Question 421/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस द्विघात समीकरण में मूलों का योग (5) और गुणनफल (6) है?
Which quadratic equation has sum of roots (5) and product (6)?
#quadratic-equations
#sum-product
#forming-equation
#medium
A \(x^2-5x+6=0\)
B \(x^2+5x+6=0\)
C \(x^2-6x+5=0\)
D \(x^2+6x+5=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x+6=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-5x+6=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-5x+6=0). A monic equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-5x+6=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-5x+6=0) सही है\)।
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Question 422/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि मूल (4) और (6) हैं, तो मूलों का गुणनफल क्या है?
If the roots are (4) and (6), what is the product of the roots?
#quadratic-equations
#roots
#product
#medium
A (10)
B (24)
C (2)
D (-24)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(4\cdot6=24\). Sum and product are both useful while forming an equation from roots.
Step 2
Why this answer is correct
The correct answer is B. (24). The product of roots is \(4\cdot6=24\). Sum and product are both useful while forming an equation from roots.
Step 3
Exam Tip
मूलों का गुणनफल \(4\cdot6=24\) है। मूलों से समीकरण बनाते समय योग और गुणनफल दोनों उपयोगी होते हैं।
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Question 423/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि (x=2) और (x=-3) किसी द्विघात समीकरण के मूल हैं, तो मूलों का योग क्या है?
If (x=2) and (x=-3) are roots of a quadratic equation, what is the sum of the roots?
#quadratic-equations
#roots
#sum
#medium
A (1)
B (-1)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (2+(-3)=-1). When adding integers with unlike signs, take the sign of the larger magnitude.
Step 2
Why this answer is correct
The correct answer is B. (-1). The sum of roots is (2+(-3)=-1). When adding integers with unlike signs, take the sign of the larger magnitude.
Step 3
Exam Tip
मूलों का योग (2+(-3)=-1) है। अलग-अलग चिन्ह वाले पूर्णांकों को जोड़ते समय बड़े परिमाण का चिन्ह लें।
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Question 424/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2+2\sqrt{3}x+3=0\) में (b) का मान क्या है?
What is the value of (b) in \(x^2+2\sqrt{3}x+3=0\)?
#quadratic-equations
#coefficients
#radicals
#medium
A \(2\sqrt{3}\)
B \(\sqrt{3}\)
C (3)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
The coefficient attached to (x) is \(2\sqrt{3}\). Radical coefficients are treated like ordinary coefficients.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). The coefficient attached to (x) is \(2\sqrt{3}\). Radical coefficients are treated like ordinary coefficients.
Step 3
Exam Tip
(x) के साथ लगा गुणांक \(2\sqrt{3}\) है। करणी वाले गुणांक भी सामान्य गुणांक की तरह लिए जाते हैं।
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Question 425/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
कौन-सा विकल्प द्विघात समीकरण नहीं है?
Which option is not a quadratic equation?
#quadratic-equations
#non-quadratic
#denominator
#medium
A \(4x^2-1=0\)
B \(x^2+2x=0\)
C \(x+\frac{1}{x}=2\)
D \(7x^2+3=0\)
Explanation opens after your attempt
Correct Answer
C. \(x+\frac{1}{x}=2\)
Step 1
Concept
In \(x+\frac{1}{x}=2\), the variable is in the denominator, so it is not directly in standard quadratic form. A quadratic polynomial form has no negative power.
Step 2
Why this answer is correct
The correct answer is C. \(x+\frac{1}{x}=2\). In \(x+\frac{1}{x}=2\), the variable is in the denominator, so it is not directly in standard quadratic form. A quadratic polynomial form has no negative power.
Step 3
Exam Tip
\(x+\frac{1}{x}=2\) में चर हर में है, इसलिए यह सीधे द्विघात मानक रूप में नहीं है। द्विघात बहुपद रूप में ऋणात्मक घात नहीं होती।
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Question 426/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(\frac{1}{3}x^2-\frac{2}{3}x+1=0\) का पूर्णांक गुणांकों वाला रूप कौन-सा है?
What is the form with integer coefficients for \(\frac{1}{3}x^2-\frac{2}{3}x+1=0\)?
#quadratic-equations
#fractional-coefficients
#medium
A \(x^2-2x+3=0\)
B \(x^2+2x+3=0\)
C \(3x^2-2x+1=0\)
D \(x^2-2x+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x+3=0\)
Step 1
Concept
Multiply the whole equation by (3) to remove the denominator (3). This gives \(x^2-2x+3=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x+3=0\). Multiply the whole equation by (3) to remove the denominator (3). This gives \(x^2-2x+3=0\).
Step 3
Exam Tip
हर (3) हटाने के लिए पूरे समीकरण को (3) से गुणा करें। इससे \(x^2-2x+3=0\) मिलता है।
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Question 427/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(\frac{x^2}{2}+3x-5=0\) को बिना भिन्न के मानक रूप में कौन-सा लिखा जाएगा?
How will \(\frac{x^2}{2}+3x-5=0\) be written in standard form without fractions?
#quadratic-equations
#fractions
#standard-form
#medium
A \(x^2+6x-10=0\)
B \(x^2+3x-5=0\)
C \(2x^2+3x-5=0\)
D \(x^2+6x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x-10=0\)
Step 1
Concept
Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-10=0\). Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 3
Exam Tip
पूरे समीकरण को (2) से गुणा करने पर \(x^2+6x-10=0\) मिलता है। भिन्न हटाने के लिए हर से गुणा करें।
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Question 428/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस समीकरण में (b=0) और (c<0) है?
Which equation has (b=0) and (c<0)?
#quadratic-equations
#coefficients
#missing-term
#medium
A \(x^2+5x-6=0\)
B \(3x^2-12=0\)
C \(2x^2+4=0\)
D \(x^2-x=0\)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-12=0\)
Step 1
Concept
In \(3x^2-12=0\), (b=0) and (c=-12). Treat the missing (x) term coefficient as (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-12=0\). In \(3x^2-12=0\), (b=0) and (c=-12). Treat the missing (x) term coefficient as (0).
Step 3
Exam Tip
\(3x^2-12=0\) में (b=0) और (c=-12) है। अनुपस्थित (x) पद का गुणांक (0) मानें।
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Question 429/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(2x^2+7x+3=0\) में (ac) का मान क्या है?
What is the value of (ac) in \(2x^2+7x+3=0\)?
#quadratic-equations
#coefficients
#ac-product
#medium
A (6)
B (7)
C (10)
D (3)
Explanation opens after your attempt
Step 1
Concept
Here (a=2) and (c=3), so (ac=6). The product (ac) is important in the splitting middle term method.
Step 2
Why this answer is correct
The correct answer is A. (6). Here (a=2) and (c=3), so (ac=6). The product (ac) is important in the splitting middle term method.
Step 3
Exam Tip
यहाँ (a=2) और (c=3), इसलिए (ac=6) है। मध्य पद विधि में (ac) महत्वपूर्ण होता है।
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Question 430/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2+7x+12=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?
Which factor form can represent \(x^2+7x+12=0\)?
#quadratic-equations
#factor-form
#medium
A ((x+3)(x+4)=0)
B ((x-3)(x-4)=0)
C ((x+2)(x+6)=0)
D ((x-1)(x+12)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+3)(x+4)=0)
Step 1
Concept
The product of (3) and (4) is (12), and their sum is (7). Therefore ((x+3)(x+4)=0) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)(x+4)=0). The product of (3) and (4) is (12), and their sum is (7). Therefore ((x+3)(x+4)=0) is correct.
Step 3
Exam Tip
(3) और (4) का गुणनफल (12) और योग (7) है। इसलिए ((x+3)(x+4)=0) सही है।
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Question 431/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(9x^2-25=0\) के मूल क्या हैं?
What are the roots of \(9x^2-25=0\)?
#quadratic-equations
#roots
#difference-of-squares
#medium
A \(x=\pm \frac{5}{3}\)
B \(x=\pm \frac{3}{5}\)
C \(x=\pm 5\)
D \(x=\pm 3\)
Explanation opens after your attempt
Correct Answer
A. \(x=\pm \frac{5}{3}\)
Step 1
Concept
\(9x^2=25\), so \(x^2=\frac{25}{9}\) and \(x=\pm \frac{5}{3}\). Take both signs while taking square roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=\pm \frac{5}{3}\). \(9x^2=25\), so \(x^2=\frac{25}{9}\) and \(x=\pm \frac{5}{3}\). Take both signs while taking square roots.
Step 3
Exam Tip
\(9x^2=25\), इसलिए \(x^2=\frac{25}{9}\) और \(x=\pm \frac{5}{3}\)। वर्गमूल लेते समय दोनों चिन्ह लें।
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Question 432/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2-8x=0\) के मूल कौन-से हैं?
What are the roots of \(x^2-8x=0\)?
#quadratic-equations
#roots
#factorisation
#medium
A (0,8)
B (0,-8)
C (1,8)
D (-1,8)
Explanation opens after your attempt
Step 1
Concept
(x-2 -8x=x(x-8)), so the roots are (0) and (8). Taking the common factor is an easy method.
Step 2
Why this answer is correct
The correct answer is A. (0,8). (x-2 -8x=x(x-8)), so the roots are (0) and (8). Taking the common factor is an easy method.
Step 3
Exam Tip
(x-2 -8x=x(x-8)), इसलिए मूल (0) और (8) हैं। समान गुणनखंड बाहर निकालना आसान तरीका है।
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Question 433/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
एक आयत की लंबाई चौड़ाई से (4) अधिक है और क्षेत्रफल (45) है। यदि चौड़ाई (x) है, तो समीकरण क्या होगा?
A rectangle has length (4) more than its breadth and area (45). If the breadth is (x), what is the equation?
#quadratic-equations
#area
#word-problem
#medium
A \(x^2+4x-45=0\)
B \(x^2-4x-45=0\)
C \(4x^2-45=0\)
D \(x^2+45x-4=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x-45=0\)
Step 1
Concept
The length is (x+4), so (x(x+4)=45). This forms \(x^2+4x-45=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x-45=0\). The length is (x+4), so (x(x+4)=45). This forms \(x^2+4x-45=0\).
Step 3
Exam Tip
लंबाई (x+4) होगी, इसलिए (x(x+4)=45)। इससे \(x^2+4x-45=0\) बनता है।
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Question 434/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
दो क्रमागत धनात्मक पूर्णांकों का गुणनफल (56) है। सही द्विघात समीकरण कौन-सा है?
The product of two consecutive positive integers is (56). Which quadratic equation is correct?
#quadratic-equations
#consecutive-integers
#word-problem
#medium
A \(x^2+x-56=0\)
B \(x^2-x-56=0\)
C (2x+1=56)
D \(x^2+2x-56=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-56=0\)
Step 1
Concept
The numbers are (x) and (x+1), so (x(x+1)=56). This gives \(x^2+x-56=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-56=0\). The numbers are (x) and (x+1), so (x(x+1)=56). This gives \(x^2+x-56=0\).
Step 3
Exam Tip
संख्याएँ (x) और (x+1) होंगी, इसलिए (x(x+1)=56)। इससे \(x^2+x-56=0\) मिलता है।
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Question 435/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
एक संख्या और उसके वर्ग का योग (42) है। सही समीकरण कौन-सा है?
The sum of a number and its square is (42). Which equation is correct?
#quadratic-equations
#word-problem
#equation-formation
#medium
A \(x^2+x-42=0\)
B \(x^2-x-42=0\)
C \(2x^2=42\)
D \(x^2+42x=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-42=0\)
Step 1
Concept
The sentence gives \(x^2+x=42\), that is \(x^2+x-42=0\). In word problems, write the algebraic form first.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-42=0\). The sentence gives \(x^2+x=42\), that is \(x^2+x-42=0\). In word problems, write the algebraic form first.
Step 3
Exam Tip
वाक्य से \(x^2+x=42\) बनता है, यानी \(x^2+x-42=0\)। शब्द प्रश्न में पहले बीजीय रूप लिखें।
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Question 436/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि मूल (-2) और (5) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-2) and (5), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2-3x-10=0\)
B \(x^2+3x-10=0\)
C \(x^2-7x+10=0\)
D \(x^2+7x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10=0\)
Step 1
Concept
The factors are ((x+2)) and ((x-5)), giving \(x^2-3x-10=0\). Make factors with signs opposite to the roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10=0\). The factors are ((x+2)) and ((x-5)), giving \(x^2-3x-10=0\). Make factors with signs opposite to the roots.
Step 3
Exam Tip
गुणनखंड ((x+2)) और ((x-5)) होंगे, जिनसे \(x^2-3x-10=0\) मिलता है। मूल के विपरीत चिन्ह वाले गुणनखंड बनाएं।
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Question 437/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस विकल्प में (x=1) और (x=4) मूल हैं?
Which option has roots (x=1) and (x=4)?
#quadratic-equations
#roots
#forming-equation
#medium
A \(x^2-5x+4=0\)
B \(x^2+5x+4=0\)
C \(x^2-4x+1=0\)
D \(x^2+4x-5=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x+4=0\)
Step 1
Concept
If the roots are (1) and (4), the factors are ((x-1)) and ((x-4)). Their product gives \(x^2-5x+4=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5x+4=0\). If the roots are (1) and (4), the factors are ((x-1)) and ((x-4)). Their product gives \(x^2-5x+4=0\).
Step 3
Exam Tip
मूल (1) और (4) हों तो गुणनखंड ((x-1)) और ((x-4)) होंगे। इनका गुणन \(x^2-5x+4=0\) देता है।
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Question 438/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(2x^2+3x+5=0\) के विवेचक का चिन्ह क्या है?
What is the sign of the discriminant of \(2x^2+3x+5=0\)?
#quadratic-equations
#discriminant
#negative
#medium
A धनात्मक / Positive
B शून्य / Zero
C ऋणात्मक / Negative
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. ऋणात्मक / Negative
Step 1
Concept
\(D=3^2-4\cdot2\cdot5=9-40=-31\), so it is negative. Calculate the full (4ac) term carefully.
Step 2
Why this answer is correct
The correct answer is C. ऋणात्मक / Negative. \(D=3^2-4\cdot2\cdot5=9-40=-31\), so it is negative. Calculate the full (4ac) term carefully.
Step 3
Exam Tip
\(D=3^2-4\cdot2\cdot5=9-40=-31\), इसलिए यह ऋणात्मक है। गणना में (4ac) को पूरा निकालें।
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Question 439/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2+6x+9=0\) में मूलों की प्रकृति क्या है?
What is the nature of roots of \(x^2+6x+9=0\)?
#quadratic-equations
#nature-of-roots
#discriminant
#medium
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
Here \(D=6^2-4\cdot1\cdot9=0\), so the roots are equal. (D=0) means two equal real roots.
Step 2
Why this answer is correct
The correct answer is B. दो समान वास्तविक मूल / Two equal real roots. Here \(D=6^2-4\cdot1\cdot9=0\), so the roots are equal. (D=0) means two equal real roots.
Step 3
Exam Tip
यहाँ \(D=6^2-4\cdot1\cdot9=0\), इसलिए मूल समान हैं। (D=0) का अर्थ दो समान वास्तविक मूल होता है।
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Question 440/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि (D=25) है, तो द्विघात समीकरण के वास्तविक मूलों के बारे में सही कथन क्या है?
If (D=25), what is correct about the real roots of the quadratic equation?
#quadratic-equations
#discriminant
#nature-of-roots
#medium
A दो भिन्न वास्तविक मूल होंगे / There will be two distinct real roots
B दो समान वास्तविक मूल होंगे / There will be two equal real roots
C कोई वास्तविक मूल नहीं होगा / There will be no real root
D घात (1) हो जाएगी / The degree will become (1)
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक मूल होंगे / There will be two distinct real roots
Step 1
Concept
Since (D=25>0), there will be two distinct real roots. The sign of (D) tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक मूल होंगे / There will be two distinct real roots. Since (D=25>0), there will be two distinct real roots. The sign of (D) tells the nature of roots.
Step 3
Exam Tip
(D=25>0), इसलिए दो भिन्न वास्तविक मूल होंगे। (D) का चिन्ह मूलों की प्रकृति बताता है।
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Question 441/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(4x^2+4x+1=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(4x^2+4x+1=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (8)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\). Correctly identifying (a,b,c) is necessary for the discriminant.
Step 2
Why this answer is correct
The correct answer is A. (0). Here \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\). Correctly identifying (a,b,c) is necessary for the discriminant.
Step 3
Exam Tip
यहाँ \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\) है। विवेचक में (a,b,c) सही पहचानना जरूरी है।
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Question 442/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि किसी द्विघात समीकरण में (a=2), (b=-7), (c=3) हैं, तो समीकरण कौन-सा है?
If a quadratic equation has (a=2), (b=-7), (c=3), which equation is it?
#quadratic-equations
#forming-equation
#coefficients
#medium
A \(2x^2+7x+3=0\)
B \(2x^2-7x+3=0\)
C \(3x^2-7x+2=0\)
D \(2x^2-3x+7=0\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2-7x+3=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(2x^2-7x+3=0\). Keep the negative sign of (b).
Step 2
Why this answer is correct
The correct answer is B. \(2x^2-7x+3=0\). Substituting in \(ax^2+bx+c=0\) gives \(2x^2-7x+3=0\). Keep the negative sign of (b).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(2x^2-7x+3=0\) मिलता है। (b) का ऋण चिन्ह साथ रखें।
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Question 443/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण ((x-5)2 =16) का मानक रूप कौन-सा है?
What is the standard form of ((x-5)2 =16)?
#quadratic-equations
#identity
#standard-form
#medium
A \(x^2-10x+9=0\)
B \(x^2-10x+41=0\)
C \(x^2+10x+9=0\)
D \(x^2-5x+16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+9=0\)
Step 1
Concept
((x-5)2 =x-2 -10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+9=0\). ((x-5)2 =x-2 -10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.
Step 3
Exam Tip
((x-5)2 =x-2 -10x+25), इसलिए \(x^2-10x+25-16=0\) मिलता है। वर्ग सूत्र लगाते समय मध्य पद न भूलें।
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Question 444/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
कौन-सा समीकरण द्विघात है लेकिन मानक रूप में नहीं लिखा गया है?
Which equation is quadratic but not written in standard form?
#quadratic-equations
#identify
#standard-form
#medium
A \(x^2+2x+1=0\)
B \(x^2=5x-4\)
C (3x+7=0)
D \(x^3+x=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2=5x-4\)
Step 1
Concept
\(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^2=5x-4\). \(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 3
Exam Tip
\(x^2=5x-4\) को \(x^2-5x+4=0\) बनाया जा सकता है, इसलिए यह द्विघात है। मानक रूप में दायां पक्ष (0) होना चाहिए।
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Question 445/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि (x=-2) समीकरण \(x^2+px-6=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-2) is a root of \(x^2+px-6=0\), what is the value of (p)?
#quadratic-equations
#parameter
#root
#medium
A (1)
B (-1)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-2) gives (4-2p-6=0), so (p=-1). When a root is given, use substitution.
Step 2
Why this answer is correct
The correct answer is B. (-1). Putting (x=-2) gives (4-2p-6=0), so (p=-1). When a root is given, use substitution.
Step 3
Exam Tip
(x=-2) रखने पर (4-2p-6=0), इसलिए (p=-1) मिलता है। मूल दिया हो तो प्रतिस्थापन करें।
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Question 446/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
क्या (x=3) समीकरण \(x^2-4x+3=0\) का मूल है?
Is (x=3) a root of \(x^2-4x+3=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=3) gives (9-12+3=0). To check a root, substitute the given value directly.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=3) gives (9-12+3=0). To check a root, substitute the given value directly.
Step 3
Exam Tip
(x=3) रखने पर (9-12+3=0) मिलता है। मूल जांचने के लिए दिए मान को सीधे समीकरण में रखें।
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Question 447/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(5x-2x^2=9\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(5x-2x^2=9\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#signs
#medium
A \(2x^2-5x+9=0\)
B \(2x^2+5x-9=0\)
C \(2x^2-5x-9=0\)
D \(2x^2+5x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+9=0\)
Step 1
Concept
Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+9=0\). Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 3
Exam Tip
सभी पद एक ओर लाकर \(-2x^2+5x-9=0\) मिलता है और (-1) से गुणा करने पर \(2x^2-5x+9=0\) मिलता है। मानक रूप में चिन्ह सावधानी से बदलें।
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Question 448/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(3x^2-2x+7=0\) के लिए (a+b+c) का मान क्या है?
For the equation \(3x^2-2x+7=0\), what is the value of (a+b+c)?
#quadratic-equations
#coefficients
#standard-form
#medium
A (8)
B (12)
C (6)
D (2)
Explanation opens after your attempt
Step 1
Concept
Here (a=3), (b=-2), (c=7), so (a+b+c=8). Always include the signs of coefficients.
Step 2
Why this answer is correct
The correct answer is A. (8). Here (a=3), (b=-2), (c=7), so (a+b+c=8). Always include the signs of coefficients.
Step 3
Exam Tip
यहाँ (a=3), (b=-2), (c=7), इसलिए (a+b+c=8) है। गुणांकों के चिन्ह हमेशा साथ लिखें।
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Question 449/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि ((k+1)x-2 -5x+6=0) एक द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?
If ((k+1)x-2 -5x+6=0) is a quadratic equation, what is the correct condition on (k)?
#quadratic-equations
#parameter
#condition
#medium
A (k=1)
B \(k\neq -1\)
C (k=-1)
D \(k\neq 1\)
Explanation opens after your attempt
Correct Answer
B. \(k\neq -1\)
Step 1
Concept
For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(k+1\neq 0\), so \(k\neq -1\).
Step 2
Why this answer is correct
The correct answer is B. \(k\neq -1\). For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(k+1\neq 0\), so \(k\neq -1\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(k+1\neq 0\), अर्थात \(k\neq -1\)।
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Question 450/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण ((2x-3)(x+4)=0) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((2x-3)(x+4)=0)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(2x^2+5x-12=0\)
B \(2x^2-5x-12=0\)
C \(2x^2+8x-3=0\)
D \(2x^2-11x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+5x-12=0\)
Step 1
Concept
Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+5x-12=0\). Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.
Step 3
Exam Tip
गुणा करने पर \(2x^2+8x-3x-12=0\), इसलिए \(2x^2+5x-12=0\) मिलता है। मध्य पदों को सही जोड़ना परीक्षा में जरूरी है।
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