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 281-290 of 600 questions.
If (x=0) is a root of \(2x^2+mx+n=0\), what will be the value of (n)?
A. (0)
(x=0) रखने पर केवल (n) बचता है। इसलिए (n=0) होना चाहिए। / Putting (x=0) leaves only (n). Therefore (n=0) must hold.
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If (x=3) and (x=8) are roots of a monic quadratic equation, what will be the coefficient of (x)?
A. (-11)
मूलों का योग (3+8=11) है। मोनिक समीकरण में (x) का गुणांक (-(योग)=-11) होता है। \(/ The sum of roots is (3+8=11). In a monic equation the coefficient of (x) is (-(\)sum\()=-11).\)
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What are the roots of \(4x^2+3x-10=0\)?
A. \(\frac{5}{4}\) और (-2)\(\frac{5}{4}\) and (-2)
(4x-2+3x-10=(4x-5)(x+2)) है। इसलिए मूल \(\frac{5}{4}\) और (-2) हैं। / (4x-2+3x-10=(4x-5)(x+2)). Therefore the roots are \(\frac{5}{4}\) and (-2).
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If the roots of \(x^2+mx+30=0\) are (-5) and (-6), what is the value of (m)?
A. (11)
मूलों का योग (-11) है और (-m=-11) होगा। इसलिए (m=11) है। / The sum of roots is (-11), and (-m=-11). Therefore (m=11).
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A. वे एक दूसरे के व्युत्क्रम हैंThey are reciprocals of each other
\(6\cdot\frac{1}{6}=1\) है इसलिए दोनों व्युत्क्रम मूल हैं। व्युत्क्रम मूलों का गुणनफल (1) होता है। / \(6\cdot\frac{1}{6}=1\), so the roots are reciprocals. Reciprocal roots have product (1).
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What is the positive root of \(x^2-7x-30=0\)?
A. (10)
(x-2-7x-30=(x-10)(x+3)) है। इसलिए मूल (10) और (-3) हैं तथा धनात्मक मूल (10) है। / (x-2-7x-30=(x-10)(x+3)). Therefore the roots are (10) and (-3), and the positive root is (10).
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If (D=0) and the sum of roots is (14), what will each root be?
A. (7)
(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{14}{2}=7\) होगा। / When (D=0), both roots are equal. Therefore each root is \(\frac{14}{2}=7\).
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What is the difference between the roots of \(x^2-8x-9=0\)?
A. (10)
(x-2-8x-9=(x-9)(x+1)) है। मूल (9) और (-1) हैं इसलिए अंतर (10) है। / (x-2-8x-9=(x-9)(x+1)). The roots are (9) and (-1), so the difference is (10).
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If \(\alpha\) and \(\beta\) are roots of \(4x^2-20x+7=0\), what is \(\alpha+\beta\)?
A. (5)
मूलों का योग \(-\frac{b}{a}=-\frac{-20}{4}=5\) है। सूत्र में (b) का चिन्ह सही रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-20}{4}=5\). Keep the sign of (b) correct in the formula.
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If \(\alpha\) and \(\beta\) are roots of \(6x^2+5x-4=0\), what is \(\alpha\beta\)?
A. -\(\frac{2}{3}\)
मूलों का गुणनफल \(\frac{c}{a}=\frac{-4}{6}=-\frac{2}{3}\) होता है। (c) का चिन्ह न भूलें। / The product of roots is \(\frac{c}{a}=\frac{-4}{6}=-\frac{2}{3}\). Do not forget the sign of (c).
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