Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 211-220 of 600 questions.
What is the discriminant (D) of \(3x^2-6x+3=0\)?
A. (0)
यहां \(D=b^2-4ac=36-36=0\) है। इसलिए दोनों वास्तविक मूल बराबर होंगे। / Here \(D=b^2-4ac=36-36=0\). Therefore the two real roots will be equal.
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If (D=64) for a quadratic equation, what will be the nature of its real roots?
A. दो भिन्न वास्तविक मूलTwo distinct real roots
क्योंकि (D=64>0) है इसलिए दो भिन्न वास्तविक मूल होंगे। (D>0) होने पर मूल अलग अलग होते हैं। / Since (D=64>0), there will be two distinct real roots. When (D>0), the roots are different.
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Which statement is correct about the real roots of \(x^2-4x+13=0\)?
C. कोई वास्तविक मूल नहीं हैIt has no real roots
यहां (D=(-4)2-4(1)(13)=-36<0) है। इसलिए कोई वास्तविक मूल नहीं है। / Here (D=(-4)2-4(1)(13)=-36<0). Therefore there are no real roots.
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For \(x^2-8x+k=0\) to have equal real roots, what should be the value of (k)?
A. (16)
बराबर मूलों के लिए (D=0) होता है। (64-4k=0) से (k=16) मिलता है। / For equal roots (D=0). From (64-4k=0), we get (k=16).
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If the sum of roots is (9) and product is (18), which monic quadratic equation is formed?
A. \(x^2-9x+18=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। इसलिए \(x^2-9x+18=0\) सही है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-9x+18=0) is correct.\)
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If one root of \(x^2-15x+54=0\) is (6), what is the other root?
A. (9)
मूलों का गुणनफल (54) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{54}{6}=9\) है। / The product of roots is (54) and one root is (6). Therefore the other root is \(\frac{54}{6}=9\).
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A. (12)
नए मूलों का योग (3\alpha+3\beta=3\(\alpha+\beta\)=12) है। गुणक लगे मूलों में योग पर भी वही गुणक लगता है। / The sum of new roots is (3\alpha+3\beta=3\(\alpha+\beta\)=12). When roots are multiplied by a factor, the sum is multiplied by the same factor.
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A. (25)
(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta=49-24=25) है। ऐसे प्रश्नों में पहचान का प्रयोग करें। / (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta=49-24=25). Use identities in such questions.
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A. \(\frac{5}{14}\)
यहां \(\alpha+\beta=-5\) और \(\alpha\beta=-14\) है। इसलिए \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{-5}{-14}=\frac{5}{14}\) है। / Here \(\alpha+\beta=-5\) and \(\alpha\beta=-14\). Therefore \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{-5}{-14}=\frac{5}{14}\).
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For \(3x^2-14x+8=0\), what are the sum and product of roots respectively?
A. \(\frac{14}{3}\) और \(\frac{8}{3}\)\(\frac{14}{3}\) and \(\frac{8}{3}\)
योग \(-\frac{b}{a}=\frac{14}{3}\) और गुणनफल \(\frac{c}{a}=\frac{8}{3}\) है। पहले (a), (b), (c) पहचानें। / The sum is \(-\frac{b}{a}=\frac{14}{3}\) and the product is \(\frac{c}{a}=\frac{8}{3}\). Identify (a), (b), and (c) first.
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