व्यंजक \(3x^2-5x+7\) में \(x^2\) का गुणांक क्या है?
In the expression \(3x^2-5x+7\), what is the coefficient of \(x^2\)?
#quadratic expressions
#coefficient
#algebra
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A (3)
B (-5)
C (7)
D (2)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^2\) is (3). Exam tip: identify the term and its coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (3). The coefficient attached to \(x^2\) is (3). Exam tip: identify the term and its coefficient separately.
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणांक (3) है। परीक्षा में पद और उसके गुणांक को अलग पहचानें।
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\(x^2-14x+49\) किस रूप में लिखा जा सकता है?
In which form can \(x^2-14x+49\) be written?
#perfect square
#negative middle term
#quadratic
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A ((x+7)2 )
B ((x-14)2 )
C ((x+49)2 )
D ((x-7)2 )
Explanation opens after your attempt
Correct Answer
D. ((x-7)2 )
Step 1
Concept
Since \(49=7^2\) and the middle term is (-14x), the form is ((x-7)2 ). Exam tip: pay attention to the negative sign.
Step 2
Why this answer is correct
The correct answer is D. ((x-7)2 ). Since \(49=7^2\) and the middle term is (-14x), the form is ((x-7)2 ). Exam tip: pay attention to the negative sign.
Step 3
Exam Tip
\(49=7^2\) और मध्य पद (-14x) है इसलिए रूप ((x-7)2 ) है। परीक्षा में ऋण चिह्न पर ध्यान दें।
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((2x-3)2 ) का सही विस्तार क्या है?
What is the correct expansion of ((2x-3)2 )?
#binomial square
#expansion
#quadratic
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A \(4x^2-6x+9\)
B \(4x^2-12x+9\)
C \(2x^2-12x+9\)
D \(4x^2+12x+9\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2-12x+9\)
Step 1
Concept
The middle term is \(-2\cdot2x\cdot3=-12x\). Exam tip: square the whole (2x) as \(4x^2\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2-12x+9\). The middle term is \(-2\cdot2x\cdot3=-12x\). Exam tip: square the whole (2x) as \(4x^2\).
Step 3
Exam Tip
मध्य पद \(-2\cdot2x\cdot3=-12x\) होगा। परीक्षा में पूरे (2x) का वर्ग \(4x^2\) लें।
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((x+5)(x-2)) में (x) का गुणांक कितना होगा?
What will be the coefficient of (x) in ((x+5)(x-2))?
#product of binomials
#middle coefficient
#quadratic
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A (7)
B (10)
C (3)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The expansion is \(x^2+3x-10\), so the coefficient of (x) is (3). Exam tip: the sum of constants gives the middle coefficient.
Step 2
Why this answer is correct
The correct answer is C. (3). The expansion is \(x^2+3x-10\), so the coefficient of (x) is (3). Exam tip: the sum of constants gives the middle coefficient.
Step 3
Exam Tip
विस्तार \(x^2+3x-10\) है इसलिए (x) का गुणांक (3) है। परीक्षा में स्थिर पदों के योग से मध्य गुणांक मिलता है।
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((x-7)(x+3)) का स्थिर पद क्या होगा?
What will be the constant term of ((x-7)(x+3))?
#constant term
#binomial product
#quadratic
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A (21)
B (4)
C (-4)
D (-21)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-7)\cdot3=-21). Exam tip: multiply the constant numbers to get the constant term.
Step 2
Why this answer is correct
The correct answer is D. (-21). The constant term is ((-7)\cdot3=-21). Exam tip: multiply the constant numbers to get the constant term.
Step 3
Exam Tip
स्थिर पद ((-7)\cdot3=-21) है। परीक्षा में स्थिर पद पाने के लिए स्थिर संख्याओं का गुणन करें।
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यदि (x=2) हो तो \(x^2+5x-6\) का मान क्या होगा?
If (x=2), what is the value of \(x^2+5x-6\)?
#value of expression
#substitution
#quadratic
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A (8)
B (10)
C (6)
D (4)
Explanation opens after your attempt
Step 1
Concept
We get \(2^2+5\cdot2-6=8\). Exam tip: do powers first, then multiplication, then addition and subtraction.
Step 2
Why this answer is correct
The correct answer is A. (8). We get \(2^2+5\cdot2-6=8\). Exam tip: do powers first, then multiplication, then addition and subtraction.
Step 3
Exam Tip
\(2^2+5\cdot2-6=8\) मिलता है। परीक्षा में पहले घात फिर गुणा और फिर जोड़ घटाव करें।
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\(x^2+8x+k\) को पूर्ण वर्ग बनाने के लिए (k) का मान क्या होना चाहिए?
What should be the value of (k) to make \(x^2+8x+k\) a perfect square?
#completing square
#perfect square
#quadratic
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A (8)
B (16)
C (4)
D (64)
Explanation opens after your attempt
Step 1
Concept
Half of (8) is (4), and \(4^2=16\). Exam tip: halve the middle coefficient and square it.
Step 2
Why this answer is correct
The correct answer is B. (16). Half of (8) is (4), and \(4^2=16\). Exam tip: halve the middle coefficient and square it.
Step 3
Exam Tip
(8) का आधा (4) है और \(4^2=16\) है। परीक्षा में मध्य गुणांक का आधा करके उसका वर्ग लें।
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\(x^2-18x+k\) को पूर्ण वर्ग बनाने के लिए (k) क्या होगा?
What will (k) be to make \(x^2-18x+k\) a perfect square?
#completing square
#negative coefficient
#quadratic
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A (81)
B (36)
C (18)
D (324)
Explanation opens after your attempt
Step 1
Concept
Half of (-18) is (-9), and ((-9)2 =81). Exam tip: the square becomes positive even with a negative sign.
Step 2
Why this answer is correct
The correct answer is A. (81). Half of (-18) is (-9), and ((-9)2 =81). Exam tip: the square becomes positive even with a negative sign.
Step 3
Exam Tip
(-18) का आधा (-9) है और ((-9)2 =81) है। परीक्षा में वर्ग लेते समय चिह्न से मान धन हो जाता है।
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\(2x^2+7x+3\) में रैखिक पद कौन सा है?
What is the linear term in \(2x^2+7x+3\)?
#linear term
#quadratic expression
#terms
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A \(2x^2\)
B (3)
C (7x)
D \(2x^2+3\)
Explanation opens after your attempt
Step 1
Concept
The term with power (1) of (x) is the linear term. Exam tip: keep \(x^2\) and (x) terms separate.
Step 2
Why this answer is correct
The correct answer is C. (7x). The term with power (1) of (x) is the linear term. Exam tip: keep \(x^2\) and (x) terms separate.
Step 3
Exam Tip
जिस पद में (x) की घात (1) हो वह रैखिक पद है। परीक्षा में \(x^2\) और (x) पद अलग रखें।
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\(5x^2-9x+2\) में स्थिर पद कौन सा है?
What is the constant term in \(5x^2-9x+2\)?
#constant term
#quadratic expression
#algebra
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A (5)
B (-9)
C \(x^2\)
D (2)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Exam tip: read the constant term with its sign.
Step 2
Why this answer is correct
The correct answer is D. (2). The term without (x) is the constant term. Exam tip: read the constant term with its sign.
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह स्थिर पद होता है। परीक्षा में चिह्न सहित स्थिर पद पढ़ें।
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((x+3)2 -(x-3)2 ) का सरल मान क्या है?
What is the simplified value of ((x+3)2 -(x-3)2 )?
#difference of squares
#binomial identity
#quadratic
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A (12x)
B (6x)
C \(x^2-9\)
D (18)
Explanation opens after your attempt
Step 1
Concept
Using ((a+b)2 -(a-b)2 =4ab), we get \(4\cdot x\cdot3=12x\). Exam tip: identities save time.
Step 2
Why this answer is correct
The correct answer is A. (12x). Using ((a+b)2 -(a-b)2 =4ab), we get \(4\cdot x\cdot3=12x\). Exam tip: identities save time.
Step 3
Exam Tip
((a+b)2 -(a-b)2 =4ab) से \(4\cdot x\cdot3=12x\) मिलता है। परीक्षा में पहचान से समय बचता है।
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\(x^2+px+16\) पूर्ण वर्ग है और (p) धन है। (p) का मान क्या है?
The expression \(x^2+px+16\) is a perfect square and (p) is positive. What is the value of (p)?
#unknown coefficient
#perfect square
#quadratic
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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: take the positive middle term for positive (p).
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: take the positive middle term for positive (p).
Step 3
Exam Tip
\(16=4^2\) है इसलिए मध्य पद \(2\cdot4\cdot x=8x\) होगा। परीक्षा में धन (p) के लिए धन मध्य पद लें।
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\(4x^2+px+25\) पूर्ण वर्ग है और (p<0) है। (p) का मान क्या है?
The expression \(4x^2+px+25\) is a perfect square and (p<0). What is the value of (p)?
#unknown coefficient
#negative middle term
#perfect square
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A (20)
B (10)
C (-20)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The parts are (2x) and (5), so the middle term is \(-2\cdot2x\cdot5=-20x\). Exam tip: choose the negative value using (p<0).
Step 2
Why this answer is correct
The correct answer is C. (-20). The parts are (2x) and (5), so the middle term is \(-2\cdot2x\cdot5=-20x\). Exam tip: choose the negative value using (p<0).
Step 3
Exam Tip
भुजाएं (2x) और (5) हैं इसलिए मध्य पद \(-2\cdot2x\cdot5=-20x\) है। परीक्षा में (p<0) देखकर ऋण मान चुनें।
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((3x+2)(x-5)) का विस्तार कौन सा है?
What is the expansion of ((3x+2)(x-5))?
#binomial product
#quadratic expansion
#like terms
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A \(3x^2-15x+2x-10\)
B \(3x^2+15x+2x-10\)
C \(3x^2-13x-10\)
D \(3x^2+13x-10\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2-13x-10\)
Step 1
Concept
Combining like terms gives (-15x+2x=-13x). Exam tip: expand first and then combine like terms.
Step 2
Why this answer is correct
The correct answer is C. \(3x^2-13x-10\). Combining like terms gives (-15x+2x=-13x). Exam tip: expand first and then combine like terms.
Step 3
Exam Tip
समान पद जोड़ने पर (-15x+2x=-13x) मिलता है। परीक्षा में पहले विस्तार फिर समान पदों को जोड़ें।
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((2x-1)(4x+3)) में \(x^2\) का गुणांक क्या होगा?
What will be the coefficient of \(x^2\) in ((2x-1)(4x+3))?
#leading coefficient
#binomial product
#quadratic
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A (6)
B (7)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\) term comes from \(2x\cdot4x=8x^2\). Exam tip: multiply the leading coefficients.
Step 2
Why this answer is correct
The correct answer is D. (8). The \(x^2\) term comes from \(2x\cdot4x=8x^2\). Exam tip: multiply the leading coefficients.
Step 3
Exam Tip
\(x^2\) पद \(2x\cdot4x=8x^2\) से आता है। परीक्षा में प्रमुख गुणांकों का गुणन करें।
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\(x^2+6x+5\) में (x=1) रखने पर मान क्या होगा?
What is the value of \(x^2+6x+5\) when (x=1)?
#substitution
#value of quadratic
#calculation
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A (12)
B (11)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
Here \(1^2+6\cdot1+5=12\). Exam tip: calculate carefully after substitution.
Step 2
Why this answer is correct
The correct answer is A. (12). Here \(1^2+6\cdot1+5=12\). Exam tip: calculate carefully after substitution.
Step 3
Exam Tip
\(1^2+6\cdot1+5=12\) है। परीक्षा में प्रतिस्थापन के बाद सरल गणना सावधानी से करें।
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\(2x^2-3x+4\) और \(x^2+5x-1\) का योग क्या है?
What is the sum of \(2x^2-3x+4\) and \(x^2+5x-1\)?
#addition of quadratics
#like terms
#algebra
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A \(3x^2-8x+3\)
B \(3x^2+2x+3\)
C \(x^2+2x+3\)
D \(3x^2+8x+5\)
Explanation opens after your attempt
Correct Answer
B. \(3x^2+2x+3\)
Step 1
Concept
Adding like terms gives \(3x^2+2x+3\). Exam tip: add \(x^2\), (x), and constant terms separately.
Step 2
Why this answer is correct
The correct answer is B. \(3x^2+2x+3\). Adding like terms gives \(3x^2+2x+3\). Exam tip: add \(x^2\), (x), and constant terms separately.
Step 3
Exam Tip
समान पद जोड़ने पर \(3x^2+2x+3\) मिलता है। परीक्षा में \(x^2\), (x) और स्थिर पद अलग जोड़ें।
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\(5x^2+2x-7\) में से \(2x^2-3x+4\) घटाने पर क्या मिलेगा?
What is obtained by subtracting \(2x^2-3x+4\) from \(5x^2+2x-7\)?
#subtraction of quadratics
#signs
#like terms
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A \(3x^2-x-11\)
B \(7x^2-x-3\)
C \(3x^2+5x-11\)
D \(3x^2-5x+11\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+5x-11\)
Step 1
Concept
On subtracting, (5x-2 +2x-7-\(2x^2-3x+4\)=3x-2 +5x-11). Exam tip: change signs when removing brackets.
Step 2
Why this answer is correct
The correct answer is C. \(3x^2+5x-11\). On subtracting, (5x-2 +2x-7-\(2x^2-3x+4\)=3x-2 +5x-11). Exam tip: change signs when removing brackets.
Step 3
Exam Tip
घटाने पर (5x-2 +2x-7-\(2x^2-3x+4\)=3x-2 +5x-11) है। परीक्षा में कोष्ठक खोलते समय चिह्न बदलें।
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किस (k) के लिए \(x^2+kx+9\) पूर्ण वर्ग होगा और मध्य पद ऋण होगा?
For which (k) will \(x^2+kx+9\) be a perfect square with negative middle term?
#unknown coefficient
#perfect square
#negative term
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A (6)
B (3)
C (9)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Since \(9=3^2\), the negative middle term is \(-2\cdot3\cdot x=-6x\). Exam tip: match the sign of the middle term with the condition.
Step 2
Why this answer is correct
The correct answer is D. (-6). Since \(9=3^2\), the negative middle term is \(-2\cdot3\cdot x=-6x\). Exam tip: match the sign of the middle term with the condition.
Step 3
Exam Tip
\(9=3^2\) है और ऋण मध्य पद \(-2\cdot3\cdot x=-6x\) होगा। परीक्षा में मध्य पद के चिह्न को शर्त से मिलाएं।
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\(x^2-4\) और \(x^2+4x+4\) में क्या संबंध है?
What is the relation between \(x^2-4\) and \(x^2+4x+4\)?
#identity recognition
#difference of squares
#perfect square
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A पहला वर्गों का अंतर है और दूसरा पूर्ण वर्ग है / The first is a difference of squares and the second is a perfect square
B दोनों समान व्यंजक हैं / Both are equal expressions
C पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है / The first is a perfect square and the second is a difference of squares
D दोनों रैखिक व्यंजक हैं / Both are linear expressions
Explanation opens after your attempt
Correct Answer
A. पहला वर्गों का अंतर है और दूसरा पूर्ण वर्ग है / The first is a difference of squares and the second is a perfect square
Step 1
Concept
Here \(x^2-4=x^2-2^2\) and (x-2 +4x+4=(x+2)2 ). Exam tip: identify the type of identity separately.
Step 2
Why this answer is correct
The correct answer is A. पहला वर्गों का अंतर है और दूसरा पूर्ण वर्ग है / The first is a difference of squares and the second is a perfect square. Here \(x^2-4=x^2-2^2\) and (x-2 +4x+4=(x+2)2 ). Exam tip: identify the type of identity separately.
Step 3
Exam Tip
\(x^2-4=x^2-2^2\) है और (x-2 +4x+4=(x+2)2 ) है। परीक्षा में पहचान का प्रकार अलग अलग पहचानें।
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((x+a)2 ) में (x) का गुणांक (14) है। (a) का मान क्या है?
In ((x+a)2 ), the coefficient of (x) is (14). What is the value of (a)?
#parameter
#binomial square
#quadratic
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A (14)
B (7)
C (28)
D (49)
Explanation opens after your attempt
Step 1
Concept
((x+a)2 =x-2 +2ax+a-2 ), so (2a=14) and (a=7). Exam tip: treat the middle coefficient as (2a).
Step 2
Why this answer is correct
The correct answer is B. (7). ((x+a)2 =x-2 +2ax+a-2 ), so (2a=14) and (a=7). Exam tip: treat the middle coefficient as (2a).
Step 3
Exam Tip
((x+a)2 =x-2 +2ax+a-2 ) है इसलिए (2a=14) और (a=7)। परीक्षा में मध्य गुणांक को (2a) मानें।
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((x-a)2 ) में स्थिर पद (36) है और (a>0) है। (x) का गुणांक क्या होगा?
In ((x-a)2 ), the constant term is (36) and (a>0). What will be the coefficient of (x)?
#constant term
#parameter
#perfect square
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A (12)
B (6)
C (-12)
D (-6)
Explanation opens after your attempt
Step 1
Concept
From \(a^2=36\), (a=6), and the middle term is (-2ax=-12x). Exam tip: the middle term is negative in a subtraction square.
Step 2
Why this answer is correct
The correct answer is C. (-12). From \(a^2=36\), (a=6), and the middle term is (-2ax=-12x). Exam tip: the middle term is negative in a subtraction square.
Step 3
Exam Tip
\(a^2=36\) से (a=6) और मध्य पद (-2ax=-12x) होगा। परीक्षा में घटाव वाले वर्ग का मध्य पद ऋण होता है।
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यदि \(x-\frac{1}{x}=4\) हो तो \(x^2+\frac{1}{x^2}\) का मान क्या होगा?
If \(x-\frac{1}{x}=4\), what is the value of \(x^2+\frac{1}{x^2}\)?
#reciprocal identity
#quadratic expression
#value
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A (16)
B (18)
C (14)
D (20)
Explanation opens after your attempt
Step 1
Concept
Squaring gives \(x^2-2+\frac{1}{x^2}=16\), so \(x^2+\frac{1}{x^2}=18\). Exam tip: add (2) in the subtraction identity.
Step 2
Why this answer is correct
The correct answer is B. (18). Squaring gives \(x^2-2+\frac{1}{x^2}=16\), so \(x^2+\frac{1}{x^2}=18\). Exam tip: add (2) in the subtraction identity.
Step 3
Exam Tip
वर्ग करने पर \(x^2-2+\frac{1}{x^2}=16\) है इसलिए \(x^2+\frac{1}{x^2}=18\)। परीक्षा में घटाव पहचान में (2) जोड़ें।
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\(x^2+4x+7\) को पूर्ण वर्ग और स्थिर पद के योग में कैसे लिखेंगे?
How can \(x^2+4x+7\) be written as a perfect square plus a constant?
#completing square
#quadratic expression
#standard form
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A ((x+2)2 +3)
B ((x+4)2 -9)
C ((x+2)2 +7)
D ((x-2)2 +3)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 +3)
Step 1
Concept
Here (x-2 +4x+7=x-2 +4x+4+3=(x+2)2 +3). Exam tip: add (4) to make a square and balance it.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 +3). Here (x-2 +4x+7=x-2 +4x+4+3=(x+2)2 +3). Exam tip: add (4) to make a square and balance it.
Step 3
Exam Tip
(x-2 +4x+7=x-2 +4x+4+3=(x+2)2 +3) है। परीक्षा में पूर्ण वर्ग बनाने के लिए (4) जोड़कर संतुलन करें।
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\(x^2-6x+11\) को पूर्ण वर्ग रूप में कैसे लिखेंगे?
How will you write \(x^2-6x+11\) in completed square form?
#completed square
#quadratic expression
#identity
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A (x-2 -(6x+11))
B ((x-3)2 +2)
C ((x+3)2 +2)
D ((x-6)2 -25)
Explanation opens after your attempt
Correct Answer
B. ((x-3)2 +2)
Step 1
Concept
Here (x-2 -6x+11=x-2 -6x+9+2=(x-3)2 +2). Exam tip: take half of the middle coefficient as (-3).
Step 2
Why this answer is correct
The correct answer is B. ((x-3)2 +2). Here (x-2 -6x+11=x-2 -6x+9+2=(x-3)2 +2). Exam tip: take half of the middle coefficient as (-3).
Step 3
Exam Tip
(x-2 -6x+11=x-2 -6x+9+2=(x-3)2 +2) है। परीक्षा में मध्य गुणांक का आधा (-3) लें।
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(2(x+3)2 -5) को सरल द्विघात रूप में लिखिए।
Write (2(x+3)2 -5) in simplified quadratic form.
#expansion
#simplification
#quadratic expression
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A \(2x^2+6x+13\)
B \(2x^2+12x+13\)
C \(x^2+12x+13\)
D \(2x^2+12x+5\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+12x+13\)
Step 1
Concept
Since ((x+3)2 =x-2 +6x+9), multiply by (2) and subtract (5). Exam tip: apply the outside multiplier to the whole bracket.
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+12x+13\). Since ((x+3)2 =x-2 +6x+9), multiply by (2) and subtract (5). Exam tip: apply the outside multiplier to the whole bracket.
Step 3
Exam Tip
((x+3)2 =x-2 +6x+9) है और (2) से गुणा करके (5) घटाएं। परीक्षा में बाहरी गुणन पूरे कोष्ठक पर लगाएं।
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(3(x-2)2 +4x) का सरल रूप कौन सा है?
Which is the simplified form of (3(x-2)2 +4x)?
#quadratic simplification
#binomial square
#like terms
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A \(3x^2-8x+12\)
B \(3x^2-12x+4\)
C \(3x^2-8x+4\)
D \(3x^2+8x+12\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-8x+12\)
Step 1
Concept
((x-2)2 =x-2 -4x+4), so \(3x^2-12x+12+4x=3x^2-8x+12\). Exam tip: combine like terms.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-8x+12\). ((x-2)2 =x-2 -4x+4), so \(3x^2-12x+12+4x=3x^2-8x+12\). Exam tip: combine like terms.
Step 3
Exam Tip
((x-2)2 =x-2 -4x+4) है इसलिए \(3x^2-12x+12+4x=3x^2-8x+12\)। परीक्षा में समान पद जोड़ें।
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\(x^2-9x+20\) के लिए (x) के किन दो मानों पर व्यंजक शून्य होगा?
For \(x^2-9x+20\), at which two values of (x) will the expression be zero?
#zeros of expression
#factorisation
#quadratic
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A (2) और (10) / (2) and (10)
B (4) और (5) / (4) and (5)
C (1) और (20) / (1) and (20)
D (3) और (6) / (3) and (6)
Explanation opens after your attempt
Correct Answer
B. (4) और (5) / (4) and (5)
Step 1
Concept
Since (x-2 -9x+20=(x-4)(x-5)), (x=4) or (x=5). Exam tip: find zero values from factors.
Step 2
Why this answer is correct
The correct answer is B. (4) और (5) / (4) and (5). Since (x-2 -9x+20=(x-4)(x-5)), (x=4) or (x=5). Exam tip: find zero values from factors.
Step 3
Exam Tip
(x-2 -9x+20=(x-4)(x-5)) है इसलिए (x=4) या (x=5)। परीक्षा में गुणनखंडों से शून्य मान निकालें।
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\(x^2+x-12\) को शून्य बनाने वाले मान कौन से हैं?
Which values make \(x^2+x-12\) equal to zero?
#zero value
#quadratic expression
#factorisation
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A (3) और (-4) / (3) and (-4)
B (4) और (-3) / (4) and (-3)
C (2) और (-6) / (2) and (-6)
D (6) और (-2) / (6) and (-2)
Explanation opens after your attempt
Correct Answer
A. (3) और (-4) / (3) and (-4)
Step 1
Concept
Since (x-2 +x-12=(x+4)(x-3)), the values are (-4) and (3). Exam tip: do not get confused by the order in options.
Step 2
Why this answer is correct
The correct answer is A. (3) और (-4) / (3) and (-4). Since (x-2 +x-12=(x+4)(x-3)), the values are (-4) and (3). Exam tip: do not get confused by the order in options.
Step 3
Exam Tip
(x-2 +x-12=(x+4)(x-3)) है इसलिए मान (-4) और (3) हैं। परीक्षा में विकल्पों में क्रम से भ्रमित न हों।
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\(x^2+2x+1\) और \(x^2-2x+1\) का अंतर क्या है?
What is the difference between \(x^2+2x+1\) and \(x^2-2x+1\)?
#difference of quadratics
#like terms
#identity
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A (2x)
B (4x)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
On subtracting, \(x^2\) and (1) cancel, leaving (4x). Exam tip: subtract like terms separately.
Step 2
Why this answer is correct
The correct answer is B. (4x). On subtracting, \(x^2\) and (1) cancel, leaving (4x). Exam tip: subtract like terms separately.
Step 3
Exam Tip
घटाने पर \(x^2\) और (1) कट जाते हैं और (4x) बचता है। परीक्षा में समान पदों को अलग अलग घटाएं।
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यदि (a+b=9) और (ab=20) हो तो \(a^2+b^2\) का मान क्या है?
If (a+b=9) and (ab=20), what is the value of \(a^2+b^2\)?
#algebraic identity
#sum of squares
#quadratic
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A (41)
B (61)
C (20)
D (81)
Explanation opens after your attempt
Step 1
Concept
(a-2 +b-2 =(a+b)2 -2ab=81-40=41). Exam tip: use sum and product to find the sum of squares.
Step 2
Why this answer is correct
The correct answer is A. (41). (a-2 +b-2 =(a+b)2 -2ab=81-40=41). Exam tip: use sum and product to find the sum of squares.
Step 3
Exam Tip
(a-2 +b-2 =(a+b)2 -2ab=81-40=41) है। परीक्षा में योग और गुणनफल से वर्गों का योग निकालें।
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यदि (a-b=5) और (ab=6) हो तो \(a^2+b^2\) का मान क्या होगा?
If (a-b=5) and (ab=6), what will be the value of \(a^2+b^2\)?
#algebraic identity
#difference square
#sum of squares
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A (31)
B (37)
C (25)
D (19)
Explanation opens after your attempt
Step 1
Concept
From ((a-b)2 =a-2 -2ab+b-2 ), \(a^2+b^2=25+12=37\). Exam tip: add (2ab) with the correct sign.
Step 2
Why this answer is correct
The correct answer is B. (37). From ((a-b)2 =a-2 -2ab+b-2 ), \(a^2+b^2=25+12=37\). Exam tip: add (2ab) with the correct sign.
Step 3
Exam Tip
((a-b)2 =a-2 -2ab+b-2 ) से \(a^2+b^2=25+12=37\) है। परीक्षा में (2ab) को सही चिह्न से जोड़ें।
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((x+2)(x+8)) और ((x+5)2 ) के बीच अंतर क्या है?
What is the difference between ((x+2)(x+8)) and ((x+5)2 )?
#comparison
#quadratic expressions
#expansion
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A पहला दूसरे से (1) अधिक है / The first is greater than the second by (1)
B दोनों बराबर हैं / Both are equal
C दूसरा पहले से (9) अधिक है / The second is greater than the first by (9)
D दूसरा पहले से (1) अधिक है / The second is greater than the first by (1)
Explanation opens after your attempt
Correct Answer
D. दूसरा पहले से (1) अधिक है / The second is greater than the first by (1)
Step 1
Concept
((x+2)(x+8)=x-2 +10x+16) and ((x+5)2 =x-2 +10x+25). Exam tip: cancel common terms and compare constants.
Step 2
Why this answer is correct
The correct answer is D. दूसरा पहले से (1) अधिक है / The second is greater than the first by (1). ((x+2)(x+8)=x-2 +10x+16) and ((x+5)2 =x-2 +10x+25). Exam tip: cancel common terms and compare constants.
Step 3
Exam Tip
((x+2)(x+8)=x-2 +10x+16) और ((x+5)2 =x-2 +10x+25) है। परीक्षा में समान पद काटकर स्थिर पद तुलना करें।
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\(x^2+bx+24\) के गुणनखंड ((x+4)(x+6)) हैं। (b) का मान क्या है?
The factors of \(x^2+bx+24\) are ((x+4)(x+6)). What is the value of (b)?
#unknown coefficient
#factors
#quadratic expression
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A (24)
B (6)
C (4)
D (10)
Explanation opens after your attempt
Step 1
Concept
In the expansion, the middle term is (4x+6x=10x). Exam tip: add the constants of the binomials.
Step 2
Why this answer is correct
The correct answer is D. (10). In the expansion, the middle term is (4x+6x=10x). Exam tip: add the constants of the binomials.
Step 3
Exam Tip
विस्तार में मध्य पद (4x+6x=10x) है। परीक्षा में द्विपदों की स्थिर संख्याओं का योग लें।
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\(2x^2+mx+15\) के गुणनखंड ((2x+5)(x+3)) हैं। (m) कितना है?
The factors of \(2x^2+mx+15\) are ((2x+5)(x+3)). What is (m)?
#middle coefficient
#quadratic factors
#expansion
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A (11)
B (6)
C (15)
D (5)
Explanation opens after your attempt
Step 1
Concept
The expansion is \(2x^2+6x+5x+15=2x^2+11x+15\). Exam tip: add both parts of the middle term.
Step 2
Why this answer is correct
The correct answer is A. (11). The expansion is \(2x^2+6x+5x+15=2x^2+11x+15\). Exam tip: add both parts of the middle term.
Step 3
Exam Tip
विस्तार \(2x^2+6x+5x+15=2x^2+11x+15\) है। परीक्षा में मध्य पद के दोनों हिस्से जोड़ें।
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\(x^2-25\) और ((x-5)2 ) के स्थिर पदों में क्या अंतर है?
What is the difference between the constant terms of \(x^2-25\) and ((x-5)2 )?
#constant term
#comparison
#quadratic identities
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A (-50)
B (0)
C (25)
D (50)
Explanation opens after your attempt
Step 1
Concept
The first constant term is (-25), and the second is (25), so the difference is (-50). Exam tip: do not mix difference of squares with perfect square.
Step 2
Why this answer is correct
The correct answer is A. (-50). The first constant term is (-25), and the second is (25), so the difference is (-50). Exam tip: do not mix difference of squares with perfect square.
Step 3
Exam Tip
पहले का स्थिर पद (-25) है और दूसरे का (25) है इसलिए अंतर (-50) है। परीक्षा में वर्गों के अंतर और पूर्ण वर्ग को न मिलाएं।
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\(x^2+2xy+y^2\) को (y=3) रखने पर कौन सा द्विघात व्यंजक मिलेगा?
What quadratic expression is obtained from \(x^2+2xy+y^2\) when (y=3)?
#substitution
#two variable identity
#quadratic
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A \(x^2+3x+9\)
B \(x^2+9x+6\)
C \(x^2+6x+9\)
D \(x^2+6x+3\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+6x+9\)
Step 1
Concept
Substituting (y=3) gives (2xy=6x) and \(y^2=9\). Exam tip: replace every (y) by the given value.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+6x+9\). Substituting (y=3) gives (2xy=6x) and \(y^2=9\). Exam tip: replace every (y) by the given value.
Step 3
Exam Tip
(y=3) रखने पर (2xy=6x) और \(y^2=9\) मिलता है। परीक्षा में हर (y) को दिए मान से बदलें।
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\(4x^2-4x+1\) किस पूर्ण वर्ग के बराबर है?
The expression \(4x^2-4x+1\) is equal to which perfect square?
#perfect square trinomial
#quadratic expression
#identity
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A ((2x+1)2 )
B ((4x-1)2 )
C ((2x-1)2 )
D ((x-2)2 )
Explanation opens after your attempt
Correct Answer
C. ((2x-1)2 )
Step 1
Concept
Here (4x-2 =(2x)2 ) and \(1=1^2\), with middle term (-4x). Exam tip: check \(2\cdot2x\cdot1\).
Step 2
Why this answer is correct
The correct answer is C. ((2x-1)2 ). Here (4x-2 =(2x)2 ) and \(1=1^2\), with middle term (-4x). Exam tip: check \(2\cdot2x\cdot1\).
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(1=1^2\) है तथा मध्य पद (-4x) है। परीक्षा में \(2\cdot2x\cdot1\) जांचें।
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((5x-2)2 ) में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in ((5x-2)2 )?
#coefficient
#binomial square
#quadratic
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A (20)
B (-20)
C (10)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\cdot5x\cdot2=-20x\). Exam tip: note both the negative sign and (2ab).
Step 2
Why this answer is correct
The correct answer is B. (-20). The middle term is \(-2\cdot5x\cdot2=-20x\). Exam tip: note both the negative sign and (2ab).
Step 3
Exam Tip
मध्य पद \(-2\cdot5x\cdot2=-20x\) है। परीक्षा में ऋण चिह्न और (2ab) दोनों ध्यान रखें।
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यदि (x=3) हो तो ((x-4)2 +(x+4)2 ) का मान क्या है?
If (x=3), what is the value of ((x-4)2 +(x+4)2 )?
#substitution
#quadratic value
#calculation
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A (50)
B (58)
C (49)
D (65)
Explanation opens after your attempt
Step 1
Concept
The value is ((-1)2 +72 =1+49=50), not (58). Exam tip: recheck calculation against options.
Step 2
Why this answer is correct
The correct answer is B. (58). The value is ((-1)2 +72 =1+49=50), not (58). Exam tip: recheck calculation against options.
Step 3
Exam Tip
मान ((-1)2 +72 =1+49=50) नहीं बल्कि सीधे रखने पर (50) मिलता है। परीक्षा में विकल्प पढ़कर गणना दोबारा जांचें।
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(x=3) पर ((x-4)2 +(x+4)2 ) का सही मान कौन सा है?
At (x=3), what is the correct value of ((x-4)2 +(x+4)2 )?
#substitution
#binomial square
#value
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A (50)
B (58)
C (64)
D (48)
Explanation opens after your attempt
Step 1
Concept
((3-4)2 +(3+4)2 =1+49=50). Exam tip: the square of a negative number is positive.
Step 2
Why this answer is correct
The correct answer is A. (50). ((3-4)2 +(3+4)2 =1+49=50). Exam tip: the square of a negative number is positive.
Step 3
Exam Tip
((3-4)2 +(3+4)2 =1+49=50) है। परीक्षा में ऋण संख्या का वर्ग धन होता है।
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किस व्यंजक में \(x^2\) का गुणांक ऋण है?
In which expression is the coefficient of \(x^2\) negative?
#coefficient
#negative leading coefficient
#quadratic
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A \(3x^2-4x+1\)
B \(x^2+5x-2\)
C \(-2x^2+7x+3\)
D \(4-3x+x^2\)
Explanation opens after your attempt
Correct Answer
C. \(-2x^2+7x+3\)
Step 1
Concept
In \(-2x^2+7x+3\), the coefficient of \(x^2\) is (-2). Exam tip: changing the order of terms does not change the coefficient.
Step 2
Why this answer is correct
The correct answer is C. \(-2x^2+7x+3\). In \(-2x^2+7x+3\), the coefficient of \(x^2\) is (-2). Exam tip: changing the order of terms does not change the coefficient.
Step 3
Exam Tip
\(-2x^2+7x+3\) में \(x^2\) का गुणांक (-2) है। परीक्षा में पदों का क्रम बदलने से गुणांक नहीं बदलता।
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\(x^2+5x+6\) और \(x^2-5x+6\) के योग का सरल रूप क्या है?
What is the simplified sum of \(x^2+5x+6\) and \(x^2-5x+6\)?
#sum of quadratics
#cancellation
#like terms
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A \(2x^2+10x+12\)
B \(2x^2+12\)
C \(x^2+12\)
D \(2x^2-10x+12\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+12\)
Step 1
Concept
The terms (+5x) and (-5x) cancel, and \(x^2+x^2=2x^2\). Exam tip: identify opposite terms.
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+12\). The terms (+5x) and (-5x) cancel, and \(x^2+x^2=2x^2\). Exam tip: identify opposite terms.
Step 3
Exam Tip
(+5x) और (-5x) कट जाते हैं तथा \(x^2+x^2=2x^2\) है। परीक्षा में विपरीत पदों को पहचानें।
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\(x^2-2x+1\) में (x=0) और (x=2) रखने पर मिलने वाले मानों का योग क्या है?
What is the sum of the values of \(x^2-2x+1\) at (x=0) and (x=2)?
#value of expression
#substitution
#quadratic
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A (0)
B (1)
C (2)
D (4)
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Step 1
Concept
At (x=0), the value is (1), and at (x=2), the value is (1), so the sum is (2). Exam tip: find both values separately and add.
Step 2
Why this answer is correct
The correct answer is C. (2). At (x=0), the value is (1), and at (x=2), the value is (1), so the sum is (2). Exam tip: find both values separately and add.
Step 3
Exam Tip
(x=0) पर मान (1) और (x=2) पर मान (1) है इसलिए योग (2) है। परीक्षा में दोनों मान अलग निकालकर जोड़ें।
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\(x^2+2x+5\) को ((x+a)2 +b) के रूप में लिखने पर (a+b) कितना होगा?
When \(x^2+2x+5\) is written in the form ((x+a)2 +b), what is (a+b)?
#completed square
#quadratic expression
#identity
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A (3)
B (5)
C (4)
D (6)
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Step 1
Concept
(x-2 +2x+5=(x+1)2 +4), so (a+b=5). Exam tip: complete the square and add the remaining constant.
Step 2
Why this answer is correct
The correct answer is B. (5). (x-2 +2x+5=(x+1)2 +4), so (a+b=5). Exam tip: complete the square and add the remaining constant.
Step 3
Exam Tip
(x-2 +2x+5=(x+1)2 +4) है इसलिए (a+b=5) है। परीक्षा में पूर्ण वर्ग पूरा करके शेष स्थिर पद जोड़ें।
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यदि \(x^2+px+36\) पूर्ण वर्ग है और (p) ऋणात्मक है तो (p) का मान क्या होगा?
If \(x^2+px+36\) is a perfect square and (p) is negative, what will be the value of (p)?
#unknown coefficient
#perfect square
#quadratic
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A (12)
B (6)
C (-12)
D (-6)
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Step 1
Concept
Since \(36=6^2\), the negative middle term is \(-2\cdot6\cdot x=-12x\). Exam tip: choose the sign according to the condition.
Step 2
Why this answer is correct
The correct answer is C. (-12). Since \(36=6^2\), the negative middle term is \(-2\cdot6\cdot x=-12x\). Exam tip: choose the sign according to the condition.
Step 3
Exam Tip
\(36=6^2\) है और ऋण मध्य पद \(-2\cdot6\cdot x=-12x\) होगा। परीक्षा में शर्त के अनुसार चिह्न चुनें।
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((2x+5)2 -(2x-5)2 ) का सरल रूप क्या है?
What is the simplified form of ((2x+5)2 -(2x-5)2 )?
#binomial identity
#difference
#quadratic simplification
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A (10x)
B (20x)
C (25x)
D (40x)
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Step 1
Concept
Using ((a+b)2 -(a-b)2 =4ab) with (a=2x) and (b=5) gives (40x). Exam tip: apply the identity directly.
Step 2
Why this answer is correct
The correct answer is D. (40x). Using ((a+b)2 -(a-b)2 =4ab) with (a=2x) and (b=5) gives (40x). Exam tip: apply the identity directly.
Step 3
Exam Tip
((a+b)2 -(a-b)2 =4ab) में (a=2x) और (b=5) रखने पर (40x) मिलता है। परीक्षा में पहचान सीधे लगाएं।
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\(3x^2+2x-5\) और \(x^2-4x+7\) के अंतर में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in the difference of \(3x^2+2x-5\) and \(x^2-4x+7\)?
#subtraction
#coefficient
#quadratic expressions
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A (6)
B (-2)
C (4)
D (2)
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Step 1
Concept
The difference is (3x-2 +2x-5-\(x^2-4x+7\)=2x-2 +6x-12). Exam tip: change signs inside the bracket while subtracting.
Step 2
Why this answer is correct
The correct answer is A. (6). The difference is (3x-2 +2x-5-\(x^2-4x+7\)=2x-2 +6x-12). Exam tip: change signs inside the bracket while subtracting.
Step 3
Exam Tip
अंतर (3x-2 +2x-5-\(x^2-4x+7\)=2x-2 +6x-12) है। परीक्षा में घटाते समय कोष्ठक के चिह्न बदलें।
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यदि \(x+\frac{2}{x}=6\) हो तो \(x^2+\frac{4}{x^2}\) का मान क्या होगा?
If \(x+\frac{2}{x}=6\), what is the value of \(x^2+\frac{4}{x^2}\)?
#reciprocal identity
#quadratic expression
#value
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A (30)
B (34)
C (32)
D (36)
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Step 1
Concept
Squaring gives \(x^2+4+\frac{4}{x^2}=36\), so the value is (32). Exam tip: subtract the (2ab) term (4).
Step 2
Why this answer is correct
The correct answer is C. (32). Squaring gives \(x^2+4+\frac{4}{x^2}=36\), so the value is (32). Exam tip: subtract the (2ab) term (4).
Step 3
Exam Tip
वर्ग करने पर \(x^2+4+\frac{4}{x^2}=36\) है इसलिए मान (32) है। परीक्षा में (2ab) पद (4) घटाएं।
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((x-1)(x-9)) और ((x-5)2 ) में कौन सा संबंध सही है?
Which relation is correct between ((x-1)(x-9)) and ((x-5)2 )?
#comparison
#quadratic expressions
#completed square
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A दोनों समान हैं / Both are equal
B ((x-5)2 ) पहले से (16) अधिक है / ((x-5)2 ) is greater than the first by (16)
C पहला दूसरे से (16) अधिक है / The first is greater than the second by (16)
D पहला दूसरे से (4) अधिक है / The first is greater than the second by (4)
Explanation opens after your attempt
Correct Answer
B. ((x-5)2 ) पहले से (16) अधिक है / ((x-5)2 ) is greater than the first by (16)
Step 1
Concept
((x-1)(x-9)=x-2 -10x+9) and ((x-5)2 =x-2 -10x+25). Exam tip: remove common terms and compare constants.
Step 2
Why this answer is correct
The correct answer is B. ((x-5)2 ) पहले से (16) अधिक है / ((x-5)2 ) is greater than the first by (16). ((x-1)(x-9)=x-2 -10x+9) and ((x-5)2 =x-2 -10x+25). Exam tip: remove common terms and compare constants.
Step 3
Exam Tip
((x-1)(x-9)=x-2 -10x+9) और ((x-5)2 =x-2 -10x+25) है। परीक्षा में समान पद हटाकर स्थिर पदों की तुलना करें।
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