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 291-300 of 600 questions.
For \(x^2+6x+k=0\) to have real roots, which condition on (k) is correct?
A. \(k\le9\)
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। \(36-4k\ge0\) से \(k\le9\) मिलता है। / For real roots \(D\ge0\) is required. From \(36-4k\ge0\), we get \(k\le9\).
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What will be the signs of both roots of \(x^2+13x+42=0\)?
A. दोनों ऋणात्मकBoth negative
मूल (-6) और (-7) हैं क्योंकि ((x+6)(x+7)=0)। योग ऋणात्मक और गुणनफल धनात्मक होने पर दोनों मूल ऋणात्मक होते हैं। / The roots are (-6) and (-7) because ((x+6)(x+7)=0). When the sum is negative and product is positive, both roots are negative.
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If the roots of \(x^2+ax+25=0\) are (5) and (5), what is the value of (a)?
A. (-10)
मूलों का योग (10) है और (-a=10) होगा। इसलिए (a=-10) है। / The sum of roots is (10), and (-a=10). Therefore (a=-10).
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What are the roots of \(10x^2-17x+3=0\)?
A. \(\frac{3}{2}\) और \(\frac{1}{5}\)\(\frac{3}{2}\) and \(\frac{1}{5}\)
(10x-2-17x+3=(2x-3)(5x-1)) है। इसलिए मूल \(\frac{3}{2}\) और \(\frac{1}{5}\) हैं। / (10x-2-17x+3=(2x-3)(5x-1)). Therefore the roots are \(\frac{3}{2}\) and \(\frac{1}{5}\).
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A. \(-c^2\)
\(\frac{d}{a}\) मूलों का गुणनफल होता है। यहां (c(-c)=-c-2) है। / \(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2).
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A. \(x^2+7x-18=0\)
मोनिक समीकरण (x-2-\(\alpha+\beta\)x+\alpha\beta=0) होता है। इसलिए \(x^2+7x-18=0\) सही है। / The monic equation is (x-2-\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+7x-18=0\) is correct.
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What is the sum of squares of the roots of \(x^2-9x+14=0\)?
A. (53)
यहां \(\alpha+\beta=9\) और \(\alpha\beta=14\) है। \(\alpha^2+\beta^2=81-28=53\) होगा। / Here \(\alpha+\beta=9\) and \(\alpha\beta=14\). Thus \(\alpha^2+\beta^2=81-28=53\).
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If (x=4) is a root of \(ax^2-10x+8=0\), what is the value of (a)?
A. (2)
(x=4) रखने पर (16a-40+8=0) इसलिए (16a=32) और (a=2)। अज्ञात गुणांक में प्रतिस्थापन करें। / Putting (x=4) gives (16a-40+8=0), so (16a=32) and (a=2). Substitute when a coefficient is unknown.
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For \(x^2-22x+121=0\), what are the sum and product of roots respectively?
A. (22) और (121)(22) and (121)
यह ((x-11)2=0) है इसलिए दोनों मूल (11) हैं। योग (22) और गुणनफल (121) होगा। / It is ((x-11)2=0), so both roots are (11). The sum is (22) and the product is (121).
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A. \(\frac{17}{4}\)
यहां \(\alpha+\beta=\frac{5}{4}\) और \(\alpha\beta=-\frac{3}{2}\) है। इसलिए \(\alpha+\beta-2\alpha\beta=\frac{5}{4}+3=\frac{17}{4}\) होगा। / Here \(\alpha+\beta=\frac{5}{4}\) and \(\alpha\beta=-\frac{3}{2}\). Therefore \(\alpha+\beta-2\alpha\beta=\frac{5}{4}+3=\frac{17}{4}\).
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