) है। परीक्षा में पद और उसके गुणांक को अलग पहचानें।
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\(2a^2+7a-4\) का स्थिर पद कौन सा है?
Which is the constant term of \(2a^2+7a-4\)?
#constant term
#quadratic expression
#terms
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A (2)
B (7)
C (a)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The term without a variable is the constant term. Here the constant term is (-4).
Step 2
Why this answer is correct
The correct answer is D. (-4). The term without a variable is the constant term. Here the constant term is (-4).
Step 3
Exam Tip
जिस पद में चर नहीं होता वह स्थिर पद होता है। यहां स्थिर पद (-4) है।
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((x+4)2 ) को विस्तारित करने पर कौन सा व्यंजक मिलेगा?
Which expression is obtained by expanding ((x+4)2 )?
#expansion
#perfect square
#quadratic expression
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A \(x^2+4x+16\)
B \(x^2+16x+8\)
C \(x^2-8x+16\)
D \(x^2+8x+16\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+8x+16\)
Step 1
Concept
((x+4)2 =x-2 +2\cdot x\cdot4+16). Exam tip: do not forget the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is D. \(x^2+8x+16\). ((x+4)2 =x-2 +2\cdot x\cdot4+16). Exam tip: do not forget the middle term (2ab).
Step 3
Exam Tip
((x+4)2 =x-2 +2\cdot x\cdot4+16) होता है। परीक्षा में मध्य पद (2ab) न भूलें।
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((y-6)2 ) का सही विस्तारित रूप क्या है?
What is the correct expanded form of ((y-6)2 )?
#perfect square
#expansion
#minus sign
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A \(y^2-6y+36\)
B \(y^2-12y+36\)
C \(y^2+12y+36\)
D \(y^2-36\)
Explanation opens after your attempt
Correct Answer
B. \(y^2-12y+36\)
Step 1
Concept
((y-6)2 =y-2 -2\cdot y\cdot6+36). Exam tip: the negative sign affects the middle term.
Step 2
Why this answer is correct
The correct answer is B. \(y^2-12y+36\). ((y-6)2 =y-2 -2\cdot y\cdot6+36). Exam tip: the negative sign affects the middle term.
Step 3
Exam Tip
((y-6)2 =y-2 -2\cdot y\cdot6+36) है। परीक्षा में ऋण चिन्ह केवल मध्य पद को प्रभावित करता है।
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((x+3)(x+5)) का गुणनफल कौन सा है?
Which is the product of ((x+3)(x+5))?
#binomial product
#quadratic expression
#expansion
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A \(x^2+15x+8\)
B \(x^2-8x+15\)
C \(x^2+8x+15\)
D \(x^2+2x+15\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+8x+15\)
Step 1
Concept
The middle term is (3x+5x=8x) and the constant term is (15). Exam tip: multiply every term of both binomials.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+8x+15\). The middle term is (3x+5x=8x) and the constant term is (15). Exam tip: multiply every term of both binomials.
Step 3
Exam Tip
मध्य पद (3x+5x=8x) और स्थिर पद (15) है। परीक्षा में दोनों द्विपदों के हर पद को गुणा करें।
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((p-2)(p+7)) का विस्तारित रूप क्या होगा?
What will be the expanded form of ((p-2)(p+7))?
#binomial product
#signs
#quadratic expression
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A \(p^2-5p-14\)
B \(p^2+9p+14\)
C \(p^2-14\)
D \(p^2+5p-14\)
Explanation opens after your attempt
Correct Answer
D. \(p^2+5p-14\)
Step 1
Concept
(-2p+7p=5p) and \(-2\cdot7=-14\). Exam tip: be careful with signs.
Step 2
Why this answer is correct
The correct answer is D. \(p^2+5p-14\). (-2p+7p=5p) and \(-2\cdot7=-14\). Exam tip: be careful with signs.
Step 3
Exam Tip
(-2p+7p=5p) और \(-2\cdot7=-14\) होता है। परीक्षा में चिन्हों का ध्यान रखें।
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\(x^2+10x+25\) किस पूर्ण वर्ग के बराबर है?
Which perfect square is equal to \(x^2+10x+25\)?
#perfect square
#quadratic expression
#identity
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A ((x+10)2 )
B ((x-5)2 )
C ((x+5)2 )
D ((x+25)2 )
Explanation opens after your attempt
Correct Answer
C. ((x+5)2 )
Step 1
Concept
It is in the form \(x^2+2\cdot x\cdot5+5^2\). Exam tip: match the middle term with (2ab).
Step 2
Why this answer is correct
The correct answer is C. ((x+5)2 ). It is in the form \(x^2+2\cdot x\cdot5+5^2\). Exam tip: match the middle term with (2ab).
Step 3
Exam Tip
यह \(x^2+2\cdot x\cdot5+5^2\) के रूप में है। परीक्षा में मध्य पद को (2ab) से मिलाएं।
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\(4x^2-12x+9\) किसके बराबर है?
What is \(4x^2-12x+9\) equal to?
#perfect square
#identity
#quadratic expression
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A ((2x+3)2 )
B ((2x-3)2 )
C ((4x-3)2 )
D ((x-6)2 )
Explanation opens after your attempt
Correct Answer
B. ((2x-3)2 )
Step 1
Concept
It is ((2x)2 -2\cdot2x\cdot3+32 ). Exam tip: identify the squares of the first and last terms.
Step 2
Why this answer is correct
The correct answer is B. ((2x-3)2 ). It is ((2x)2 -2\cdot2x\cdot3+32 ). Exam tip: identify the squares of the first and last terms.
Step 3
Exam Tip
यह ((2x)2 -2\cdot2x\cdot3+32 ) है। परीक्षा में पहले और अंतिम पद के वर्ग पहचानें।
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\(x^2-9\) किस प्रकार का द्विघात व्यंजक है?
What type of quadratic expression is \(x^2-9\)?
#difference of squares
#quadratic expression
#identity
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A पूर्ण वर्ग त्रिपद / Perfect square trinomial
B घनों का योग / Sum of cubes
C रेखीय व्यंजक / Linear expression
D दो वर्गों का अंतर / Difference of two squares
Explanation opens after your attempt
Correct Answer
D. दो वर्गों का अंतर / Difference of two squares
Step 1
Concept
\(x^2-9=x^2-3^2\). Exam tip: recognise the form ((a-b)(a+b)).
Step 2
Why this answer is correct
The correct answer is D. दो वर्गों का अंतर / Difference of two squares. \(x^2-9=x^2-3^2\). Exam tip: recognise the form ((a-b)(a+b)).
Step 3
Exam Tip
\(x^2-9=x^2-3^2\) है। परीक्षा में ((a-b)(a+b)) रूप को पहचानें।
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\(3x^2+2x-1\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(3x^2+2x-1\)?
#coefficient
#linear term
#quadratic expression
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A (3)
B (2)
C (-1)
D (1)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the (x)-term (2x) is (2). Exam tip: keep the coefficients of \(x^2\) and (x) separate.
Step 2
Why this answer is correct
The correct answer is B. (2). The coefficient of the (x)-term (2x) is (2). Exam tip: keep the coefficients of \(x^2\) and (x) separate.
Step 3
Exam Tip
(x) वाले पद (2x) का गुणांक (2) है। परीक्षा में \(x^2\) और (x) के गुणांक अलग रखें।
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मानक रूप \(ax^2+bx+c\) में \(7x^2-5x+11\) के लिए (b) क्या है?
In the standard form \(ax^2+bx+c\), what is (b) for \(7x^2-5x+11\)?
#standard form
#coefficient
#quadratic expression
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A (7)
B (5)
C (-5)
D (11)
Explanation opens after your attempt
Step 1
Concept
(b) is the coefficient of the (x)-term. Here the coefficient of (x) is (-5).
Step 2
Why this answer is correct
The correct answer is C. (-5). (b) is the coefficient of the (x)-term. Here the coefficient of (x) is (-5).
Step 3
Exam Tip
(b) (x) वाले पद का गुणांक होता है। यहां (x) का गुणांक (-5) है।
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मानक रूप \(ax^2+bx+c\) में \(2x^2+9x-4\) के लिए (c) क्या है?
In the standard form \(ax^2+bx+c\), what is (c) for \(2x^2+9x-4\)?
#standard form
#constant term
#quadratic expression
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A (2)
B (9)
C (-9)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(c) is the constant term without (x). Here (c=-4).
Step 2
Why this answer is correct
The correct answer is D. (-4). (c) is the constant term without (x). Here (c=-4).
Step 3
Exam Tip
(c) स्थिर पद होता है जिसमें (x) नहीं होता। यहां (c=-4) है।
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(x=-1) होने पर \(2x^2-5x+3\) का मान क्या है?
What is the value of \(2x^2-5x+3\) when (x=-1)?
#substitution
#negative value
#quadratic expression
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A (0)
B (5)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(2(-1)2 -5(-1)+3=2+5+3=10). Exam tip: put negative values in brackets.
Step 2
Why this answer is correct
The correct answer is C. (10). (2(-1)2 -5(-1)+3=2+5+3=10). Exam tip: put negative values in brackets.
Step 3
Exam Tip
(2(-1)2 -5(-1)+3=2+5+3=10) है। परीक्षा में ऋणात्मक मान को ब्रैकेट में रखें।
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\(3x^2-4x+1\) में कुल कितने पद हैं?
How many terms are there in \(3x^2-4x+1\)?
#terms
#trinomial
#quadratic expression
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The terms are \(3x^2\), (-4x), and (1). Exam tip: separate terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (3). The terms are \(3x^2\), (-4x), and (1). Exam tip: separate terms with their signs.
Step 3
Exam Tip
पद हैं \(3x^2\), (-4x) और (1)। परीक्षा में चिन्ह सहित पद अलग करें।
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\(x^2+px+12\) को ((x+3)(x+4)) के बराबर करने के लिए (p) क्या होगा?
What is (p) if \(x^2+px+12\) equals ((x+3)(x+4))?
#coefficient comparison
#quadratic expression
#binomial product
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A (12)
B (3)
C (7)
D (4)
Explanation opens after your attempt
Step 1
Concept
((x+3)(x+4)=x-2 +7x+12). Therefore (p=7).
Step 2
Why this answer is correct
The correct answer is C. (7). ((x+3)(x+4)=x-2 +7x+12). Therefore (p=7).
Step 3
Exam Tip
((x+3)(x+4)=x-2 +7x+12) होता है। इसलिए (p=7) है।
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\(x^2-kx+16\) को ((x-8)(x-2)) के बराबर करने के लिए (k) क्या है?
What is (k) if \(x^2-kx+16\) equals ((x-8)(x-2))?
#coefficient comparison
#quadratic expression
#signs
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A (6)
B (10)
C (-10)
D (16)
Explanation opens after your attempt
Step 1
Concept
((x-8)(x-2)=x-2 -10x+16). Therefore (k=10).
Step 2
Why this answer is correct
The correct answer is B. (10). ((x-8)(x-2)=x-2 -10x+16). Therefore (k=10).
Step 3
Exam Tip
((x-8)(x-2)=x-2 -10x+16) है। इसलिए (k=10) होगा।
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किस (m) के लिए \(x^2+mx+49\) पूर्ण वर्ग त्रिपद बनेगा?
For which (m) will \(x^2+mx+49\) be a perfect square trinomial?
#perfect square
#missing coefficient
#quadratic expression
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A (7)
B (14)
C (21)
D (49)
Explanation opens after your attempt
Step 1
Concept
\(49=7^2\), and a perfect square needs middle term \(2\cdot7x=14x\). Exam tip: take the square root of the last term.
Step 2
Why this answer is correct
The correct answer is B. (14). \(49=7^2\), and a perfect square needs middle term \(2\cdot7x=14x\). Exam tip: take the square root of the last term.
Step 3
Exam Tip
\(49=7^2\) और पूर्ण वर्ग के लिए मध्य पद \(2\cdot7x=14x\) चाहिए। परीक्षा में अंतिम पद का वर्गमूल लें।
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\(x^2-mx+36\) को पूर्ण वर्ग बनाने के लिए (m) का धनात्मक मान क्या होगा?
What is the positive value of (m) to make \(x^2-mx+36\) a perfect square?
#perfect square
#missing coefficient
#quadratic expression
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A (6)
B (9)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(36=6^2\) and ((x-6)2 =x-2 -12x+36). So (m=12).
Step 2
Why this answer is correct
The correct answer is C. (12). \(36=6^2\) and ((x-6)2 =x-2 -12x+36). So (m=12).
Step 3
Exam Tip
\(36=6^2\) है और ((x-6)2 =x-2 -12x+36) होता है। इसलिए (m=12) है।
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\(4x^2+mx+25\) पूर्ण वर्ग हो तो (m) का धनात्मक मान क्या है?
If \(4x^2+mx+25\) is a perfect square, what is the positive value of (m)?
#perfect square
#coefficient
#quadratic expression
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A (10)
B (20)
C (25)
D (40)
Explanation opens after your attempt
Step 1
Concept
(4x-2 =(2x)2 ) and \(25=5^2\). The middle term will be \(2\cdot2x\cdot5=20x\).
Step 2
Why this answer is correct
The correct answer is B. (20). (4x-2 =(2x)2 ) and \(25=5^2\). The middle term will be \(2\cdot2x\cdot5=20x\).
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(25=5^2\) हैं। मध्य पद \(2\cdot2x\cdot5=20x\) होगा।
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\(x^2+8x\) को पूर्ण वर्ग बनाने के लिए कौन सा पद जोड़ना चाहिए?
Which term should be added to \(x^2+8x\) to make it a perfect square?
#completing square
#quadratic expression
#identity
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A (4)
B (8)
C (64)
D (16)
Explanation opens after your attempt
Step 1
Concept
Half of (8) is (4), and \(4^2=16\). Exam tip: add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is D. (16). Half of (8) is (4), and \(4^2=16\). Exam tip: add the square of half the coefficient.
Step 3
Exam Tip
(8) का आधा (4) और \(4^2=16\) है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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\(x^2-12x\) को पूर्ण वर्ग बनाने के लिए कौन सा पद जोड़ना चाहिए?
Which term should be added to \(x^2-12x\) to make it a perfect square?
#completing square
#perfect square
#quadratic expression
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A (12)
B (24)
C (36)
D (144)
Explanation opens after your attempt
Step 1
Concept
Half of (-12) is (-6), and ((-6)2 =36). Exam tip: the square remains positive.
Step 2
Why this answer is correct
The correct answer is C. (36). Half of (-12) is (-6), and ((-6)2 =36). Exam tip: the square remains positive.
Step 3
Exam Tip
(-12) का आधा (-6) और ((-6)2 =36) है। परीक्षा में चिन्ह से वर्ग का मान धनात्मक रहता है।
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\(x^2+6x+9\) का न्यूनतम मान क्या है?
What is the minimum value of \(x^2+6x+9\)?
#minimum value
#perfect square
#quadratic expression
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A (-9)
B (0)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
(x-2 +6x+9=(x+3)2 ), and the minimum value of a square is (0). Exam tip: recognise the perfect square form.
Step 2
Why this answer is correct
The correct answer is B. (0). (x-2 +6x+9=(x+3)2 ), and the minimum value of a square is (0). Exam tip: recognise the perfect square form.
Step 3
Exam Tip
(x-2 +6x+9=(x+3)2 ) है और वर्ग का न्यूनतम मान (0) होता है। परीक्षा में पूर्ण वर्ग रूप पहचानें।
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\(x^2-4x+7\) का न्यूनतम मान क्या है?
What is the minimum value of \(x^2-4x+7\)?
#minimum value
#completing square
#quadratic expression
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A (2)
B (3)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
(x-2 -4x+7=(x-2)2 +3). Since the minimum of a square is (0), the value is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). (x-2 -4x+7=(x-2)2 +3). Since the minimum of a square is (0), the value is (3).
Step 3
Exam Tip
(x-2 -4x+7=(x-2)2 +3) है। वर्ग का न्यूनतम (0) होने से मान (3) है।
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\(x^2+2x+5\) को पूर्ण वर्ग और स्थिर पद के रूप में कैसे लिखेंगे?
How will \(x^2+2x+5\) be written as a square plus a constant?
#completing square
#quadratic expression
#standard transformation
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A ((x+1)2 +4)
B ((x+2)2 +1)
C ((x-1)2 +4)
D ((x+1)2 -4)
Explanation opens after your attempt
Correct Answer
A. ((x+1)2 +4)
Step 1
Concept
Make \(x^2+2x+1\) as ((x+1)2 ), leaving (4). Exam tip: keep addition and subtraction balanced.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)2 +4). Make \(x^2+2x+1\) as ((x+1)2 ), leaving (4). Exam tip: keep addition and subtraction balanced.
Step 3
Exam Tip
\(x^2+2x+1\) को ((x+1)2 ) बनाकर (4) शेष रहता है। परीक्षा में जोड़ और घटाव संतुलित रखें।
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\(2x^2+8x+6\) में (2) बाहर निकालने के बाद ब्रैकेट में क्या बचेगा?
After taking out (2) from \(2x^2+8x+6\), what remains inside the bracket?
#common factor
#quadratic expression
#simplification
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A \(x^2+4x+3\)
B \(x^2+8x+6\)
C \(2x^2+4x+3\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+3\)
Step 1
Concept
Dividing each term by (2) gives \(x^2+4x+3\). Exam tip: after taking a common factor, check all terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+3\). Dividing each term by (2) gives \(x^2+4x+3\). Exam tip: after taking a common factor, check all terms.
Step 3
Exam Tip
हर पद को (2) से भाग देने पर \(x^2+4x+3\) मिलता है। परीक्षा में सार्व गुणनखंड निकालने के बाद सभी पद जांचें।
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\(3x^2+12x+12\) का सही रूप कौन सा है?
Which is the correct form of \(3x^2+12x+12\)?
#common factor
#perfect square
#quadratic expression
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A ((3x+2)2 )
B (3(x-2)2 )
C (3(x+4)2 )
D (3(x+2)2 )
Explanation opens after your attempt
Correct Answer
D. (3(x+2)2 )
Step 1
Concept
(3x-2 +12x+12=3\(x^2+4x+4\)=3(x+2)2 ). Exam tip: take out (3) first.
Step 2
Why this answer is correct
The correct answer is D. (3(x+2)2 ). (3x-2 +12x+12=3\(x^2+4x+4\)=3(x+2)2 ). Exam tip: take out (3) first.
Step 3
Exam Tip
(3x-2 +12x+12=3\(x^2+4x+4\)=3(x+2)2 ) है। परीक्षा में पहले (3) बाहर निकालें।
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कौन सा व्यंजक (x) में द्विघात नहीं है?
Which expression is not quadratic in (x)?
#degree
#not quadratic
#identification
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A \(x^2+1\)
B \(4x^2-7x\)
C \(x^3+x^2+1\)
D \(9-2x+x^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^3+x^2+1\)
Step 1
Concept
The highest power of \(x^3+x^2+1\) is (3). Exam tip: the highest power tells the degree.
Step 2
Why this answer is correct
The correct answer is C. \(x^3+x^2+1\). The highest power of \(x^3+x^2+1\) is (3). Exam tip: the highest power tells the degree.
Step 3
Exam Tip
\(x^3+x^2+1\) की अधिकतम घात (3) है। परीक्षा में अधिकतम घात ही डिग्री बताती है।
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\(x^2+8x+16-y^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+8x+16-y^2\).
#difference of squares
#completion
#quadratic expression
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A ( (x+4)(x+4-y) )
B ( (x-y+8)(x+y+2) )
C ( (x+y+4)2 )
D ( (x+4-y)(x+4+y) )
Explanation opens after your attempt
Correct Answer
D. ( (x+4-y)(x+4+y) )
Step 1
Concept
Write it as ((x+4)2 -y-2 ) and apply the difference of squares identity. Exam tip: form the perfect square first.
Step 2
Why this answer is correct
The correct answer is D. ( (x+4-y)(x+4+y) ). Write it as ((x+4)2 -y-2 ) and apply the difference of squares identity. Exam tip: form the perfect square first.
Step 3
Exam Tip
इसे ((x+4)2 -y-2 ) लिखकर अंतर वर्ग पहचान लगती है। परीक्षा में पहले पूर्ण वर्ग बनाएं।
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((2x+1)(x-4)) का विस्तारित रूप क्या है?
What is the expanded form of ((2x+1)(x-4))?
#binomial product
#expansion
#quadratic expression
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A \(2x^2-7x-4\)
B \(2x^2+7x-4\)
C \(2x^2-8x+1\)
D \(2x^2-4\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-7x-4\)
Step 1
Concept
\(2x^2-8x+x-4=2x^2-7x-4\). Exam tip: combine like terms at the end.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-7x-4\). \(2x^2-8x+x-4=2x^2-7x-4\). Exam tip: combine like terms at the end.
Step 3
Exam Tip
\(2x^2-8x+x-4=2x^2-7x-4\) है। परीक्षा में समान पदों को अंत में जोड़ें।
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((3x-2)(x+5)) का गुणनफल क्या है?
What is the product of ((3x-2)(x+5))?
#binomial product
#quadratic expression
#expansion
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A \(3x^2+13x-10\)
B \(3x^2-13x-10\)
C \(3x^2+15x-2\)
D \(3x^2+10x-5\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+13x-10\)
Step 1
Concept
\(3x^2+15x-2x-10=3x^2+13x-10\). Exam tip: add the two terms forming the middle term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+13x-10\). \(3x^2+15x-2x-10=3x^2+13x-10\). Exam tip: add the two terms forming the middle term.
Step 3
Exam Tip
\(3x^2+15x-2x-10=3x^2+13x-10\) है। परीक्षा में मध्य पद बनाने वाले दोनों पद जोड़ें।
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((x-7)(x+7)) का परिणाम क्या है?
What is the result of ((x-7)(x+7))?
#difference of squares
#binomial product
#quadratic expression
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A \(x^2+49\)
B \(x^2-14x+49\)
C \(x^2-49\)
D \(x^2+14x-49\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-49\)
Step 1
Concept
This is the form ((a-b)(a+b)=a-2 -b-2 ). Exam tip: quickly identify conjugate binomials.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-49\). This is the form ((a-b)(a+b)=a-2 -b-2 ). Exam tip: quickly identify conjugate binomials.
Step 3
Exam Tip
यह ((a-b)(a+b)=a-2 -b-2 ) का रूप है। परीक्षा में विपरीत चिन्ह वाले समान द्विपद तुरंत पहचानें।
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((5x+2)2 ) में (x) वाले पद का गुणांक क्या होगा?
What will be the coefficient of the (x)-term in ((5x+2)2 )?
#coefficient
#perfect square
#quadratic expression
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A (10)
B (20)
C (25)
D (4)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot5x\cdot2=20x\). So the coefficient of (x) is (20).
Step 2
Why this answer is correct
The correct answer is B. (20). The middle term is \(2\cdot5x\cdot2=20x\). So the coefficient of (x) is (20).
Step 3
Exam Tip
मध्य पद \(2\cdot5x\cdot2=20x\) है। इसलिए (x) का गुणांक (20) है।
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((4x-3)2 ) में स्थिर पद क्या होगा?
What will be the constant term in ((4x-3)2 )?
#constant term
#perfect square
#quadratic expression
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A (16)
B (-24)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-3)2 =9). Exam tip: a negative sign becomes positive after squaring.
Step 2
Why this answer is correct
The correct answer is C. (9). The constant term is ((-3)2 =9). Exam tip: a negative sign becomes positive after squaring.
Step 3
Exam Tip
स्थिर पद ((-3)2 =9) होता है। परीक्षा में वर्ग करने पर ऋण चिन्ह धनात्मक बनता है।
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\(x^2+ax+20\) में यदि गुणनखंड ((x+4)(x+5)) हैं तो (a) क्या है?
If the factors of \(x^2+ax+20\) are ((x+4)(x+5)), what is (a)?
#coefficient comparison
#factors
#quadratic expression
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A (9)
B (20)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
((x+4)(x+5)=x-2 +9x+20). Therefore (a=9).
Step 2
Why this answer is correct
The correct answer is A. (9). ((x+4)(x+5)=x-2 +9x+20). Therefore (a=9).
Step 3
Exam Tip
((x+4)(x+5)=x-2 +9x+20) होता है। इसलिए (a=9) है।
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\(x^2-11x+b\) में यदि गुणनखंड ((x-6)(x-5)) हैं तो (b) क्या है?
If the factors of \(x^2-11x+b\) are ((x-6)(x-5)), what is (b)?
#constant comparison
#factors
#quadratic expression
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A (11)
B (30)
C (-30)
D (-11)
Explanation opens after your attempt
Step 1
Concept
((x-6)(x-5)=x-2 -11x+30). Therefore the constant term is (b=30).
Step 2
Why this answer is correct
The correct answer is B. (30). ((x-6)(x-5)=x-2 -11x+30). Therefore the constant term is (b=30).
Step 3
Exam Tip
((x-6)(x-5)=x-2 -11x+30) है। इसलिए स्थिर पद (b=30) है।
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\(x^2+3x-28\) में मध्य पद तोड़ने के लिए सही जोड़ी कौन सी है?
Which pair is correct for splitting the middle term in \(x^2+3x-28\)?
#middle term splitting
#quadratic expression
#factorisation
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A (7x) और (-4x) / (7x) and (-4x)
B (-7x) और (4x) / (-7x) and (4x)
C (14x) और (-2x) / (14x) and (-2x)
D (28x) और (-x) / (28x) and (-x)
Explanation opens after your attempt
Correct Answer
A. (7x) और (-4x) / (7x) and (-4x)
Step 1
Concept
(7x-4x=3x) and (7\cdot(-4)=-28). Exam tip: match both sum and product.
Step 2
Why this answer is correct
The correct answer is A. (7x) और (-4x) / (7x) and (-4x). (7x-4x=3x) and (7\cdot(-4)=-28). Exam tip: match both sum and product.
Step 3
Exam Tip
(7x-4x=3x) और (7\cdot(-4)=-28) है। परीक्षा में योग और गुणनफल दोनों मिलाएं।
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\(2x^2+9x+10\) में मध्य पद तोड़ने की सही जोड़ी कौन सी है?
Which pair is correct for splitting the middle term in \(2x^2+9x+10\)?
#middle term splitting
#ac method
#quadratic expression
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A (4x) और (5x) / (4x) and (5x)
B (2x) और (7x) / (2x) and (7x)
C (5x) और (4x) / (5x) and (4x)
D (x) और (8x) / (x) and (8x)
Explanation opens after your attempt
Correct Answer
C. (5x) और (4x) / (5x) and (4x)
Step 1
Concept
(5x+4x=9x), and \(5\cdot4=20\), which equals \(2\cdot10\). Exam tip: remember the (ac) method.
Step 2
Why this answer is correct
The correct answer is C. (5x) और (4x) / (5x) and (4x). (5x+4x=9x), and \(5\cdot4=20\), which equals \(2\cdot10\). Exam tip: remember the (ac) method.
Step 3
Exam Tip
(5x+4x=9x) और \(5\cdot4=20\) जो \(2\cdot10\) के बराबर है। परीक्षा में (ac) विधि याद रखें।
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\(3x^2-8x+4\) में मध्य पद तोड़ने की सही जोड़ी कौन सी है?
Which pair correctly splits the middle term in \(3x^2-8x+4\)?
#middle term splitting
#ac method
#quadratic expression
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A (-6x) और (-2x) / (-6x) and (-2x)
B (-4x) और (-4x) / (-4x) and (-4x)
C (6x) और (2x) / (6x) and (2x)
D (-12x) और (4x) / (-12x) and (4x)
Explanation opens after your attempt
Correct Answer
A. (-6x) और (-2x) / (-6x) and (-2x)
Step 1
Concept
(-6x-2x=-8x), and ((-6)(-2)=12), which equals \(3\cdot4\). Exam tip: the product of the two numbers must be (ac).
Step 2
Why this answer is correct
The correct answer is A. (-6x) और (-2x) / (-6x) and (-2x). (-6x-2x=-8x), and ((-6)(-2)=12), which equals \(3\cdot4\). Exam tip: the product of the two numbers must be (ac).
Step 3
Exam Tip
(-6x-2x=-8x) और ((-6)(-2)=12) जो \(3\cdot4\) के बराबर है। परीक्षा में दोनों संख्याओं का गुणनफल (ac) होना चाहिए।
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\(x^2+bx+15\) के गुणनखंड ((x+3)(x+5)) हों तो (b) कितना होगा?
If the factors of \(x^2+bx+15\) are ((x+3)(x+5)), what is (b)?
#coefficient comparison
#binomial factors
#quadratic expression
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A (3)
B (5)
C (15)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum of the constant parts of the binomials is (3+5=8). Therefore (b=8).
Step 2
Why this answer is correct
The correct answer is D. (8). The sum of the constant parts of the binomials is (3+5=8). Therefore (b=8).
Step 3
Exam Tip
द्विपदों के स्थिर भागों का योग (3+5=8) है। इसलिए (b=8) है।
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\(x^2+6x+c\) पूर्ण वर्ग त्रिपद हो और (c) धनात्मक हो तो (c) क्या है?
If \(x^2+6x+c\) is a perfect square trinomial and (c) is positive, what is (c)?
#perfect square
#missing constant
#quadratic expression
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Half of (6) is (3), and \(3^2=9\). Exam tip: square half of the middle coefficient.
Step 2
Why this answer is correct
The correct answer is C. (9). Half of (6) is (3), and \(3^2=9\). Exam tip: square half of the middle coefficient.
Step 3
Exam Tip
(6) का आधा (3) है और \(3^2=9\) है। परीक्षा में आधे मध्य गुणांक का वर्ग लें।
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\(x^2-14x+c\) पूर्ण वर्ग त्रिपद हो तो (c) क्या होगा?
If \(x^2-14x+c\) is a perfect square trinomial, what will (c) be?
#perfect square
#missing constant
#quadratic expression
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A (14)
B (28)
C (49)
D (196)
Explanation opens after your attempt
Step 1
Concept
Half of (-14) is (-7), and ((-7)2 =49). Exam tip: the constant term is a square.
Step 2
Why this answer is correct
The correct answer is C. (49). Half of (-14) is (-7), and ((-7)2 =49). Exam tip: the constant term is a square.
Step 3
Exam Tip
(-14) का आधा (-7) और ((-7)2 =49) है। परीक्षा में स्थिर पद हमेशा वर्ग होता है।
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कौन सा व्यंजक (x) में द्विघात द्विपद है?
Which expression is a quadratic binomial in (x)?
#binomial
#quadratic expression
#degree
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A \(x^2+5x+6\)
B \(x^2-16\)
C (x+16)
D \(x^3-16\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-16\)
Step 1
Concept
\(x^2-16\) has two terms and highest power (2). Exam tip: check both binomial and quadratic conditions.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-16\). \(x^2-16\) has two terms and highest power (2). Exam tip: check both binomial and quadratic conditions.
Step 3
Exam Tip
\(x^2-16\) में दो पद हैं और अधिकतम घात (2) है। परीक्षा में द्विपद और द्विघात दोनों शर्तें जांचें।
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\(5x^2-20\) को (5) बाहर निकालकर कैसे लिखा जाएगा?
How will \(5x^2-20\) be written after taking out (5)?
#common factor
#quadratic binomial
#simplification
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A (5\(x^2-20\))
B (5(x-4))
C (5\(x^2+4\))
D (5\(x^2-4\))
Explanation opens after your attempt
Correct Answer
D. (5\(x^2-4\))
Step 1
Concept
Both \(5x^2\) and (-20) have (5) in common. After taking it out, \(x^2-4\) remains.
Step 2
Why this answer is correct
The correct answer is D. (5\(x^2-4\)). Both \(5x^2\) and (-20) have (5) in common. After taking it out, \(x^2-4\) remains.
Step 3
Exam Tip
\(5x^2\) और (-20) दोनों में (5) समान है। बाहर निकालने पर \(x^2-4\) बचता है।
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\(2x^2+3x+1\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(2x^2+3x+1\)?
#factorisation
#quadratic expression
#binomial factors
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A ((2x+1)(x+1))
B ((2x-1)(x-1))
C ((x+2)(x+1))
D ((2x+3)(x+1))
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x+1))
Step 1
Concept
Expanding gives \(2x^2+2x+x+1=2x^2+3x+1\). Exam tip: verify the option by expansion.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x+1)). Expanding gives \(2x^2+2x+x+1=2x^2+3x+1\). Exam tip: verify the option by expansion.
Step 3
Exam Tip
फैलाने पर \(2x^2+2x+x+1=2x^2+3x+1\) मिलता है। परीक्षा में विकल्प को फैलाकर जांचें।
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\(x^2-5x+6\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2-5x+6\)?
#factorisation
#quadratic expression
#middle term
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A ((x+2)(x+3))
B ((x-2)(x-3))
C ((x-1)(x-6))
D ((x+1)(x+6))
Explanation opens after your attempt
Correct Answer
B. ((x-2)(x-3))
Step 1
Concept
The numbers (-2) and (-3) have sum (-5) and product (6). Exam tip: match signs with the constant term.
Step 2
Why this answer is correct
The correct answer is B. ((x-2)(x-3)). The numbers (-2) and (-3) have sum (-5) and product (6). Exam tip: match signs with the constant term.
Step 3
Exam Tip
(-2) और (-3) का योग (-5) और गुणनफल (6) है। परीक्षा में चिन्हों को स्थिर पद से मिलाएं।
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\(3x^2+11x+6\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(3x^2+11x+6\)?
#factorisation
#ac method
#quadratic expression
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A ((3x+2)(x+3))
B ((3x+6)(x+1))
C ((x+2)(3x+3))
D ((3x-2)(x-3))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(x+3))
Step 1
Concept
\(3x^2+9x+2x+6\) gives (11x). Exam tip: choose the correct pair using the (ac) method.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(x+3)). \(3x^2+9x+2x+6\) gives (11x). Exam tip: choose the correct pair using the (ac) method.
Step 3
Exam Tip
\(3x^2+9x+2x+6\) से (11x) बनता है। परीक्षा में (ac) विधि से सही जोड़ी चुनें।
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\(x^2+4x+4\) और \(x^2-4\) में मुख्य अंतर क्या है?
What is the main difference between \(x^2+4x+4\) and \(x^2-4\)?
#identity comparison
#perfect square
#difference of squares
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A पहला पूर्ण वर्ग है और दूसरा दो वर्गों का अंतर है / The first is a perfect square and the second is a difference of two squares
B दोनों रेखीय व्यंजक हैं / Both are linear expressions
C पहला घन है और दूसरा त्रिघात है / The first is a cube and the second is cubic
D दोनों में कोई पहचान लागू नहीं होती / No identity applies to either
Explanation opens after your attempt
Correct Answer
A. पहला पूर्ण वर्ग है और दूसरा दो वर्गों का अंतर है / The first is a perfect square and the second is a difference of two squares
Step 1
Concept
(x-2 +4x+4=(x+2)2 ) and (x-2 -4=(x-2)(x+2)). Exam tip: distinguish similar-looking quadratics by identity.
Step 2
Why this answer is correct
The correct answer is A. पहला पूर्ण वर्ग है और दूसरा दो वर्गों का अंतर है / The first is a perfect square and the second is a difference of two squares. (x-2 +4x+4=(x+2)2 ) and (x-2 -4=(x-2)(x+2)). Exam tip: distinguish similar-looking quadratics by identity.
Step 3
Exam Tip
(x-2 +4x+4=(x+2)2 ) और (x-2 -4=(x-2)(x+2)) है। परीक्षा में समान दिखने वाले द्विघातों की पहचान अलग करें।
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\(4x^2-9\) का गुणनखंड रूप क्या है?
What is the factorised form of \(4x^2-9\)?
#difference of squares
#quadratic expression
#factorisation
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A ( (2x-3)(2x+3) )
B ( (4x-3)(x+3) )
C ( (2x+3)2 )
D ( (2x-3)2 )
Explanation opens after your attempt
Correct Answer
A. ( (2x-3)(2x+3) )
Step 1
Concept
Here (4x-2 =(2x)2 ) and \(9=3^2\), so it is a difference of two squares. Exam tip: apply the \(a^2-b^2\) identity quickly.
Step 2
Why this answer is correct
The correct answer is A. ( (2x-3)(2x+3) ). Here (4x-2 =(2x)2 ) and \(9=3^2\), so it is a difference of two squares. Exam tip: apply the \(a^2-b^2\) identity quickly.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(9=3^2\) हैं इसलिए दो वर्गों का अंतर है। परीक्षा में \(a^2-b^2\) पहचान तुरंत लगाएं।
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\(x^2-2x+1\) किस पूर्ण वर्ग के बराबर है?
Which perfect square is equal to \(x^2-2x+1\)?
#perfect square
#quadratic expression
#identity
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A ( (x+1)2 )
B ( (x-1)2 )
C ( (x-2)2 )
D \( x^2-1 \)
Explanation opens after your attempt
Correct Answer
B. ( (x-1)2 )
Step 1
Concept
It is in the form \(x^2-2\cdot x\cdot1+1^2\). Exam tip: in ((a-b)2 ), the middle term is negative.
Step 2
Why this answer is correct
The correct answer is B. ( (x-1)2 ). It is in the form \(x^2-2\cdot x\cdot1+1^2\). Exam tip: in ((a-b)2 ), the middle term is negative.
Step 3
Exam Tip
यह \(x^2-2\cdot x\cdot1+1^2\) के रूप में है। परीक्षा में ((a-b)2 ) में मध्य पद ऋणात्मक होता है।
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