समीकरण \(7x^2+2x-5=0\) में (a) का मान क्या है?
What is the value of (a) in \(7x^2+2x-5=0\)?
#quadratic equations
#coefficient
#a value
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A (7)
B (2)
C (-5)
D (0)
Explanation opens after your attempt
Step 1
Concept
In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). So (a=7).
Step 2
Why this answer is correct
The correct answer is A. (7). In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). So (a=7).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में (a) \(x^2\) का गुणांक होता है। इसलिए (a=7) है।
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समीकरण \(5x^2-9x+4=0\) में (b) का मान क्या है?
What is the value of (b) in \(5x^2-9x+4=0\)?
#quadratic equations
#coefficient
#b value
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A (5)
B (-9)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
In standard form, (b) is the coefficient of (x). Here (b=-9).
Step 2
Why this answer is correct
The correct answer is B. (-9). In standard form, (b) is the coefficient of (x). Here (b=-9).
Step 3
Exam Tip
मानक रूप में (b) (x) का गुणांक होता है। यहां (b=-9) है।
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समीकरण \(8x^2+3x+12=0\) में (c) का मान क्या है?
What is the value of (c) in \(8x^2+3x+12=0\)?
#quadratic equations
#constant term
#c value
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A (8)
B (3)
C (12)
D (0)
Explanation opens after your attempt
Step 1
Concept
In standard form, (c) is the constant term. Here the constant term is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). In standard form, (c) is the constant term. Here the constant term is (12).
Step 3
Exam Tip
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (12) है।
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समीकरण \(11x^2-6x=0\) में (c) का मान क्या होगा?
What will be the value of (c) in \(11x^2-6x=0\)?
#quadratic equations
#missing constant
#standard form
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A (11)
B (-6)
C (0)
D (6)
Explanation opens after your attempt
Step 1
Concept
It can be written as \(11x^2-6x+0=0\). So (c=0).
Step 2
Why this answer is correct
The correct answer is C. (0). It can be written as \(11x^2-6x+0=0\). So (c=0).
Step 3
Exam Tip
इसे \(11x^2-6x+0=0\) लिखा जा सकता है। इसलिए (c=0) है।
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समीकरण \(13x^2-20=0\) में (b) का मान क्या है?
What is the value of (b) in \(13x^2-20=0\)?
#quadratic equations
#missing linear term
#b value
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A (13)
B (0)
C (-20)
D (20)
Explanation opens after your attempt
Step 1
Concept
We write it as \(13x^2+0x-20=0\). So (b=0).
Step 2
Why this answer is correct
The correct answer is B. (0). We write it as \(13x^2+0x-20=0\). So (b=0).
Step 3
Exam Tip
इसे \(13x^2+0x-20=0\) लिखते हैं। इसलिए (b=0) है।
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किस शर्त पर \(px^2+qx+r=0\) द्विघात समीकरण होगा?
Under which condition will \(px^2+qx+r=0\) be a quadratic equation?
#quadratic equations
#condition
#leading coefficient
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A (p=0)
B \(p\neq0\)
C (q=0)
D (r=0)
Explanation opens after your attempt
Correct Answer
B. \(p\neq0\)
Step 1
Concept
The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 2
Why this answer is correct
The correct answer is B. \(p\neq0\). The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 3
Exam Tip
द्विघात पद \(px^2\) बना रहे इसलिए \(p\neq0\) होना चाहिए। यदि (p=0) हो तो घात (2) नहीं रहेगी।
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समीकरण \(4x^2+7x=9\) का मानक रूप क्या है?
What is the standard form of \(4x^2+7x=9\)?
#quadratic equations
#standard form
#transposition
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A \(4x^2+7x+9=0\)
B \(4x^2+7x-9=0\)
C \(4x^2-7x-9=0\)
D \(4x^2-7x+9=0\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+7x-9=0\)
Step 1
Concept
Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+7x-9=0\). Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
Step 3
Exam Tip
दाईं ओर के (9) को बाईं ओर लाने पर (-9) बनता है। इसलिए मानक रूप \(4x^2+7x-9=0\) है।
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समीकरण \(2x^2=5x+3\) का मानक रूप कौन सा है?
Which is the standard form of \(2x^2=5x+3\)?
#quadratic equations
#standard form
#sign change
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A \(2x^2-5x-3=0\)
B \(2x^2+5x+3=0\)
C \(2x^2-5x+3=0\)
D \(2x^2+5x-3=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x-3=0\)
Step 1
Concept
Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x-3=0\). Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
Step 3
Exam Tip
सभी पद एक तरफ लाने पर \(2x^2-5x-3=0\) मिलता है। चिन्ह बदलना जरूरी है।
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यदि (x=3) है तो \(x^2-4x+3=0\) में बायां पक्ष कितना होगा?
If (x=3), what is the left side of \(x^2-4x+3=0\)?
#quadratic equations
#substitution
#solution check
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A (0)
B (3)
C (6)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
Step 3
Exam Tip
रखने पर \(3^2-4\cdot3+3=0\) मिलता है। इसलिए (x=3) हल है।
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कौन सा मान \(x^2-25=0\) का एक हल है?
Which value is one solution of \(x^2-25=0\)?
#quadratic equations
#solution
#substitution
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A (2)
B (5)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
Since \(5^2-25=0\), (5) is a solution of this equation.
Step 2
Why this answer is correct
The correct answer is B. (5). Since \(5^2-25=0\), (5) is a solution of this equation.
Step 3
Exam Tip
\(5^2-25=0\) है। इसलिए (5) इस समीकरण का हल है।
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समीकरण \(x^2-8x+16=0\) में (x=4) रखने पर क्या मिलता है?
What do we get by putting (x=4) in \(x^2-8x+16=0\)?
#quadratic equations
#root checking
#perfect square
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A (0=0)
B (4=0)
C (8=0)
D (-4=0)
Explanation opens after your attempt
Step 1
Concept
We get \(4^2-8\cdot4+16=0\). So (x=4) satisfies the equation.
Step 2
Why this answer is correct
The correct answer is A. (0=0). We get \(4^2-8\cdot4+16=0\). So (x=4) satisfies the equation.
Step 3
Exam Tip
\(4^2-8\cdot4+16=0\) मिलता है। इसलिए (x=4) समीकरण को संतुष्ट करता है।
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समीकरण \(12x^2=0\) के लिए (a), (b), (c) क्रमशः क्या हैं?
For \(12x^2=0\), what are (a), (b), (c) respectively?
#quadratic equations
#coefficients
#pure quadratic
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A (12,0,0)
B (0,12,0)
C (12,1,0)
D (0,0,12)
Explanation opens after your attempt
Correct Answer
A. (12,0,0)
Step 1
Concept
It is written as \(12x^2+0x+0=0\). Therefore (a=12), (b=0), (c=0).
Step 2
Why this answer is correct
The correct answer is A. (12,0,0). It is written as \(12x^2+0x+0=0\). Therefore (a=12), (b=0), (c=0).
Step 3
Exam Tip
इसे \(12x^2+0x+0=0\) लिखा जाता है। इसलिए (a=12), (b=0), (c=0) हैं।
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(2x(x+7)=0) को मानक रूप में लिखिए।
Write (2x(x+7)=0) in standard form.
#quadratic equations
#expansion
#standard form
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A \(2x^2+14x=0\)
B \(2x^2-14x=0\)
C \(14x^2+2x=0\)
D (2x+7=0)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+14x=0\)
Step 1
Concept
Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+14x=0\). Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
Step 3
Exam Tip
(2x) को कोष्ठक के दोनों पदों से गुणा करें। इससे \(2x^2+14x=0\) मिलता है।
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((x+4)(x+5)=0) का विस्तृत रूप क्या है?
What is the expanded form of ((x+4)(x+5)=0)?
#quadratic equations
#binomial expansion
#standard form
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A \(x^2+9x+20=0\)
B \(x^2+20x+9=0\)
C \(x^2-9x+20=0\)
D \(x^2+9x-20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+9x+20=0\)
Step 1
Concept
Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+9x+20=0\). Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
Step 3
Exam Tip
विस्तार करने पर \(x^2+5x+4x+20=0\) मिलता है। समान पद जोड़कर \(x^2+9x+20=0\) बनता है।
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((x-6)(x+2)=0) का मानक रूप कौन सा है?
Which is the standard form of ((x-6)(x+2)=0)?
#quadratic equations
#expansion
#standard form
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A \(x^2-4x-12=0\)
B \(x^2+4x-12=0\)
C \(x^2-8x+12=0\)
D \(x^2+8x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-12=0\)
Step 1
Concept
Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-12=0\). Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
Step 3
Exam Tip
विस्तार से \(x^2+2x-6x-12=0\) मिलता है। इसलिए \(x^2-4x-12=0\) सही है।
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समीकरण \(x^2+12x+36=0\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(x^2+12x+36=0\)?
#quadratic equations
#implicit coefficient
#coefficient
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A (0)
B (1)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
When no number is written before \(x^2\), its coefficient is (1). This is often asked.
Step 2
Why this answer is correct
The correct answer is B. (1). When no number is written before \(x^2\), its coefficient is (1). This is often asked.
Step 3
Exam Tip
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह अक्सर पूछी जाने वाली बात है।
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समीकरण \(-2x^2+5x-1=0\) में (a) का मान क्या है?
What is the value of (a) in \(-2x^2+5x-1=0\)?
#quadratic equations
#negative coefficient
#a value
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A (2)
B (-2)
C (5)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^2\) is (-2). So in standard form (a=-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). The coefficient of \(x^2\) is (-2). So in standard form (a=-2).
Step 3
Exam Tip
\(x^2\) का गुणांक (-2) है। इसलिए मानक रूप में (a=-2) है।
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कौन सा विकल्प \(x^2+10x+25=0\) को गुणनखंड रूप में दिखाता है?
Which option shows \(x^2+10x+25=0\) in factor form?
#quadratic equations
#factor form
#perfect square
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A ((x+5)2 =0)
B ((x-5)2 =0)
C ((x+10)2 =0)
D ((x+25)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((x+5)2 =0)
Step 1
Concept
\(x^2+10x+25\) is a perfect square. It equals ((x+5)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+5)2 =0). \(x^2+10x+25\) is a perfect square. It equals ((x+5)2 ).
Step 3
Exam Tip
\(x^2+10x+25\) पूर्ण वर्ग है। यह ((x+5)2 ) के बराबर है।
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कौन सा मान \(x^2-3x-10=0\) का हल है?
Which value is a solution of \(x^2-3x-10=0\)?
#quadratic equations
#solution check
#substitution
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A (1)
B (2)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
Step 2
Why this answer is correct
The correct answer is C. (5). Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
Step 3
Exam Tip
\(5^2-3\cdot5-10=0\) है। इसलिए (x=5) हल है।
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यदि किसी समीकरण में चर की सबसे बड़ी घात (2) है तो उसे क्या कहा जाता है?
If the highest power of the variable in an equation is (2), what is it called?
#quadratic equations
#definition
#degree
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A रैखिक समीकरण / Linear equation
B द्विघात समीकरण / Quadratic equation
C घन समीकरण / Cubic equation
D चर रहित समीकरण / Equation without variable
Explanation opens after your attempt
Correct Answer
B. द्विघात समीकरण / Quadratic equation
Step 1
Concept
When the highest power is (2), the equation is called quadratic. Identifying degree is the first step.
Step 2
Why this answer is correct
The correct answer is B. द्विघात समीकरण / Quadratic equation. When the highest power is (2), the equation is called quadratic. Identifying degree is the first step.
Step 3
Exam Tip
सबसे बड़ी घात (2) होने पर समीकरण द्विघात कहलाता है। घात पहचानना पहला कदम है।
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निम्न में से किसमें \(x^2\) पद स्पष्ट रूप से है?
Which of the following clearly contains the \(x^2\) term?
#quadratic equations
#quadratic term
#recognition
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A (10x-1=0)
B (2x+9=0)
C \(4x^2+1=0\)
D (x+12=0)
Explanation opens after your attempt
Correct Answer
C. \(4x^2+1=0\)
Step 1
Concept
The quadratic term is the term containing \(x^2\). Option (C) has \(4x^2\).
Step 2
Why this answer is correct
The correct answer is C. \(4x^2+1=0\). The quadratic term is the term containing \(x^2\). Option (C) has \(4x^2\).
Step 3
Exam Tip
द्विघात पद \(x^2\) वाला पद होता है। विकल्प (C) में \(4x^2\) है।
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समीकरण \(9x^2+0x+2=0\) में रैखिक पद क्या है?
What is the linear term in \(9x^2+0x+2=0\)?
#quadratic equations
#linear term
#term identification
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A \(9x^2\)
B (0x)
C (2)
D (9x)
Explanation opens after your attempt
Step 1
Concept
The linear term is the term containing (x). Here the linear term is (0x).
Step 2
Why this answer is correct
The correct answer is B. (0x). The linear term is the term containing (x). Here the linear term is (0x).
Step 3
Exam Tip
रैखिक पद (x) वाला पद होता है। यहां रैखिक पद (0x) है।
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कौन सा समीकरण \(x^2-6x+9=0\) के बराबर है?
Which equation is equivalent to \(x^2-6x+9=0\)?
#quadratic equations
#perfect square
#equivalent form
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A ((x-3)2 =0)
B ((x+3)2 =0)
C ((x-6)2 =0)
D ((x+6)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 =0)
Step 1
Concept
((x-3)2 =x-2 -6x+9). Recognising perfect squares saves time.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 =0). ((x-3)2 =x-2 -6x+9). Recognising perfect squares saves time.
Step 3
Exam Tip
((x-3)2 =x-2 -6x+9) होता है। पूर्ण वर्ग पहचानने से समय बचता है।
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\(x^2-49=0\) को गुणनखंड रूप में कैसे लिखेंगे?
How do we write \(x^2-49=0\) in factor form?
#quadratic equations
#difference of squares
#factor form
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A ((x-7)(x+7)=0)
B ((x-49)(x+1)=0)
C ((x+7)(x+7)=0)
D ((x-7)(x-7)=0)
Explanation opens after your attempt
Correct Answer
A. ((x-7)(x+7)=0)
Step 1
Concept
\(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).
Step 2
Why this answer is correct
The correct answer is A. ((x-7)(x+7)=0). \(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).
Step 3
Exam Tip
\(x^2-49\) वर्गों का अंतर है। इसलिए यह ((x-7)(x+7)) बनता है।
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यदि (x=2) है तो \(x^2+5x-14=0\) में बायां पक्ष कितना होगा?
If (x=2), what is the left side of \(x^2+5x-14=0\)?
#quadratic equations
#substitution
#root
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A (0)
B (2)
C (4)
D (-14)
Explanation opens after your attempt
Step 1
Concept
Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
Step 3
Exam Tip
रखने पर \(2^2+5\cdot2-14=0\) मिलता है। इसलिए (2) एक हल है।
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समीकरण \(3x^2-21=0\) में (a), (b), (c) कौन से हैं?
What are (a), (b), (c) in \(3x^2-21=0\)?
#quadratic equations
#coefficients
#missing term
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A (3,0,-21)
B (3,-21,0)
C (0,3,-21)
D (-21,0,3)
Explanation opens after your attempt
Correct Answer
A. (3,0,-21)
Step 1
Concept
Write it as \(3x^2+0x-21=0\). So (a=3), (b=0), (c=-21).
Step 2
Why this answer is correct
The correct answer is A. (3,0,-21). Write it as \(3x^2+0x-21=0\). So (a=3), (b=0), (c=-21).
Step 3
Exam Tip
इसे \(3x^2+0x-21=0\) लिखें। इसलिए (a=3), (b=0), (c=-21) हैं।
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कौन सा समीकरण (t) में द्विघात है?
Which equation is quadratic in (t)?
#quadratic equations
#variable
#degree
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A \(t^2+3t+2=0\)
B \(x^2+3x+2=0\)
C (t+3=0)
D (3t-2=0)
Explanation opens after your attempt
Correct Answer
A. \(t^2+3t+2=0\)
Step 1
Concept
In option (A), the variable (t) has highest power (2). So it is quadratic in (t).
Step 2
Why this answer is correct
The correct answer is A. \(t^2+3t+2=0\). In option (A), the variable (t) has highest power (2). So it is quadratic in (t).
Step 3
Exam Tip
विकल्प (A) में चर (t) की सबसे बड़ी घात (2) है। इसलिए यह (t) में द्विघात है।
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(4x(x-3)=0) का मानक रूप क्या है?
What is the standard form of (4x(x-3)=0)?
#quadratic equations
#expansion
#standard form
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A \(4x^2-12x=0\)
B \(4x^2+12x=0\)
C \(x^2-12x=0\)
D (4x-12=0)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-12x=0\)
Step 1
Concept
Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-12x=0\). Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
Step 3
Exam Tip
(4x) को दोनों पदों से गुणा करने पर \(4x^2-12x=0\) मिलता है। ऋण चिन्ह पर ध्यान दें।
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यदि (p(x)=x-2 -4) है तो (p(2)) कितना है?
If (p(x)=x-2 -4), what is (p(2))?
#quadratic equations
#polynomial value
#zero
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A (0)
B (2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=22 -4=0). So (2) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(2)=22 -4=0). So (2) is a zero of this polynomial.
Step 3
Exam Tip
(p(2)=22 -4=0) है। इसलिए (2) इस बहुपद का शून्यक है।
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कौन सा विकल्प \(6x^2+x-8=0\) में स्थिर पद है?
Which option is the constant term in \(6x^2+x-8=0\)?
#quadratic equations
#constant term
#term identification
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A \(6x^2\)
B (x)
C (-8)
D (0)
Explanation opens after your attempt
Step 1
Concept
The constant term has no variable. Here the constant term is (-8).
Step 2
Why this answer is correct
The correct answer is C. (-8). The constant term has no variable. Here the constant term is (-8).
Step 3
Exam Tip
स्थिर पद में चर नहीं होता। यहां स्थिर पद (-8) है।
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समीकरण \(x^2-13x=0\) में कौन सा पद अनुपस्थित है?
Which term is absent in \(x^2-13x=0\)?
#quadratic equations
#missing term
#constant
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A द्विघात पद / Quadratic term
B रैखिक पद / Linear term
C स्थिर पद / Constant term
D चर पद / Variable term
Explanation opens after your attempt
Correct Answer
C. स्थिर पद / Constant term
Step 1
Concept
It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 2
Why this answer is correct
The correct answer is C. स्थिर पद / Constant term. It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 3
Exam Tip
इसे \(x^2-13x+0=0\) लिखा जा सकता है। इसलिए स्थिर पद अनुपस्थित है।
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कौन सा समीकरण शुद्ध द्विघात समीकरण है?
Which equation is a pure quadratic equation?
#quadratic equations
#pure quadratic
#recognition
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A \(4x^2-16=0\)
B \(x^2+5x+6=0\)
C (x+16=0)
D \(x^3-16=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-16=0\)
Step 1
Concept
A pure quadratic has no linear (x) term. \(4x^2-16=0\) is such an equation.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-16=0\). A pure quadratic has no linear (x) term. \(4x^2-16=0\) is such an equation.
Step 3
Exam Tip
शुद्ध द्विघात में (x) वाला रैखिक पद नहीं होता। \(4x^2-16=0\) ऐसा समीकरण है।
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\(x^2+6x+9=0\) में (x=-3) रखने पर क्या होगा?
What happens when (x=-3) is put in \(x^2+6x+9=0\)?
#quadratic equations
#negative root
#verification
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A समीकरण संतुष्ट होता है / The equation is satisfied
B समीकरण असत्य होता है / The equation is false
C बायां पक्ष (6) होता है / The left side is (6)
D बायां पक्ष (-6) होता है / The left side is (-6)
Explanation opens after your attempt
Correct Answer
A. समीकरण संतुष्ट होता है / The equation is satisfied
Step 1
Concept
((-3)2 +6(-3)+9=0). Hence (x=-3) is a solution.
Step 2
Why this answer is correct
The correct answer is A. समीकरण संतुष्ट होता है / The equation is satisfied. ((-3)2 +6(-3)+9=0). Hence (x=-3) is a solution.
Step 3
Exam Tip
((-3)2 +6(-3)+9=0) है। अतः (x=-3) हल है।
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कौन सा रूप (a=3), (b=-4), (c=-2) को दर्शाता है?
Which form represents (a=3), (b=-4), (c=-2)?
#quadratic equations
#forming equation
#coefficients
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A \(3x^2-4x-2=0\)
B \(3x^2+4x-2=0\)
C \(3x^2-2x-4=0\)
D \(4x^2-3x-2=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-4x-2=0\)
Step 1
Concept
Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-4x-2=0\). Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2-4x-2=0\) मिलता है। (b) का चिन्ह ध्यान रखें।
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यदि (a=2), (b=0), (c=-18) हैं तो समीकरण क्या होगा?
If (a=2), (b=0), (c=-18), what is the equation?
#quadratic equations
#forming equation
#standard form
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A \(2x^2-18=0\)
B \(2x^2+18=0\)
C \(2x^2+18x=0\)
D \(18x^2-2=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-18=0\)
Step 1
Concept
Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-18=0\). Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
Step 3
Exam Tip
मानक रूप में रखने पर \(2x^2+0x-18=0\) मिलता है। इसे \(2x^2-18=0\) लिखते हैं।
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कौन सा समीकरण मानक रूप में लाने पर \(x^2+2x-8=0\) बनता है?
Which equation becomes \(x^2+2x-8=0\) after writing in standard form?
#quadratic equations
#standard form
#reverse form
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A \(x^2+2x=8\)
B \(x^2+2x=-8\)
C \(x^2-2x=8\)
D \(x^2-2x=-8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x=8\)
Step 1
Concept
Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x=8\). Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
Step 3
Exam Tip
(8) को बाईं ओर लाने पर (-8) बनता है। इसलिए \(x^2+2x-8=0\) मिलता है।
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\(2x^2+7x+3=0\) के अधिकतम कितने वास्तविक हल हो सकते हैं?
What is the maximum number of real solutions possible for \(2x^2+7x+3=0\)?
#quadratic equations
#number of solutions
#degree
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
A quadratic equation can have at most (2) real solutions. The degree indicates the maximum number of solutions.
Step 2
Why this answer is correct
The correct answer is B. (2). A quadratic equation can have at most (2) real solutions. The degree indicates the maximum number of solutions.
Step 3
Exam Tip
द्विघात समीकरण के अधिकतम (2) वास्तविक हल हो सकते हैं। घात से अधिकतम हलों का संकेत मिलता है।
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समीकरण \(5x^2+5x+5=0\) में (a+b+c) का मान क्या है?
What is the value of (a+b+c) for \(5x^2+5x+5=0\)?
#quadratic equations
#coefficients
#sum
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A (5)
B (10)
C (15)
D (25)
Explanation opens after your attempt
Step 1
Concept
Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).
Step 2
Why this answer is correct
The correct answer is C. (15). Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).
Step 3
Exam Tip
यहां (a=5), (b=5), (c=5) हैं। इसलिए (a+b+c=15) है।
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समीकरण \(4x^2-2x-6=0\) में (a-b+c) का मान क्या है?
What is the value of (a-b+c) for \(4x^2-2x-6=0\)?
#quadratic equations
#coefficients
#expression value
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A (0)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
Step 3
Exam Tip
यहां (a=4), (b=-2), (c=-6) हैं। इसलिए (a-b+c=4-(-2)-6=0) है।
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\(6x^2-5x+2=0\) की घात क्या है?
What is the degree of \(6x^2-5x+2=0\)?
#quadratic equations
#degree
#identification
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A (0)
B (1)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2). Therefore it is a quadratic equation.
Step 2
Why this answer is correct
The correct answer is C. (2). The highest power is (2). Therefore it is a quadratic equation.
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए यह द्विघात समीकरण है।
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कौन सा विकल्प \(x^2+x-12=0\) का गुणनखंड रूप है?
Which option is the factor form of \(x^2+x-12=0\)?
#quadratic equations
#factor form
#verification
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A ((x+4)(x-3)=0)
B ((x-4)(x+3)=0)
C ((x+4)(x+3)=0)
D ((x-4)(x-3)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x-3)=0)
Step 1
Concept
Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x-3)=0). Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 3
Exam Tip
((x+4)(x-3)) फैलाने पर \(x^2+x-12\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।
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यदि एक वर्ग की भुजा (x+2) है और क्षेत्रफल (49) है तो समीकरण क्या बनेगा?
If the side of a square is (x+2) and the area is (49), what equation is formed?
#quadratic equations
#word problem
#area
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A ((x+2)2 =49)
B (x+2=49)
C (2x+2=49)
D \(x^2+2=49\)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =49)
Step 1
Concept
The area of a square is the square of its side. So the equation is ((x+2)2 =49).
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =49). The area of a square is the square of its side. So the equation is ((x+2)2 =49).
Step 3
Exam Tip
वर्ग का क्षेत्रफल भुजा का वर्ग होता है। इसलिए समीकरण ((x+2)2 =49) बनेगा।
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दो लगातार धन सम संख्याओं का गुणनफल (48) है। यदि छोटी संख्या (x) है तो समीकरण क्या होगा?
The product of two consecutive positive even numbers is (48). If the smaller number is (x), what is the equation?
#quadratic equations
#word problem
#consecutive even numbers
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A (x(x+2)=48)
B (x(x+1)=48)
C (x+x+2=48)
D (2x=48)
Explanation opens after your attempt
Correct Answer
A. (x(x+2)=48)
Step 1
Concept
The next consecutive even number is (x+2). So the product equation is (x(x+2)=48).
Step 2
Why this answer is correct
The correct answer is A. (x(x+2)=48). The next consecutive even number is (x+2). So the product equation is (x(x+2)=48).
Step 3
Exam Tip
लगातार सम संख्या (x+2) होगी। इसलिए गुणनफल का समीकरण (x(x+2)=48) है।
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किस विकल्प में गलती है जब \(x^2=6x+7\) को मानक रूप में बदला जाता है?
Which option shows the mistake while converting \(x^2=6x+7\) to standard form?
#quadratic equations
#common mistake
#standard form
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A \(x^2-6x-7=0\)
B \(x^2+6x+7=0\)
C \(x^2-6x=7\)
D \(x^2=6x+7\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x+7=0\)
Step 1
Concept
The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x+7=0\). The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.
Step 3
Exam Tip
सही मानक रूप \(x^2-6x-7=0\) है। विकल्प (B) में दाईं ओर के पदों के चिन्ह नहीं बदले गए।
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((x+3)2 =25) को मानक रूप में लिखने पर कौन सा समीकरण मिलेगा?
Which equation is obtained when ((x+3)2 =25) is written in standard form?
#quadratic equations
#standard form
#perfect square
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A \(x^2+6x-16=0\)
B \(x^2+6x+16=0\)
C \(x^2+3x-25=0\)
D \(x^2+9x-25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x-16=0\)
Step 1
Concept
Here ((x+3)2 =x-2 +6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-16=0\). Here ((x+3)2 =x-2 +6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.
Step 3
Exam Tip
((x+3)2 =x-2 +6x+9) है और (25) को बाईं ओर लाने पर (-25) बनता है। इसलिए \(x^2+6x-16=0\) सही है।
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समीकरण ((k-1)x-2 +3x+2=0) द्विघात रहे इसके लिए कौन सी शर्त सही है?
Which condition is correct for ((k-1)x-2 +3x+2=0) to remain quadratic?
#quadratic equations
#parameter
#leading coefficient
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A (k=1)
B \(k\neq1\)
C (k=0)
D (k=-1)
Explanation opens after your attempt
Correct Answer
B. \(k\neq1\)
Step 1
Concept
The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq1\). The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 3
Exam Tip
द्विघात पद का गुणांक ((k-1)) है जो (0) नहीं होना चाहिए। इसलिए \(k\neq1\) होना जरूरी है।
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द्विघात समीकरण के बारे में कौन सा कथन गलत है?
Which statement about a quadratic equation is false?
#quadratic equations
#true false
#concept clarity
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A इसकी घात (2) होती है / Its degree is (2)
B मानक रूप \(ax^2+bx+c=0\) है / Its standard form is \(ax^2+bx+c=0\)
C इसमें \(a\neq0\) होना चाहिए / It must have \(a\neq0\)
D इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\)
Explanation opens after your attempt
Correct Answer
D. इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\)
Step 1
Concept
In a quadratic equation, (c) can also be (0). The necessary condition is only \(a\neq0\).
Step 2
Why this answer is correct
The correct answer is D. इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\). In a quadratic equation, (c) can also be (0). The necessary condition is only \(a\neq0\).
Step 3
Exam Tip
द्विघात समीकरण में (c) (0) भी हो सकता है। जरूरी शर्त केवल \(a\neq0\) है।
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((2x+1)(x-4)=0) का विस्तृत रूप क्या है?
What is the expanded form of ((2x+1)(x-4)=0)?
#quadratic equations
#expansion
#binomial product
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A \(2x^2-7x-4=0\)
B \(2x^2+7x-4=0\)
C \(2x^2-8x+1=0\)
D \(2x^2-7x+4=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-7x-4=0\)
Step 1
Concept
Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-7x-4=0\). Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
Step 3
Exam Tip
विस्तार करने पर \(2x^2-8x+x-4=0\) मिलता है। समान पद जोड़कर \(2x^2-7x-4=0\) बनता है।
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यदि (x=-1) समीकरण \(x^2+mx-6=0\) का हल है तो (m) का मान क्या होगा?
If (x=-1) is a solution of \(x^2+mx-6=0\), what is the value of (m)?
#quadratic equations
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#parameter
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A (5)
B (-5)
C (7)
D (-7)
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Step 1
Concept
Putting (x=-1) gives (1-m-6 =0). So (-m-5 =0) and (m=-5).
Step 2
Why this answer is correct
The correct answer is B. (-5). Putting (x=-1) gives (1-m-6 =0). So (-m-5 =0) and (m=-5).
Step 3
Exam Tip
(x=-1) रखने पर (1-m-6 =0) मिलता है। इसलिए (-m-5 =0) और (m=-5) है।
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किसी संख्या का वर्ग उस संख्या के (5) गुने से (6) अधिक है। यदि संख्या (x) है तो समीकरण क्या होगा?
The square of a number is (6) more than (5) times the number. If the number is (x), what is the equation?
#quadratic equations
#word problem
#forming equation
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A \(x^2=5x+6\)
B \(x^2+5x=6\)
C \(5x^2=x+6\)
D \(x^2=6x+5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2=5x+6\)
Step 1
Concept
The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2=5x+6\). The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 3
Exam Tip
संख्या का वर्ग \(x^2\) और (5) गुने से (6) अधिक (5x+6) है। इसलिए समीकरण \(x^2=5x+6\) बनेगा।
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