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 241-250 of 600 questions.
For \(x^2+4x+k=0\) to have real roots, which condition on (k) is correct?
A. \(k\le4\)
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। \(16-4k\ge0\) से \(k\le4\) मिलता है। / For real roots \(D\ge0\) is required. From \(16-4k\ge0\), we get \(k\le4\).
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What will be the signs of both roots of \(x^2+9x+18=0\)?
A. दोनों ऋणात्मकBoth negative
मूल (-3) और (-6) हैं क्योंकि ((x+3)(x+6)=0)। योग ऋणात्मक और गुणनफल धनात्मक होने पर दोनों मूल ऋणात्मक होते हैं। / The roots are (-3) and (-6) because ((x+3)(x+6)=0). When the sum is negative and product is positive, both roots are negative.
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If the roots of \(x^2+ax+16=0\) are (4) and (4), what is the value of (a)?
A. (-8)
मूलों का योग (8) है और (-a=8) होगा। इसलिए (a=-8) है। / The sum of roots is (8), and (-a=8). Therefore (a=-8).
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What are the roots of \(8x^2-10x+3=0\)?
A. \(\frac{1}{2}\) और \(\frac{3}{4}\)\(\frac{1}{2}\) and \(\frac{3}{4}\)
(8x-2-10x+3=(2x-1)(4x-3)) है। इसलिए मूल \(\frac{1}{2}\) और \(\frac{3}{4}\) हैं। / (8x-2-10x+3=(2x-1)(4x-3)). Therefore the roots are \(\frac{1}{2}\) and \(\frac{3}{4}\).
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A. \(-b^2\)
\(\frac{c}{a}\) मूलों का गुणनफल होता है। यहां (b(-b)=-b-2) है। / \(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2).
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A. \(x^2+5x-14=0\)
मोनिक समीकरण (x-2-\(\alpha+\beta\)x+\alpha\beta=0) होता है। इसलिए \(x^2+5x-14=0\) सही है। / The monic equation is (x-2-\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+5x-14=0\) is correct.
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What is the sum of squares of the roots of \(x^2-7x+10=0\)?
A. (29)
यहां \(\alpha+\beta=7\) और \(\alpha\beta=10\) है। \(\alpha^2+\beta^2=49-20=29\) होगा। / Here \(\alpha+\beta=7\) and \(\alpha\beta=10\). Thus \(\alpha^2+\beta^2=49-20=29\).
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If (x=3) is a root of \(ax^2-8x+6=0\), what is the value of (a)?
A. (2)
(x=3) रखने पर (9a-24+6=0) इसलिए (9a=18) और (a=2)। अज्ञात गुणांक वाले प्रश्न में प्रतिस्थापन करें। / Putting (x=3) gives (9a-24+6=0), so (9a=18) and (a=2). Substitute in questions with an unknown coefficient.
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For \(x^2-18x+81=0\), what are the sum and product of roots respectively?
A. (18) और (81)(18) and (81)
यह ((x-9)2=0) है इसलिए दोनों मूल (9) हैं। योग (18) और गुणनफल (81) होगा। / It is ((x-9)2=0), so both roots are (9). The sum is (18) and the product is (81).
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A. (2)
यहां \(\alpha+\beta=\frac{7}{2}\) और \(\alpha\beta=\frac{3}{2}\) है। इसलिए \(\alpha+\beta-\alpha\beta=\frac{7}{2}-\frac{3}{2}=2\) होगा। / Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\). Therefore \(\alpha+\beta-\alpha\beta=\frac{7}{2}-\frac{3}{2}=2\).
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