Question 451/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
एक आयत की लंबाई (x+3) और चौड़ाई (x) है। क्षेत्रफल (10) हो तो सही द्विघात समीकरण कौन-सा है?
A rectangle has length (x+3) and breadth (x). If its area is (10), which quadratic equation is correct?
#quadratic-equations
#word-problem
#area-model
A \(x^2+3x-10=0\)
B \(x^2-3x-10=0\)
C \(x^2+3x+10=0\)
D \(3x^2+x-10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-10=0\)
Step 1
Concept
The area is (x(x+3)=10), which gives \(x^2+3x-10=0\). In geometry questions, form the equation using the formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-10=0\). The area is (x(x+3)=10), which gives \(x^2+3x-10=0\). In geometry questions, form the equation using the formula.
Step 3
Exam Tip
क्षेत्रफल (x(x+3)=10) होगा जिससे \(x^2+3x-10=0\) मिलता है। ज्यामिति प्रश्न में सूत्र से समीकरण बनाएं।
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Question 452/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या \(2x^2=0\) एक द्विघात समीकरण है?
Is \(2x^2=0\) a quadratic equation?
#quadratic-equations
#pure-quadratic
#identify
A नहीं क्योंकि केवल एक पद है / No because it has only one term
B नहीं क्योंकि (x) पद नहीं है / No because there is no (x) term
C नहीं क्योंकि स्थिर पद नहीं है / No because there is no constant term
D हाँ क्योंकि \(x^2\) का गुणांक (2) है / Yes because the coefficient of \(x^2\) is (2)
Explanation opens after your attempt
Correct Answer
D. हाँ क्योंकि \(x^2\) का गुणांक (2) है / Yes because the coefficient of \(x^2\) is (2)
Step 1
Concept
In \(2x^2=0\), the coefficient of \(x^2\) is \(2\neq 0\). It can be quadratic even without linear and constant terms.
Step 2
Why this answer is correct
The correct answer is D. हाँ क्योंकि \(x^2\) का गुणांक (2) है / Yes because the coefficient of \(x^2\) is (2). In \(2x^2=0\), the coefficient of \(x^2\) is \(2\neq 0\). It can be quadratic even without linear and constant terms.
Step 3
Exam Tip
\(2x^2=0\) में \(x^2\) का गुणांक \(2\neq 0\) है। रैखिक और स्थिर पद न होने पर भी यह द्विघात हो सकता है।
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Question 453/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मानक द्विघात समीकरण \(ax^2+bx+c=0\) में अधिकतम कितने अलग-अलग पद हो सकते हैं?
In the standard quadratic equation \(ax^2+bx+c=0\), what is the maximum number of different terms?
#quadratic-equations
#terms
#standard-form
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).
Step 3
Exam Tip
मानक रूप में \(x^2\) पद, (x) पद और स्थिर पद हो सकते हैं। इसलिए अधिकतम (3) पद होते हैं।
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Question 454/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या \(x^2+4=0\) एक द्विघात समीकरण है?
Is \(x^2+4=0\) a quadratic equation?
#quadratic-equations
#quadratic-identification
#roots-concept
A हाँ क्योंकि \(x^2\) का गुणांक (1) है / Yes because the coefficient of \(x^2\) is (1)
B नहीं क्योंकि वास्तविक मूल नहीं हैं / No because it has no real roots
C नहीं क्योंकि (x) पद नहीं है / No because there is no (x) term
D नहीं क्योंकि स्थिर पद है / No because it has a constant term
Explanation opens after your attempt
Correct Answer
A. हाँ क्योंकि \(x^2\) का गुणांक (1) है / Yes because the coefficient of \(x^2\) is (1)
Step 1
Concept
In \(x^2+4=0\), the coefficient of \(x^2\) is (1), so it is quadratic. Having real roots is not a condition for being quadratic.
Step 2
Why this answer is correct
The correct answer is A. हाँ क्योंकि \(x^2\) का गुणांक (1) है / Yes because the coefficient of \(x^2\) is (1). In \(x^2+4=0\), the coefficient of \(x^2\) is (1), so it is quadratic. Having real roots is not a condition for being quadratic.
Step 3
Exam Tip
\(x^2+4=0\) में \(x^2\) का गुणांक (1) है इसलिए यह द्विघात है। वास्तविक मूल होना द्विघात होने की शर्त नहीं है।
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Question 455/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मानक रूप \(ax^2+bx+c=0\) में \(x^2\) का गुणांक किससे दर्शाया जाता है?
In the standard form \(ax^2+bx+c=0\), which symbol denotes the coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#coefficient-a
A (b)
B (a)
C (c)
D (x)
Explanation opens after your attempt
Step 1
Concept
In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 2
Why this answer is correct
The correct answer is B. (a). In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 3
Exam Tip
मानक रूप में \(x^2\) का गुणांक (a) होता है। यही गुणांक (0) नहीं होना चाहिए।
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Question 456/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से (y) में द्विघात समीकरण कौन-सा है?
Which of the following is a quadratic equation in (y)?
#quadratic-equations
#variable-y
#identify
A \(2y^2-3y+1=0\)
B (2y+1=0)
C \(y^3-y=0\)
D \(\frac{1}{y}+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(2y^2-3y+1=0\)
Step 1
Concept
The highest power of (y) is (2), so it is quadratic in (y). The variable may be different, but the degree must be (2).
Step 2
Why this answer is correct
The correct answer is A. \(2y^2-3y+1=0\). The highest power of (y) is (2), so it is quadratic in (y). The variable may be different, but the degree must be (2).
Step 3
Exam Tip
चर (y) की सबसे बड़ी घात (2) है इसलिए यह (y) में द्विघात है। चर कोई भी हो सकता है पर घात (2) होनी चाहिए।
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Question 457/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(2x^2+5=0\) में कौन-सा पद अनुपस्थित है?
Which term is absent in \(2x^2+5=0\)?
#quadratic-equations
#missing-linear-term
#easy
A द्विघात पद / Quadratic term
B स्थिर पद / Constant term
C रैखिक पद / Linear term
D समीकरण चिह्न / Equation sign
Explanation opens after your attempt
Correct Answer
C. रैखिक पद / Linear term
Step 1
Concept
There is no (x) term, so the linear term is absent. The coefficient of a missing term is considered (0).
Step 2
Why this answer is correct
The correct answer is C. रैखिक पद / Linear term. There is no (x) term, so the linear term is absent. The coefficient of a missing term is considered (0).
Step 3
Exam Tip
इसमें (x) वाला पद नहीं है इसलिए रैखिक पद अनुपस्थित है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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Question 458/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (a=3,\ b=0,\ c=-12) हैं तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=3,\ b=0,\ c=-12), which is the corresponding quadratic equation?
#quadratic-equations
#forming-equation
#coefficients
A \(3x^2-12=0\)
B \(3x^2+12=0\)
C \(3x^2-12x=0\)
D \(12x^2+3=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-12=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(3x^2+0x-12=0\). Simplifying gives \(3x^2-12=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-12=0\). Substituting in \(ax^2+bx+c=0\) gives \(3x^2+0x-12=0\). Simplifying gives \(3x^2-12=0\).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2+0x-12=0\) मिलता है। इसे सरल करने पर \(3x^2-12=0\) है।
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Question 459/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x=2) समीकरण \(x^2+kx+2=0\) का मूल है तो (k) का मान क्या होगा?
If (x=2) is a root of \(x^2+kx+2=0\), what is the value of (k)?
#quadratic-equations
#parameter
#root-substitution
A (3)
B (-3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4+2k+2=0), so (k=-3). If a root is given, substitute it in the equation.
Step 2
Why this answer is correct
The correct answer is B. (-3). Putting (x=2) gives (4+2k+2=0), so (k=-3). If a root is given, substitute it in the equation.
Step 3
Exam Tip
(x=2) रखने पर (4+2k+2=0) इसलिए (k=-3) मिलता है। मूल दिया हो तो उसे समीकरण में रखें।
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Question 460/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
((x+1)2 =0) का मानक रूप क्या है?
What is the standard form of ((x+1)2 =0)?
#quadratic-equations
#identity
#standard-form
A \(x^2+x+1=0\)
B \(x^2-2x+1=0\)
C \(x^2+2x+1=0\)
D \(x^2+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+2x+1=0\)
Step 1
Concept
((x+1)2 =x-2 +2x+1). Remember the formula ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+2x+1=0\). ((x+1)2 =x-2 +2x+1). Remember the formula ((a+b)2 =a-2 +2ab+b-2 ).
Step 3
Exam Tip
((x+1)2 =x-2 +2x+1) होता है। सूत्र ((a+b)2 =a-2 +2ab+b-2 ) याद रखें।
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Question 461/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(\sqrt{x}+x^2=0\) को सामान्य रूप में द्विघात क्यों नहीं माना जाता?
Why is \(\sqrt{x}+x^2=0\) not considered a quadratic equation in the usual form?
#quadratic-equations
#non-example
#radical
A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (0) है / Because it has (0)
C क्योंकि इसमें (x) नहीं है / Because it has no (x)
D क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation opens after your attempt
Correct Answer
D. क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Step 1
Concept
The term \(\sqrt{x}\) shows a fractional power of the variable, so it is not in usual quadratic form. A quadratic equation has only \(x^2\), (x), and constant terms.
Step 2
Why this answer is correct
The correct answer is D. क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term. The term \(\sqrt{x}\) shows a fractional power of the variable, so it is not in usual quadratic form. A quadratic equation has only \(x^2\), (x), and constant terms.
Step 3
Exam Tip
\(\sqrt{x}\) चर की भिन्न घात दिखाता है इसलिए यह सामान्य द्विघात रूप में नहीं है। द्विघात में केवल \(x^2\), (x) और स्थिर पद होते हैं।
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Question 462/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(\frac{1}{x^2}+x+1=0\) द्विघात समीकरण क्यों नहीं है?
Why is \(\frac{1}{x^2}+x+1=0\) not a quadratic equation?
#quadratic-equations
#non-example
#negative-exponent
A क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x)
B क्योंकि इसमें (x) पद है / Because it has an (x) term
C क्योंकि इसमें स्थिर पद है / Because it has a constant term
D क्योंकि इसमें (1) है / Because it has (1)
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x)
Step 1
Concept
\(\frac{1}{x^2}=x^{-2}\), which is not polynomial form. A quadratic equation cannot have a negative power of the variable.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x). \(\frac{1}{x^2}=x^{-2}\), which is not polynomial form. A quadratic equation cannot have a negative power of the variable.
Step 3
Exam Tip
\(\frac{1}{x^2}=x^{-2}\) है जो बहुपद रूप नहीं है। द्विघात समीकरण में चर की ऋणात्मक घात नहीं होती।
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Question 463/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से किस समीकरण में चर की सबसे बड़ी घात (2) है?
Which equation has highest power (2) of the variable?
#quadratic-equations
#identify-degree
#easy
A (5x+1=0)
B \(x^3+1=0\)
C \(3x^2+1=0\)
D \(\sqrt{x}+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+1=0\)
Step 1
Concept
In \(3x^2+1=0\), the highest power is (2). To identify a quadratic equation, look at the power of the variable.
Step 2
Why this answer is correct
The correct answer is C. \(3x^2+1=0\). In \(3x^2+1=0\), the highest power is (2). To identify a quadratic equation, look at the power of the variable.
Step 3
Exam Tip
\(3x^2+1=0\) में सबसे बड़ी घात (2) है। द्विघात पहचानने के लिए चर की घात देखें।
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Question 464/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2=6x\) का मानक रूप कौन-सा है?
What is the standard form of \(x^2=6x\)?
#quadratic-equations
#standard-form
#transposition
A \(x^2+6x=0\)
B \(x^2-6x=0\)
C \(6x^2-x=0\)
D \(x^2-6=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-6x=0\)
Step 1
Concept
Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-6x=0\). Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.
Step 3
Exam Tip
(6x) को बाईं ओर लाने पर \(x^2-6x=0\) मिलता है। स्थानांतरण करते समय चिन्ह बदलता है।
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Question 465/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण (x(x-5)=0) का मानक रूप कौन-सा है?
What is the standard form of (x(x-5)=0)?
#quadratic-equations
#expansion
#standard-form
A \(x^2+5x=0\)
B \(x^2-5x=0\)
C \(5x^2-x=0\)
D \(x^2-5=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-5x=0\)
Step 1
Concept
Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-5x=0\). Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.
Step 3
Exam Tip
(x(x-5)) को फैलाने पर \(x^2-5x\) मिलता है। कोष्ठक हटाते समय चिन्ह सही रखें।
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Question 466/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+7x=0\) में (c) का मान क्या है?
What is the value of (c) in \(x^2+7x=0\)?
#quadratic-equations
#coefficient-c
#missing-term
A (1)
B (7)
C \(-7\)
D (0)
Explanation opens after your attempt
Step 1
Concept
Comparing with standard form, the constant term is absent, so (c=0). Treat a missing constant term as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). Comparing with standard form, the constant term is absent, so (c=0). Treat a missing constant term as (0).
Step 3
Exam Tip
मानक रूप से मिलाने पर स्थिर पद अनुपस्थित है इसलिए (c=0) है। अनुपस्थित स्थिर पद को (0) मानें।
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Question 467/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(2x^2-x+8=0\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(2x^2-x+8=0\)?
#quadratic-equations
#coefficient-b
#signs
A (-1)
B (1)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-1). The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.
Step 3
Exam Tip
(-x) का गुणांक (-1) होता है। चिन्ह सहित गुणांक लिखना जरूरी है।
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Question 468/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+1=0\) की घात क्या है?
What is the degree of \(x^2+1=0\)?
#quadratic-equations
#degree
#constant-term
A (1)
B (2)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
The highest power of (x) is (2). The constant term does not change the degree.
Step 2
Why this answer is correct
The correct answer is B. (2). The highest power of (x) is (2). The constant term does not change the degree.
Step 3
Exam Tip
इसमें (x) की सबसे बड़ी घात (2) है। स्थिर पद घात को नहीं बदलता।
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Question 469/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
व्यंजक (p(x)=x-2 +2x+1) क्या है?
What is the expression (p(x)=x-2 +2x+1)?
#quadratic-equations
#polynomial-vs-equation
#easy
A रैखिक समीकरण / Linear equation
B द्विघात समीकरण / Quadratic equation
C द्विघात बहुपद / Quadratic polynomial
D घन समीकरण / Cubic equation
Explanation opens after your attempt
Correct Answer
C. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
(p(x)=x-2 +2x+1) is a polynomial because it is not set equal to (0). It becomes an equation when written as equal to (0).
Step 2
Why this answer is correct
The correct answer is C. द्विघात बहुपद / Quadratic polynomial. (p(x)=x-2 +2x+1) is a polynomial because it is not set equal to (0). It becomes an equation when written as equal to (0).
Step 3
Exam Tip
(p(x)=x-2 +2x+1) एक बहुपद है क्योंकि इसे (0) के बराबर नहीं रखा गया है। (=0) लगाने पर यह समीकरण बनेगा।
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Question 470/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=1) समीकरण \(x^2-x=0\) का मूल है?
Is (x=1) a root of \(x^2-x=0\)?
#quadratic-equations
#root-check
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=0) मूल है / Only (x=0) is a root
D कोई मूल नहीं है / There is no root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=1) gives \(1^2-1=0\). To check a root, directly substitute the given value.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=1) gives \(1^2-1=0\). To check a root, directly substitute the given value.
Step 3
Exam Tip
(x=1) रखने पर \(1^2-1=0\) मिलता है। मूल की जांच में दिया हुआ मान सीधे रखें।
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Question 471/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(\alpha\) समीकरण (p(x)=0) का मूल है तो कौन-सा कथन सही है?
If \(\alpha\) is a root of (p(x)=0), which statement is correct?
#quadratic-equations
#root-definition
#easy
A (p\(\alpha\)>0)
B (p\(\alpha\)=0)
C (p\(\alpha\)<0)
D (p(x)=\alpha)
Explanation opens after your attempt
Correct Answer
B. (p\(\alpha\)=0)
Step 1
Concept
A root is a value that makes the left side of the equation (0). Therefore (p\(\alpha\)=0) is correct.
Step 2
Why this answer is correct
The correct answer is B. (p\(\alpha\)=0). A root is a value that makes the left side of the equation (0). Therefore (p\(\alpha\)=0) is correct.
Step 3
Exam Tip
मूल वह मान है जिसे रखने पर समीकरण का बायां पक्ष (0) हो जाता है। इसलिए (p\(\alpha\)=0) सही है।
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Question 472/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
जिन मूलों में (0) और (-3) हों उनके लिए सही द्विघात समीकरण कौन-सा है?
Which quadratic equation has roots (0) and (-3)?
#quadratic-equations
#forming-equation
#roots
A \(x^2+3x=0\)
B \(x^2-3x=0\)
C \(x^2+3=0\)
D \(x^2-3=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x=0\)
Step 1
Concept
For roots (0) and (-3), the factors are (x) and (x+3). So the equation is (x(x+3)=0), that is \(x^2+3x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x=0\). For roots (0) and (-3), the factors are (x) and (x+3). So the equation is (x(x+3)=0), that is \(x^2+3x=0\).
Step 3
Exam Tip
मूल (0) और (-3) होने पर गुणनखंड (x) और (x+3) होंगे। इसलिए समीकरण (x(x+3)=0) यानी \(x^2+3x=0\) है।
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Question 473/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2=9\) के मूल कौन-से हैं?
What are the roots of \(x^2=9\)?
#quadratic-equations
#square-roots
#roots
A (0,9)
B (3,9)
C (-3,3)
D (-9,9)
Explanation opens after your attempt
Step 1
Concept
From \(x^2=9\), we get \(x=\pm3\). While taking square roots, take both positive and negative values.
Step 2
Why this answer is correct
The correct answer is C. (-3,3). From \(x^2=9\), we get \(x=\pm3\). While taking square roots, take both positive and negative values.
Step 3
Exam Tip
\(x^2=9\) से \(x=\pm3\) मिलता है। वर्गमूल लेते समय धन और ऋण दोनों मान लें।
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Question 474/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-1=0\) के मूल कौन-से हैं?
What are the roots of \(x^2-1=0\)?
#quadratic-equations
#simple-roots
#difference-of-squares
A (0,1)
B (-1,1)
C (1,2)
D (-2,2)
Explanation opens after your attempt
Step 1
Concept
(x-2 -1=(x-1)(x+1)). Therefore the roots are (1) and (-1).
Step 2
Why this answer is correct
The correct answer is B. (-1,1). (x-2 -1=(x-1)(x+1)). Therefore the roots are (1) and (-1).
Step 3
Exam Tip
(x-2 -1=(x-1)(x+1)) होता है। इसलिए मूल (1) और (-1) हैं।
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Question 475/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2=7\) का मानक रूप कौन-सा है?
What is the standard form of \(x^2=7\)?
#quadratic-equations
#standard-form
#easy
A \(x^2+7=0\)
B \(7x^2=0\)
C \(x^2-7x=0\)
D \(x^2-7=0\)
Explanation opens after your attempt
Correct Answer
D. \(x^2-7=0\)
Step 1
Concept
Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.
Step 2
Why this answer is correct
The correct answer is D. \(x^2-7=0\). Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.
Step 3
Exam Tip
(7) को बाईं ओर लाने पर \(x^2-7=0\) मिलता है। मानक रूप में सभी पद एक तरफ होते हैं।
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Question 476/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
((x+1)(x+2)=0) को फैलाने पर कौन-सा समीकरण मिलेगा?
Which equation is obtained by expanding ((x+1)(x+2)=0)?
#quadratic-equations
#expansion
#standard-form
A \(x^2+3x+2=0\)
B \(x^2+2x+3=0\)
C \(x^2+x+2=0\)
D \(x^2+3x-2=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+2=0\)
Step 1
Concept
((x+1)(x+2)=x-2 +3x+2). Do not forget to add the middle terms while multiplying.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+2=0\). ((x+1)(x+2)=x-2 +3x+2). Do not forget to add the middle terms while multiplying.
Step 3
Exam Tip
((x+1)(x+2)=x-2 +3x+2) होता है। गुणा करते समय मध्य पदों को जोड़ना न भूलें।
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Question 477/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(0x^2+2x+3=0\) द्विघात क्यों नहीं है?
Why is \(0x^2+2x+3=0\) not quadratic?
#quadratic-equations
#non-quadratic
#a-zero
A क्योंकि (c=3) है / Because (c=3)
B क्योंकि \(x^2\) का गुणांक (0) है / Because the coefficient of \(x^2\) is (0)
C क्योंकि (x) का गुणांक (2) है / Because the coefficient of (x) is (2)
D क्योंकि इसमें स्थिर पद है / Because it has a constant term
Explanation opens after your attempt
Correct Answer
B. क्योंकि \(x^2\) का गुणांक (0) है / Because the coefficient of \(x^2\) is (0)
Step 1
Concept
Here the coefficient of \(x^2\) is (0), so the \(x^2\) term disappears. For a quadratic equation, \(a\neq 0\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(x^2\) का गुणांक (0) है / Because the coefficient of \(x^2\) is (0). Here the coefficient of \(x^2\) is (0), so the \(x^2\) term disappears. For a quadratic equation, \(a\neq 0\) is necessary.
Step 3
Exam Tip
यहाँ \(x^2\) का गुणांक (0) है इसलिए \(x^2\) पद समाप्त हो जाता है। द्विघात के लिए \(a\neq 0\) जरूरी है।
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Question 478/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(-x^2+4x-1=0\) में (a,b,c) के सही मान कौन-से हैं?
Which are the correct values of (a,b,c) in \(-x^2+4x-1=0\)?
#quadratic-equations
#coefficients
#signs
A (a=-1,\ b=4,\ c=-1)
B (a=1,\ b=4,\ c=-1)
C (a=-1,\ b=-4,\ c=-1)
D (a=4,\ b=-1,\ c=-1)
Explanation opens after your attempt
Correct Answer
A. (a=-1,\ b=4,\ c=-1)
Step 1
Concept
The coefficient of \(x^2\) is (-1), the coefficient of (x) is (4), and the constant term is (-1). Never ignore the negative sign.
Step 2
Why this answer is correct
The correct answer is A. (a=-1,\ b=4,\ c=-1). The coefficient of \(x^2\) is (-1), the coefficient of (x) is (4), and the constant term is (-1). Never ignore the negative sign.
Step 3
Exam Tip
\(x^2\) का गुणांक (-1), (x) का गुणांक (4) और स्थिर पद (-1) है। ऋण चिन्ह को कभी न छोड़ें।
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Question 479/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी द्विघात समीकरण का विवेचक (D<0) है तो वास्तविक मूलों के बारे में क्या सही है?
If the discriminant (D<0), what is true about real roots?
#quadratic-equations
#discriminant
#no-real-roots
A दो समान वास्तविक मूल होते हैं / It has two equal real roots
B दो भिन्न वास्तविक मूल होते हैं / It has two distinct real roots
C कोई वास्तविक मूल नहीं होता / It has no real roots
D एक वास्तविक मूल होता है / It has one real root
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं होता / It has no real roots
Step 1
Concept
When (D<0), there are no real roots. A negative discriminant gives no roots on the real number line.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं होता / It has no real roots. When (D<0), there are no real roots. A negative discriminant gives no roots on the real number line.
Step 3
Exam Tip
(D<0) होने पर वास्तविक मूल नहीं होते। विवेचक नकारात्मक हो तो वास्तविक संख्या रेखा पर मूल नहीं मिलते।
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Question 480/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी द्विघात समीकरण का विवेचक (D=0) है तो मूल कैसे होंगे?
If the discriminant (D=0) for a quadratic equation, how will the roots be?
#quadratic-equations
#discriminant
#equal-roots
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो समान वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real roots
D तीन वास्तविक मूल / Three real roots
Explanation opens after your attempt
Correct Answer
B. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
When (D=0), both real roots are equal. In such questions, compare (D) with (0).
Step 2
Why this answer is correct
The correct answer is B. दो समान वास्तविक मूल / Two equal real roots. When (D=0), both real roots are equal. In such questions, compare (D) with (0).
Step 3
Exam Tip
(D=0) होने पर दोनों वास्तविक मूल समान होते हैं। ऐसे प्रश्नों में (D) की तुलना (0) से करें।
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