कौन सा व्यंजक द्विघात व्यंजक है?
Which expression is a quadratic expression?
#quadratic expression
#degree
#identification
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A (9)
B (5x+7)
C \(4x^3+x\)
D \(3x^2+2x+1\)
Explanation opens after your attempt
Correct Answer
D. \(3x^2+2x+1\)
Step 1
Concept
A quadratic expression has highest power (2). Exam tip: first check the highest power.
Step 2
Why this answer is correct
The correct answer is D. \(3x^2+2x+1\). A quadratic expression has highest power (2). Exam tip: first check the highest power.
Step 3
Exam Tip
द्विघात व्यंजक में सबसे बड़ी घात (2) होती है। परीक्षा में पहले उच्चतम घात देखें।
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\(2x^2-5x+8\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(2x^2-5x+8\)?
#coefficient
#quadratic term
#basics
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A (8)
B (-5)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
The number attached to \(x^2\) is (2). Exam tip: identify the coefficient with its term.
Step 2
Why this answer is correct
The correct answer is C. (2). The number attached to \(x^2\) is (2). Exam tip: identify the coefficient with its term.
Step 3
Exam Tip
\(x^2\) के साथ लगी संख्या (2) है। परीक्षा में गुणांक को उसके पद के साथ पहचानें।
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\(x^2+7x+12\) में स्थिर पद कौन सा है?
What is the constant term in \(x^2+7x+12\)?
#constant term
#quadratic expression
#term identification
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A \(x^2\)
B (7x)
C (12)
D (7)
Explanation opens after your attempt
Step 1
Concept
The term without a variable is the constant term. Here the constant term is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). The term without a variable is the constant term. Here the constant term is (12).
Step 3
Exam Tip
जिस पद में चर नहीं होता वह स्थिर पद होता है। यहां स्थिर पद (12) है।
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\(4x^2-3x+6\) का मान (x=2) पर कितना होगा?
What is the value of \(4x^2-3x+6\) at (x=2)?
#evaluation
#quadratic value
#substitution
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A (12)
B (20)
C (18)
D (16)
Explanation opens after your attempt
Step 1
Concept
(4(2)2 -3(2)+6=16). Exam tip: calculate the square first.
Step 2
Why this answer is correct
The correct answer is D. (16). (4(2)2 -3(2)+6=16). Exam tip: calculate the square first.
Step 3
Exam Tip
(4(2)2 -3(2)+6=16) होता है। परीक्षा में पहले वर्ग का मान निकालें।
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\(x^2+4x+4\) किस रूप में लिखा जा सकता है?
How can \(x^2+4x+4\) be written?
#perfect square
#quadratic expression
#identity
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A (x(x+4))
B ((x-2)2 )
C ((x+4)2 )
D ((x+2)2 )
Explanation opens after your attempt
Correct Answer
D. ((x+2)2 )
Step 1
Concept
\(4=2^2\) and \(4x=2\cdot2x\). So it is ((x+2)2 ).
Step 2
Why this answer is correct
The correct answer is D. ((x+2)2 ). \(4=2^2\) and \(4x=2\cdot2x\). So it is ((x+2)2 ).
Step 3
Exam Tip
\(4=2^2\) और \(4x=2\cdot2x\) है। इसलिए यह ((x+2)2 ) है।
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\(x^2-6x+9\) का पूर्ण वर्ग रूप कौन सा है?
What is the perfect square form of \(x^2-6x+9\)?
#perfect square
#negative middle term
#quadratic
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A ((x+3)2 )
B ((x-3)2 )
C ((x-6)2 )
D \(x^2-9\)
Explanation opens after your attempt
Correct Answer
B. ((x-3)2 )
Step 1
Concept
\(9=3^2\) and the middle term is (-6x). So the form is ((x-3)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((x-3)2 ). \(9=3^2\) and the middle term is (-6x). So the form is ((x-3)2 ).
Step 3
Exam Tip
\(9=3^2\) और मध्य पद (-6x) है। इसलिए रूप ((x-3)2 ) होगा।
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((x+5)2 ) को फैलाने पर कौन सा द्विघात व्यंजक मिलेगा?
Which quadratic expression is obtained by expanding ((x+5)2 )?
#expansion
#binomial square
#quadratic expression
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A \(x^2+5x+25\)
B \(x^2-10x+25\)
C \(x^2+25x+10\)
D \(x^2+10x+25\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+10x+25\)
Step 1
Concept
Using ((a+b)2 =a-2 +2ab+b-2 ), we get \(x^2+10x+25\). Exam tip: the middle term is doubled.
Step 2
Why this answer is correct
The correct answer is D. \(x^2+10x+25\). Using ((a+b)2 =a-2 +2ab+b-2 ), we get \(x^2+10x+25\). Exam tip: the middle term is doubled.
Step 3
Exam Tip
((a+b)2 =a-2 +2ab+b-2 ) से \(x^2+10x+25\) मिलता है। परीक्षा में मध्य पद दुगुना होता है।
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((x-4)2 ) का विस्तार क्या है?
What is the expansion of ((x-4)2 )?
#minus square
#expansion
#quadratic
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A \(x^2-4x+16\)
B \(x^2+8x+16\)
C \(x^2-8x+16\)
D \(x^2-16\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-8x+16\)
Step 1
Concept
((x-4)2 =x-2 -2\cdot x\cdot4+16). So \(x^2-8x+16\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-8x+16\). ((x-4)2 =x-2 -2\cdot x\cdot4+16). So \(x^2-8x+16\) is correct.
Step 3
Exam Tip
((x-4)2 =x-2 -2\cdot x\cdot4+16) है। इसलिए \(x^2-8x+16\) सही है।
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((x+3)(x+2)) का विस्तार कौन सा है?
Which is the expansion of ((x+3)(x+2))?
#product expansion
#quadratic expression
#algebra
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A \(x^2+3x+2\)
B \(x^2+6x+5\)
C \(x^2+5x+6\)
D \(x^2+2x+6\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+5x+6\)
Step 1
Concept
Multiplying gives \(x^2+2x+3x+6=x^2+5x+6\). Exam tip: combine like terms.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+5x+6\). Multiplying gives \(x^2+2x+3x+6=x^2+5x+6\). Exam tip: combine like terms.
Step 3
Exam Tip
गुणा करने पर \(x^2+2x+3x+6=x^2+5x+6\) मिलता है। परीक्षा में समान पद जोड़ें।
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\(x^2+9x+20\) के लिए ऐसे दो संख्याएं कौन सी हैं जिनका योग (9) और गुणन (20) है?
For \(x^2+9x+20\), which two numbers have sum (9) and product (20)?
#sum product
#quadratic factorisation
#medium
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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
(4+5=9) and \(4\cdot5=20\). Exam tip: match both middle and constant terms.
Step 2
Why this answer is correct
The correct answer is B. (4) और (5) / (4) and (5). (4+5=9) and \(4\cdot5=20\). Exam tip: match both middle and constant terms.
Step 3
Exam Tip
(4+5=9) और \(4\cdot5=20\) है। परीक्षा में मध्य पद और स्थिर पद दोनों मिलाएं।
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\(x^2-5x+6\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2-5x+6\)?
#negative middle
#factorisation
#quadratic
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A ((x+2)(x+3))
B ((x-1)(x-6))
C ((x-2)(x-3))
D ((x+1)(x+6))
Explanation opens after your attempt
Correct Answer
C. ((x-2)(x-3))
Step 1
Concept
(-2+(-3)=-5) and ((-2)(-3)=6). Exam tip: for a positive constant term, check same signs.
Step 2
Why this answer is correct
The correct answer is C. ((x-2)(x-3)). (-2+(-3)=-5) and ((-2)(-3)=6). Exam tip: for a positive constant term, check same signs.
Step 3
Exam Tip
(-2+(-3)=-5) और ((-2)(-3)=6) है। परीक्षा में धन स्थिर पद के लिए समान चिह्न देखें।
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\(x^2+x-12\) का सही गुणनखंडन कौन सा है?
Which is the correct factorisation of \(x^2+x-12\)?
#quadratic factorisation
#negative constant
#signs
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A ((x-6)(x+2))
B ((x-4)(x+3))
C ((x+6)(x-2))
D ((x+4)(x-3))
Explanation opens after your attempt
Correct Answer
D. ((x+4)(x-3))
Step 1
Concept
(4+(-3)=1) and (4\cdot(-3)=-12). Exam tip: check factors with opposite signs.
Step 2
Why this answer is correct
The correct answer is D. ((x+4)(x-3)). (4+(-3)=1) and (4\cdot(-3)=-12). Exam tip: check factors with opposite signs.
Step 3
Exam Tip
(4+(-3)=1) और (4\cdot(-3)=-12) है। परीक्षा में विपरीत चिह्न वाले कारक जांचें।
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\(2x^2+7x+3\) में मध्य पद तोड़ने के लिए कौन सा विभाजन सही है?
Which split of the middle term is correct for \(2x^2+7x+3\)?
#split middle term
#quadratic
#factorisation
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A \(2x^2+7x+6+3\)
B \(2x^2+5x+2x+3\)
C \(2x^2+4x+3x+3\)
D \(2x^2+6x+x+3\)
Explanation opens after your attempt
Correct Answer
D. \(2x^2+6x+x+3\)
Step 1
Concept
(6x+x=7x) and \(6\cdot1=6\), equal to \(2\cdot3\). Exam tip: match the product with (ac).
Step 2
Why this answer is correct
The correct answer is D. \(2x^2+6x+x+3\). (6x+x=7x) and \(6\cdot1=6\), equal to \(2\cdot3\). Exam tip: match the product with (ac).
Step 3
Exam Tip
(6x+x=7x) और \(6\cdot1=6\), जो \(2\cdot3\) के बराबर है। परीक्षा में गुणन (ac) से मिलाएं।
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\(2x^2+7x+3\) का गुणनखंडन क्या है?
What is the factorisation of \(2x^2+7x+3\)?
#quadratic factorisation
#coefficient
#medium
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A ((x+1)(x+3))
B ((2x+3)(x+1))
C ((2x+7)(x+3))
D ((2x+1)(x+3))
Explanation opens after your attempt
Correct Answer
D. ((2x+1)(x+3))
Step 1
Concept
((2x+1)(x+3)=2x-2 +6x+x+3). Thus the middle term is (7x).
Step 2
Why this answer is correct
The correct answer is D. ((2x+1)(x+3)). ((2x+1)(x+3)=2x-2 +6x+x+3). Thus the middle term is (7x).
Step 3
Exam Tip
((2x+1)(x+3)=2x-2 +6x+x+3) है। इसलिए मध्य पद (7x) बनता है।
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\(3x^2+10x+8\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(3x^2+10x+8\).
#quadratic factors
#product checking
#medium
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A ((3x+2)(x+4))
B ((3x+4)(x+2))
C ((x+4)(x+6))
D ((3x+8)(x+1))
Explanation opens after your attempt
Correct Answer
B. ((3x+4)(x+2))
Step 1
Concept
((3x+4)(x+2)=3x-2 +6x+4x+8). The middle term (10x) is correct.
Step 2
Why this answer is correct
The correct answer is B. ((3x+4)(x+2)). ((3x+4)(x+2)=3x-2 +6x+4x+8). The middle term (10x) is correct.
Step 3
Exam Tip
((3x+4)(x+2)=3x-2 +6x+4x+8) है। मध्य पद (10x) सही है।
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\(4x^2-9\) किस प्रकार का द्विघात व्यंजक है?
What type of quadratic expression is \(4x^2-9\)?
#difference of squares
#quadratic expression
#classification
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A पूर्ण वर्ग त्रिपद / Perfect square trinomial
B वर्गों का अंतर / Difference of squares
C रेखीय व्यंजक / Linear expression
D घन व्यंजक / Cubic expression
Explanation opens after your attempt
Correct Answer
B. वर्गों का अंतर / Difference of squares
Step 1
Concept
(4x-2 =(2x)2 ) and \(9=3^2\). So it is a difference of squares.
Step 2
Why this answer is correct
The correct answer is B. वर्गों का अंतर / Difference of squares. (4x-2 =(2x)2 ) and \(9=3^2\). So it is a difference of squares.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(9=3^2\) है। इसलिए यह वर्गों का अंतर है।
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\(9x^2-24x+16\) का गुणनखंड रूप क्या है?
What is the factor form of \(9x^2-24x+16\)?
#perfect square trinomial
#quadratic factor
#coefficient
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A ((3x+4)2 )
B ((9x-4)2 )
C ((3x-4)2 )
D ((3x-8)2 )
Explanation opens after your attempt
Correct Answer
C. ((3x-4)2 )
Step 1
Concept
(9x-2 =(3x)2 ), \(16=4^2\), and the middle term is (-24x). So ((3x-4)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is C. ((3x-4)2 ). (9x-2 =(3x)2 ), \(16=4^2\), and the middle term is (-24x). So ((3x-4)2 ) is correct.
Step 3
Exam Tip
(9x-2 =(3x)2 ), \(16=4^2\), और मध्य पद (-24x) है। इसलिए ((3x-4)2 ) सही है।
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\(x^2+2xy+y^2\) में चर कौन से हैं?
Which variables are present in \(x^2+2xy+y^2\)?
#variables
#quadratic expression
#two variables
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A केवल (y) / Only (y)
B केवल (x) / Only (x)
C (2) और (1) / (2) and (1)
D (x) और (y) / (x) and (y)
Explanation opens after your attempt
Correct Answer
D. (x) और (y) / (x) and (y)
Step 1
Concept
Both (x) and (y) are present in the expression. Exam tip: distinguish variables and coefficients.
Step 2
Why this answer is correct
The correct answer is D. (x) और (y) / (x) and (y). Both (x) and (y) are present in the expression. Exam tip: distinguish variables and coefficients.
Step 3
Exam Tip
व्यंजक में (x) और (y) दोनों मौजूद हैं। परीक्षा में चर और गुणांक अलग पहचानें।
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\(a^2+2ab+b^2\) का गुणनखंड रूप क्या है?
What is the factor form of \(a^2+2ab+b^2\)?
#perfect square
#two variables
#identity
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A ((a-b)2 )
B ((a+b)2 )
C ((a+b)(a-b))
D (a(a+2b))
Explanation opens after your attempt
Correct Answer
B. ((a+b)2 )
Step 1
Concept
It is an addition perfect square trinomial. Therefore (a-2 +2ab+b-2 =(a+b)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((a+b)2 ). It is an addition perfect square trinomial. Therefore (a-2 +2ab+b-2 =(a+b)2 ).
Step 3
Exam Tip
यह जोड़ वाला पूर्ण वर्ग त्रिपद है। इसलिए (a-2 +2ab+b-2 =(a+b)2 ) है।
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\(a^2-2ab+b^2\) किसके बराबर है?
What is \(a^2-2ab+b^2\) equal to?
#minus square
#quadratic identity
#factor form
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A ((a+b)2 )
B ((a-b)2 )
C \(a^2-b^2\)
D (2ab)
Explanation opens after your attempt
Correct Answer
B. ((a-b)2 )
Step 1
Concept
The middle term is negative, so it is a subtraction perfect square. The correct form is ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((a-b)2 ). The middle term is negative, so it is a subtraction perfect square. The correct form is ((a-b)2 ).
Step 3
Exam Tip
मध्य पद ऋण है इसलिए यह घटाव वाला पूर्ण वर्ग है। सही रूप ((a-b)2 ) है।
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\(x^2-25\) का गुणनखंड रूप कौन सा है?
Which is the factor form of \(x^2-25\)?
#difference of squares
#factorisation
#quadratic
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A ((x-5)2 )
B ((x+5)2 )
C ((x-5)(x+5))
D ((x-25)(x+25))
Explanation opens after your attempt
Correct Answer
C. ((x-5)(x+5))
Step 1
Concept
\(25=5^2\) and this is a difference of squares. So ((x-5)(x+5)) is obtained.
Step 2
Why this answer is correct
The correct answer is C. ((x-5)(x+5)). \(25=5^2\) and this is a difference of squares. So ((x-5)(x+5)) is obtained.
Step 3
Exam Tip
\(25=5^2\) है और यह वर्गों का अंतर है। इसलिए ((x-5)(x+5)) मिलेगा।
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\(2x^2-5x+3\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(2x^2-5x+3\)?
#quadratic factorisation
#signs
#coefficient
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A ((x-3)(x-2))
B ((2x+3)(x+1))
C ((2x-3)(x-1))
D ((2x-1)(x-3))
Explanation opens after your attempt
Correct Answer
C. ((2x-3)(x-1))
Step 1
Concept
((2x-3)(x-1)=2x-2 -2x-3x+3). The middle term becomes (-5x).
Step 2
Why this answer is correct
The correct answer is C. ((2x-3)(x-1)). ((2x-3)(x-1)=2x-2 -2x-3x+3). The middle term becomes (-5x).
Step 3
Exam Tip
((2x-3)(x-1)=2x-2 -2x-3x+3) है। मध्य पद (-5x) बनता है।
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\(3x^2-x-2\) का गुणनखंडन चुनिए।
Choose the factorisation of \(3x^2-x-2\).
#quadratic factorisation
#negative constant
#checking
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? Hint Small clue
A ((3x-1)(x+2))
B ((3x-2)(x+1))
C ((x-2)(3x+1))
D ((3x+2)(x-1))
Explanation opens after your attempt
Correct Answer
D. ((3x+2)(x-1))
Step 1
Concept
((3x+2)(x-1)=3x-2 -3x+2x-2). This gives \(3x^2-x-2\).
Step 2
Why this answer is correct
The correct answer is D. ((3x+2)(x-1)). ((3x+2)(x-1)=3x-2 -3x+2x-2). This gives \(3x^2-x-2\).
Step 3
Exam Tip
((3x+2)(x-1)=3x-2 -3x+2x-2) है। इससे \(3x^2-x-2\) मिलता है।
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\(x^2+6x+5\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+6x+5\)?
#quadratic factorisation
#sum product
#medium
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? Hint Small clue
A ((x+3)(x+3))
B ((x+2)(x+4))
C ((x-1)(x-5))
D ((x+1)(x+5))
Explanation opens after your attempt
Correct Answer
D. ((x+1)(x+5))
Step 1
Concept
(1+5=6) and \(1\cdot5=5\). Exam tip: add the factors of the last term.
Step 2
Why this answer is correct
The correct answer is D. ((x+1)(x+5)). (1+5=6) and \(1\cdot5=5\). Exam tip: add the factors of the last term.
Step 3
Exam Tip
(1+5=6) और \(1\cdot5=5\) है। परीक्षा में अंतिम पद के कारक जोड़कर देखें।
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\(x^2-7x+10\) का सही गुणनखंड रूप क्या है?
What is the correct factor form of \(x^2-7x+10\)?
#quadratic factorisation
#negative sum
#signs
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A ((x+5)(x+2))
B ((x-5)(x-2))
C ((x-10)(x-1))
D ((x+10)(x+1))
Explanation opens after your attempt
Correct Answer
B. ((x-5)(x-2))
Step 1
Concept
(-5+(-2)=-7) and ((-5)(-2)=10). Therefore both factors are negative.
Step 2
Why this answer is correct
The correct answer is B. ((x-5)(x-2)). (-5+(-2)=-7) and ((-5)(-2)=10). Therefore both factors are negative.
Step 3
Exam Tip
(-5+(-2)=-7) और ((-5)(-2)=10) है। इसलिए दोनों गुणनखंड ऋण होंगे।
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\(x^2-4x-12\) के लिए सही कारक कौन से हैं?
Which are the correct factors for \(x^2-4x-12\)?
#negative constant
#factorisation
#quadratic
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? Hint Small clue
A ((x+4)(x-3))
B ((x+6)(x-2))
C ((x-4)(x+3))
D ((x-6)(x+2))
Explanation opens after your attempt
Correct Answer
D. ((x-6)(x+2))
Step 1
Concept
(-6+2=-4) and \(-6\cdot2=-12\). Exam tip: match the sum of opposite-sign factors.
Step 2
Why this answer is correct
The correct answer is D. ((x-6)(x+2)). (-6+2=-4) and \(-6\cdot2=-12\). Exam tip: match the sum of opposite-sign factors.
Step 3
Exam Tip
(-6+2=-4) और \(-6\cdot2=-12\) है। परीक्षा में विपरीत चिह्न वाले कारकों का योग मिलाएं।
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\(5x^2+13x+6\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(5x^2+13x+6\)?
#quadratic factorisation
#coefficient
#cross terms
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? Hint Small clue
A ((5x+2)(x+3))
B ((5x+6)(x+1))
C ((x+2)(x+3))
D ((5x+3)(x+2))
Explanation opens after your attempt
Correct Answer
D. ((5x+3)(x+2))
Step 1
Concept
((5x+3)(x+2)=5x-2 +10x+3x+6). The middle term (13x) is obtained.
Step 2
Why this answer is correct
The correct answer is D. ((5x+3)(x+2)). ((5x+3)(x+2)=5x-2 +10x+3x+6). The middle term (13x) is obtained.
Step 3
Exam Tip
((5x+3)(x+2)=5x-2 +10x+3x+6) है। मध्य पद (13x) मिलता है।
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\(6x^2+11x+3\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(6x^2+11x+3\).
#quadratic factorisation
#medium
#cross multiplication
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+10 Time+ 10 sec extra
? Hint Small clue
A ((6x+3)(x+1))
B ((3x+1)(2x+3))
C ((6x+1)(x+3))
D ((2x+1)(3x+3))
Explanation opens after your attempt
Correct Answer
B. ((3x+1)(2x+3))
Step 1
Concept
((3x+1)(2x+3)=6x-2 +9x+2x+3). Thus the middle term is (11x).
Step 2
Why this answer is correct
The correct answer is B. ((3x+1)(2x+3)). ((3x+1)(2x+3)=6x-2 +9x+2x+3). Thus the middle term is (11x).
Step 3
Exam Tip
((3x+1)(2x+3)=6x-2 +9x+2x+3) है। इसलिए मध्य पद (11x) बनता है।
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\(x^2+4x-21\) का गुणनखंडन क्या है?
What is the factorisation of \(x^2+4x-21\)?
#quadratic factorisation
#negative constant
#sum product
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? Hint Small clue
A ((x-4)(x+21))
B ((x-7)(x+3))
C ((x+4)(x-21))
D ((x+7)(x-3))
Explanation opens after your attempt
Correct Answer
D. ((x+7)(x-3))
Step 1
Concept
(7+(-3)=4) and (7\cdot(-3)=-21). Exam tip: choose the larger factor with the correct sign.
Step 2
Why this answer is correct
The correct answer is D. ((x+7)(x-3)). (7+(-3)=4) and (7\cdot(-3)=-21). Exam tip: choose the larger factor with the correct sign.
Step 3
Exam Tip
(7+(-3)=4) और (7\cdot(-3)=-21) है। परीक्षा में बड़ा कारक सही चिह्न के साथ लें।
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\(x^2-2x-15\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factor form of \(x^2-2x-15\)?
#quadratic factorisation
#sign selection
#medium
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+10 Time+ 10 sec extra
? Hint Small clue
A ((x+15)(x-1))
B ((x+5)(x-3))
C ((x-15)(x+1))
D ((x-5)(x+3))
Explanation opens after your attempt
Correct Answer
D. ((x-5)(x+3))
Step 1
Concept
(-5+3=-2) and \(-5\cdot3=-15\). So ((x-5)(x+3)) is correct.
Step 2
Why this answer is correct
The correct answer is D. ((x-5)(x+3)). (-5+3=-2) and \(-5\cdot3=-15\). So ((x-5)(x+3)) is correct.
Step 3
Exam Tip
(-5+3=-2) और \(-5\cdot3=-15\) है। इसलिए ((x-5)(x+3)) सही है।
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\(4x^2+4x+1\) किसका वर्ग है?
\(4x^2+4x+1\) is the square of what?
#perfect square
#coefficient
#quadratic expression
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? Hint Small clue
A (2) और (1) / (2) and (1)
B (4x+1)
C (2x+1)
D (x+1)
Explanation opens after your attempt
Step 1
Concept
(4x-2 =(2x)2 ) and \(1=1^2\). The middle term is \(2\cdot2x\cdot1=4x\).
Step 2
Why this answer is correct
The correct answer is C. (2x+1). (4x-2 =(2x)2 ) and \(1=1^2\). The middle term is \(2\cdot2x\cdot1=4x\).
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(1=1^2\) है। मध्य पद \(2\cdot2x\cdot1=4x\) है।
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\(4x^2+4x+1\) का गुणनखंड रूप क्या है?
What is the factor form of \(4x^2+4x+1\)?
#factor form
#perfect square
#quadratic
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? Hint Small clue
A ((4x+1)2 )
B ((2x+1)2 )
C ((2x-1)2 )
D ((x+2)2 )
Explanation opens after your attempt
Correct Answer
B. ((2x+1)2 )
Step 1
Concept
It is the perfect square of (2x+1). Therefore the factor form is ((2x+1)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((2x+1)2 ). It is the perfect square of (2x+1). Therefore the factor form is ((2x+1)2 ).
Step 3
Exam Tip
यह (2x+1) का पूर्ण वर्ग है। इसलिए गुणनखंड रूप ((2x+1)2 ) है।
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\(25x^2-1\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(25x^2-1\)?
#difference of squares
#quadratic factorisation
#coefficient
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? Hint Small clue
A ((5x-1)2 )
B ((25x-1)(x+1))
C ((5x-1)(5x+1))
D ((5x+1)2 )
Explanation opens after your attempt
Correct Answer
C. ((5x-1)(5x+1))
Step 1
Concept
(25x-2 =(5x)2 ) and \(1=1^2\). Difference of squares gives two factors.
Step 2
Why this answer is correct
The correct answer is C. ((5x-1)(5x+1)). (25x-2 =(5x)2 ) and \(1=1^2\). Difference of squares gives two factors.
Step 3
Exam Tip
(25x-2 =(5x)2 ) और \(1=1^2\) है। वर्गों के अंतर से दो गुणनखंड मिलते हैं।
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\(16x^2-24x+9\) का गुणनखंड रूप क्या है?
What is the factor form of \(16x^2-24x+9\)?
#perfect square trinomial
#negative middle
#quadratic
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? Hint Small clue
A ((4x+3)2 )
B ((4x-9)2 )
C ((16x-9)2 )
D ((4x-3)2 )
Explanation opens after your attempt
Correct Answer
D. ((4x-3)2 )
Step 1
Concept
(16x-2 =(4x)2 ), \(9=3^2\), and the middle term is (-24x). So ((4x-3)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is D. ((4x-3)2 ). (16x-2 =(4x)2 ), \(9=3^2\), and the middle term is (-24x). So ((4x-3)2 ) is correct.
Step 3
Exam Tip
(16x-2 =(4x)2 ), \(9=3^2\), और मध्य पद (-24x) है। इसलिए ((4x-3)2 ) सही है।
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\(x^2+10x+24\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2+10x+24\)?
#quadratic factors
#sum product
#medium
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? Hint Small clue
A ((x+3)(x+8))
B ((x+2)(x+12))
C ((x+1)(x+24))
D ((x+4)(x+6))
Explanation opens after your attempt
Correct Answer
D. ((x+4)(x+6))
Step 1
Concept
(4+6=10) and \(4\cdot6=24\). Exam tip: check the sum of factors of the last term.
Step 2
Why this answer is correct
The correct answer is D. ((x+4)(x+6)). (4+6=10) and \(4\cdot6=24\). Exam tip: check the sum of factors of the last term.
Step 3
Exam Tip
(4+6=10) और \(4\cdot6=24\) है। परीक्षा में अंतिम पद के कारकों का योग देखें।
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\(x^2-9x+20\) का सही गुणनखंडन क्या होगा?
What will be the correct factorisation of \(x^2-9x+20\)?
#quadratic factorisation
#negative middle
#signs
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? Hint Small clue
A ((x+2)(x+10))
B ((x+4)(x+5))
C ((x-2)(x-10))
D ((x-4)(x-5))
Explanation opens after your attempt
Correct Answer
D. ((x-4)(x-5))
Step 1
Concept
(-4+(-5)=-9) and ((-4)(-5)=20). Therefore both factors are negative.
Step 2
Why this answer is correct
The correct answer is D. ((x-4)(x-5)). (-4+(-5)=-9) and ((-4)(-5)=20). Therefore both factors are negative.
Step 3
Exam Tip
(-4+(-5)=-9) और ((-4)(-5)=20) है। इसलिए दोनों कारक ऋण हैं।
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\(x^2+3x-18\) का गुणनखंड रूप कौन सा है?
Which is the factor form of \(x^2+3x-18\)?
#quadratic factorisation
#negative constant
#medium
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? Hint Small clue
A ((x-9)(x+2))
B ((x-6)(x+3))
C ((x+9)(x-2))
D ((x+6)(x-3))
Explanation opens after your attempt
Correct Answer
D. ((x+6)(x-3))
Step 1
Concept
(6+(-3)=3) and (6\cdot(-3)=-18). Exam tip: match the sum of opposite signs.
Step 2
Why this answer is correct
The correct answer is D. ((x+6)(x-3)). (6+(-3)=3) and (6\cdot(-3)=-18). Exam tip: match the sum of opposite signs.
Step 3
Exam Tip
(6+(-3)=3) और (6\cdot(-3)=-18) है। परीक्षा में विपरीत चिह्नों का योग मिलाएं।
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\(3x^2+5x+2\) का गुणनखंडन चुनिए।
Choose the factorisation of \(3x^2+5x+2\).
#quadratic factorisation
#coefficient
#cross terms
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? Hint Small clue
A ((3x+2)(x+1))
B ((3x+1)(x+2))
C ((x+2)(x+3))
D ((3x+5)(x+2))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(x+1))
Step 1
Concept
((3x+2)(x+1)=3x-2 +3x+2x+2). The middle term (5x) is obtained.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(x+1)). ((3x+2)(x+1)=3x-2 +3x+2x+2). The middle term (5x) is obtained.
Step 3
Exam Tip
((3x+2)(x+1)=3x-2 +3x+2x+2) है। मध्य पद (5x) मिलता है।
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\(2x^2+5x-3\) का सही गुणनखंडन कौन सा है?
Which is the correct factorisation of \(2x^2+5x-3\)?
#quadratic factorisation
#negative constant
#checking
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? Hint Small clue
A ((2x-1)(x+3))
B ((2x+1)(x-3))
C ((2x+3)(x-1))
D ((x+3)(x-1))
Explanation opens after your attempt
Correct Answer
A. ((2x-1)(x+3))
Step 1
Concept
((2x-1)(x+3)=2x-2 +6x-x-3). This gives \(2x^2+5x-3\).
Step 2
Why this answer is correct
The correct answer is A. ((2x-1)(x+3)). ((2x-1)(x+3)=2x-2 +6x-x-3). This gives \(2x^2+5x-3\).
Step 3
Exam Tip
((2x-1)(x+3)=2x-2 +6x-x-3) है। इससे \(2x^2+5x-3\) मिलता है।
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\(x^2+bx+c\) में (b) किस पद से जुड़ा होता है?
In \(x^2+bx+c\), with which term is (b) associated?
#standard form
#linear term
#quadratic expression
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A द्विघात पद / Quadratic term
B रेखीय पद / Linear term
C स्थिर पद / Constant term
D घन पद / Cubic term
Explanation opens after your attempt
Correct Answer
B. रेखीय पद / Linear term
Step 1
Concept
(bx) is the linear term because the power of (x) is (1). Exam tip: identify the term type from its power.
Step 2
Why this answer is correct
The correct answer is B. रेखीय पद / Linear term. (bx) is the linear term because the power of (x) is (1). Exam tip: identify the term type from its power.
Step 3
Exam Tip
(bx) रेखीय पद है क्योंकि इसमें (x) की घात (1) है। परीक्षा में पद की घात से उसका प्रकार पहचानें।
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\(ax^2+bx+c\) में \(a\neq0\) क्यों जरूरी है?
Why is \(a\neq0\) necessary in \(ax^2+bx+c\)?
#standard form
#quadratic coefficient
#definition
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A ताकि घात (3) हो जाए / So that the power becomes (3)
B ताकि स्थिर पद शून्य हो जाए / So that the constant term becomes zero
C ताकि (x) हट जाए / So that (x) disappears
D ताकि व्यंजक द्विघात रहे / So that the expression remains quadratic
Explanation opens after your attempt
Correct Answer
D. ताकि व्यंजक द्विघात रहे / So that the expression remains quadratic
Step 1
Concept
If (a=0), the \(x^2\) term will not remain. Then the expression will not be quadratic.
Step 2
Why this answer is correct
The correct answer is D. ताकि व्यंजक द्विघात रहे / So that the expression remains quadratic. If (a=0), the \(x^2\) term will not remain. Then the expression will not be quadratic.
Step 3
Exam Tip
यदि (a=0) हो तो \(x^2\) पद नहीं रहेगा। तब व्यंजक द्विघात नहीं रहेगा।
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\(7-3x+2x^2\) को मानक रूप में कैसे लिखेंगे?
How will \(7-3x+2x^2\) be written in standard form?
#standard form
#quadratic expression
#ordering terms
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? Hint Small clue
A \(2x-3x^2+7\)
B \(7+2x^2-3x\)
C \(-3x+7+2x^2\)
D \(2x^2-3x+7\)
Explanation opens after your attempt
Correct Answer
D. \(2x^2-3x+7\)
Step 1
Concept
In standard form, powers are written in decreasing order. So \(2x^2-3x+7\) is correct.
Step 2
Why this answer is correct
The correct answer is D. \(2x^2-3x+7\). In standard form, powers are written in decreasing order. So \(2x^2-3x+7\) is correct.
Step 3
Exam Tip
मानक रूप में घातों को घटते क्रम में लिखते हैं। इसलिए \(2x^2-3x+7\) सही है।
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\(3x^2+2x-1\) में (x=1) रखने पर मान क्या होगा?
What is the value of \(3x^2+2x-1\) when (x=1)?
#evaluation
#substitution
#quadratic expression
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? Hint Small clue
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(3(1)2 +2(1)-1=4). Exam tip: handle the negative constant term at the end.
Step 2
Why this answer is correct
The correct answer is C. (4). (3(1)2 +2(1)-1=4). Exam tip: handle the negative constant term at the end.
Step 3
Exam Tip
(3(1)2 +2(1)-1=4) है। परीक्षा में ऋण स्थिर पद को अंत में जोड़ें।
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\(x^2-4x+7\) में (x=3) रखने पर मान क्या होगा?
What is the value of \(x^2-4x+7\) when (x=3)?
#value of expression
#quadratic
#evaluation
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? Hint Small clue
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: pay attention to 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: pay attention to signs.
Step 3
Exam Tip
\(3^2-4\cdot3+7=9-12+7=4\) है। परीक्षा में संकेतों पर ध्यान दें।
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((2x+3)(x-2)) का विस्तार कौन सा है?
Which is the expansion of ((2x+3)(x-2))?
#expansion
#quadratic product
#algebra
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? Hint Small clue
A \(2x^2+6x-2\)
B \(2x^2+7x-6\)
C \(2x^2-x+6\)
D \(2x^2-x-6\)
Explanation opens after your attempt
Correct Answer
D. \(2x^2-x-6\)
Step 1
Concept
Multiplying gives \(2x^2-4x+3x-6=2x^2-x-6\). Exam tip: combine like terms.
Step 2
Why this answer is correct
The correct answer is D. \(2x^2-x-6\). Multiplying gives \(2x^2-4x+3x-6=2x^2-x-6\). Exam tip: combine like terms.
Step 3
Exam Tip
गुणा करने पर \(2x^2-4x+3x-6=2x^2-x-6\) मिलता है। परीक्षा में समान पद जोड़ें।
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((3x-1)(x+4)) का विस्तार क्या है?
What is the expansion of ((3x-1)(x+4))?
#binomial product
#expansion
#quadratic
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A \(3x^2+x-4\)
B \(3x^2+12x-1\)
C \(3x^2-13x-4\)
D \(3x^2+11x-4\)
Explanation opens after your attempt
Correct Answer
D. \(3x^2+11x-4\)
Step 1
Concept
((3x-1)(x+4)=3x-2 +12x-x-4). So \(3x^2+11x-4\) is obtained.
Step 2
Why this answer is correct
The correct answer is D. \(3x^2+11x-4\). ((3x-1)(x+4)=3x-2 +12x-x-4). So \(3x^2+11x-4\) is obtained.
Step 3
Exam Tip
((3x-1)(x+4)=3x-2 +12x-x-4) है। इसलिए \(3x^2+11x-4\) मिलेगा।
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\(x^2+2x+1\) और \(x^2-1\) में कौन सा व्यंजक पूर्ण वर्ग है?
Which expression is a perfect square between \(x^2+2x+1\) and \(x^2-1\)?
#perfect square
#classification
#quadratic
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A कोई नहीं / None
B \(x^2-1\)
C दोनों / Both
D \(x^2+2x+1\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+2x+1\)
Step 1
Concept
(x-2 +2x+1=(x+1)2 ). But \(x^2-1\) is a difference of squares.
Step 2
Why this answer is correct
The correct answer is D. \(x^2+2x+1\). (x-2 +2x+1=(x+1)2 ). But \(x^2-1\) is a difference of squares.
Step 3
Exam Tip
(x-2 +2x+1=(x+1)2 ) है। जबकि \(x^2-1\) वर्गों का अंतर है।
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\(x^2+px+16\) पूर्ण वर्ग हो और (p) धनात्मक हो तो (p) का मान क्या होगा?
If \(x^2+px+16\) 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)
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Step 1
Concept
\(16=4^2\), so the middle term is \(2\cdot4x=8x\). Hence (p=8).
Step 2
Why this answer is correct
The correct answer is B. (8). \(16=4^2\), so the middle term is \(2\cdot4x=8x\). Hence (p=8).
Step 3
Exam Tip
\(16=4^2\) है इसलिए मध्य पद \(2\cdot4x=8x\) होगा। अतः (p=8) है।
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\(x^2-10x+k\) पूर्ण वर्ग हो तो (k) का मान क्या होगा?
If \(x^2-10x+k\) is a perfect square, what is the value of (k)?
#completing square
#unknown constant
#quadratic expression
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A (10)
B (20)
C (25)
D (100)
Explanation opens after your attempt
Step 1
Concept
Half the coefficient in (-10x) is (-5), and its square is (25). Exam tip: square half of the coefficient.
Step 2
Why this answer is correct
The correct answer is C. (25). Half the coefficient in (-10x) is (-5), and its square is (25). Exam tip: square half of the coefficient.
Step 3
Exam Tip
(-10x) में आधा गुणांक (-5) है और उसका वर्ग (25) है। परीक्षा में आधे गुणांक का वर्ग लें।
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यदि \(9x^2+mx+25\) पूर्ण वर्ग हो और मध्य पद धनात्मक हो, तो (m) का मान क्या होगा?
If \(9x^2+mx+25\) is a perfect square and the middle term is positive, what is the value of (m)?
#unknown coefficient
#perfect square
#quadratic expression
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A (15)
B (30)
C (45)
D (75)
Explanation opens after your attempt
Step 1
Concept
(9x-2 =(3x)2 ) and \(25=5^2\), so the middle term will be \(2\cdot3x\cdot5=30x\). Exam tip: take the roots of both square terms and multiply twice.
Step 2
Why this answer is correct
The correct answer is B. (30). (9x-2 =(3x)2 ) and \(25=5^2\), so the middle term will be \(2\cdot3x\cdot5=30x\). Exam tip: take the roots of both square terms and multiply twice.
Step 3
Exam Tip
(9x-2 =(3x)2 ) और \(25=5^2\) है इसलिए मध्य पद \(2\cdot3x\cdot5=30x\) होगा। परीक्षा में दोनों वर्ग पदों की जड़ें लेकर दुगुना गुणन करें।
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