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 431-440 of 550 questions.
If ((x+a)2=x-2+18x+81), what is the value of (a)?
A. (9)
((x+a)2=x-2+2ax+a-2) होता है। (2a=18) से (a=9) मिलता है। / ((x+a)2=x-2+2ax+a-2). From (2a=18), we get (a=9).
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What is the nature of roots of \(16x^2-24kx+9k^2=0\)?
A. दो समान वास्तविक मूलTwo equal real roots
यह ((4x-3k)2=0) के रूप में लिखा जा सकता है। इसलिए दोनों मूल समान वास्तविक होते हैं। / It can be written as ((4x-3k)2=0). Therefore both roots are equal and real.
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If one root of \(x^2+mx+36=0\) is the reciprocal of the other, what can be said about (m)?
A. ऐसा संभव नहीं हैIt is not possible
एक मूल दूसरे का व्युत्क्रम हो तो मूलों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (36) है, इसलिए ऐसा संभव नहीं है। / If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (36), so it is not possible.
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The roots of \(x^2+px+25=0\) are equal and positive. What is the value of (p)?
A. (-10)
समान मूलों के लिए \(p^2-100=0\) से \(p=\pm10\) मिलता है। धनात्मक समान मूल के लिए \(-\frac{p}{2}>0\), इसलिए (p=-10)। / For equal roots, \(p^2-100=0\) gives \(p=\pm10\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-10).
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If (x=2) is not a root of \(kx^2-7x+3=0\), what condition must (k) satisfy?
A. \(k\neq \frac{11}{4}\)
(x=2) रखने पर बायां पक्ष (4k-14+3=4k-11) होता है। मूल न होने के लिए \(4k-11\neq0\), इसलिए \(k\neq\frac{11}{4}\)। / Putting (x=2), the left side becomes (4k-14+3=4k-11). For it not to be a root, \(4k-11\neq0\), so \(k\neq\frac{11}{4}\).
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Which quadratic equation has sum of roots (0) and product (-121)?
A. \(x^2-121=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। योग (0) और गुणनफल (-121) रखने पर \(x^2-121=0\) मिलता है। \(/ The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-121) gives (x^2-121=0).\)
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If in \(4x^2+kx+28=0\), the product of roots is (-2) times the sum of roots, what is (k)?
A. (14)
गुणनफल (7) और योग \(-\frac{k}{4}\) है। (7=-2\left\(-\frac{k}{4}\right\)) से (k=14) मिलता है। / The product is (7) and the sum is \(-\frac{k}{4}\). From (7=-2\left\(-\frac{k}{4}\right\)), we get (k=14).
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What is the sum of cubes of the roots of \(x^2-5x-14=0\)?
A. (335)
मूलों का योग (5) और गुणनफल (-14) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=125+210=335)। / The sum of roots is (5) and the product is (-14). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=125+210=335).
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If the roots of \(x^2+bx+c=0\) are (-4) and (9), what is the value of (b+c)?
A. (-41)
मूलों का योग (5) है, इसलिए (b=-5), और गुणनफल (-36) है, इसलिए (c=-36)। अतः (b+c=-41)। / The sum of roots is (5), so (b=-5), and the product is (-36), so (c=-36). Therefore (b+c=-41).
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If (a=-2), what type of statement will ((a+2)x-2+\(a^2-4\)x+7=0) become?
A. विरोधाभासी कथनContradictory statement
(a=-2) रखने पर \(0x^2+0x+7=0\) मिलता है। यह (7=0) है, जो विरोधाभासी कथन है। / Putting (a=-2) gives \(0x^2+0x+7=0\). This is (7=0), which is a contradictory statement.
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