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 471-480 of 550 questions.
If \(x^2-18x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
A. (81)
पूर्ण वर्ग के लिए (x-2-18x+c=(x-9)2) होना चाहिए। इसलिए (c=81) होगा। / For a perfect square, (x-2-18x+c=(x-9)2) is needed. Hence (c=81).
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If both roots of \(x^2+bx+100=0\) are equal and their value is (-10), what is (b)?
A. (20)
दोनों मूल (-10) हैं, इसलिए योग (-20) है। यहाँ मूलों का योग (-b) है, अतः (b=20)। / Both roots are (-10), so the sum is (-20). Here the sum of roots is (-b), so (b=20).
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In which option will the sum of roots be negative and the product of roots be negative?
A. \(x^2+5x-24=0\)
पहले विकल्प में योग \(-\frac{b}{a}=-5\) और गुणनफल \(\frac{c}{a}=-24\) है। इसलिए दोनों ऋणात्मक हैं। / In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.
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A rectangle has length (x+9) and breadth (x-6). If its area is (130), which equation is correct?
A. \(x^2+3x-184=0\)
क्षेत्रफल ((x+9)(x-6)=130) होगा। विस्तार से \(x^2+3x-54=130\), इसलिए \(x^2+3x-184=0\)। / The area is ((x+9)(x-6)=130). Expanding gives \(x^2+3x-54=130\), so \(x^2+3x-184=0\).
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Two numbers have sum (17) and product (72). They can be roots of which quadratic equation?
A. \(x^2-17x+72=0\)
यदि मूलों का योग (17) और गुणनफल (72) है, तो समीकरण \(x^2-17x+72=0\) होगा। मोनिक रूप का सूत्र याद रखें। / If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
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If \(\alpha,\beta\) are roots of \(x^2-13x+42=0\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
A. \( \frac{13}{42} \)
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ मान \(\frac{13}{42}\) है। / \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{13}{42}\).
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If ((x+a)2=x-2-20x+100), what is the value of (a)?
A. (-10)
((x+a)2=x-2+2ax+a-2) होता है। (2a=-20) से (a=-10) मिलता है। / ((x+a)2=x-2+2ax+a-2). From (2a=-20), we get (a=-10).
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What is the nature of roots of \(25x^2+40kx+16k^2=0\)?
A. दो समान वास्तविक मूलTwo equal real roots
यह ((5x+4k)2=0) के रूप में लिखा जा सकता है। इसलिए दोनों मूल समान वास्तविक होते हैं। / It can be written as ((5x+4k)2=0). Therefore both roots are equal and real.
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If one root of \(x^2+mx+49=0\) 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 (49) 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 (49), so it is not possible.
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The roots of \(x^2+px+36=0\) are equal and positive. What is the value of (p)?
A. (-12)
समान मूलों के लिए \(p^2-144=0\) से \(p=\pm12\) मिलता है। धनात्मक समान मूल के लिए \(-\frac{p}{2}>0\), इसलिए (p=-12)। / For equal roots, \(p^2-144=0\) gives \(p=\pm12\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-12).
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