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 421-430 of 550 questions.
A. (48)
(r+3r=16) से (r=4) मिलता है, इसलिए मूल (4) और (12) हैं। स्थिर पद मूलों का गुणनफल (48) होगा। / From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).
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Which statement is correct for \(x^2-8x+17=0\)?
A. वास्तविक मूल नहीं हैंIt has no real roots
यहाँ (D=(-8)2-4\cdot1\cdot17=-4<0) है। इसलिए वास्तविक मूल नहीं होंगे। / Here (D=(-8)2-4\cdot1\cdot17=-4<0). Therefore it has no real roots.
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If one root of (x-2-(m+5)x+5m=0) is (5), what is the other root?
A. (m)
मूलों का गुणनफल (5m) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{5m}{5}=m\) है। / The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).
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What is the difference between the roots of \(3x^2-14x+16=0\)?
A. \( \frac{2}{3} \)
मूल (2) और \(\frac{8}{3}\) हैं। उनका अंतर \(\frac{8}{3}-2=\frac{2}{3}\) है। / The roots are (2) and \(\frac{8}{3}\). Their difference is \(\frac{8}{3}-2=\frac{2}{3}\).
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If \(x^2+10x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
A. (25)
पूर्ण वर्ग के लिए (x-2+10x+c=(x+5)2) होना चाहिए। इसलिए (c=25) होगा। / For a perfect square, (x-2+10x+c=(x+5)2) is needed. Hence (c=25).
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If both roots of \(x^2+bx+64=0\) are equal and their value is (-8), what is (b)?
A. (16)
दोनों मूल (-8) हैं, इसलिए योग (-16) है। यहाँ मूलों का योग (-b) है, अतः (b=16)। / Both roots are (-8), so the sum is (-16). Here the sum of roots is (-b), so (b=16).
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In which option will the sum of roots be positive and the product of roots be negative?
A. \(x^2-6x-16=0\)
पहले विकल्प में योग \(-\frac{b}{a}=6\) और गुणनफल \(\frac{c}{a}=-16\) है। इसलिए योग धनात्मक और गुणनफल ऋणात्मक है। / In the first option, the sum is \(-\frac{b}{a}=6\) and the product is \(\frac{c}{a}=-16\). So the sum is positive and the product is negative.
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A rectangle has length (x+8) and breadth (x-5). If its area is (104), which equation is correct?
A. \(x^2+3x-144=0\)
क्षेत्रफल ((x+8)(x-5)=104) होगा। विस्तार से \(x^2+3x-40=104\), इसलिए \(x^2+3x-144=0\)। / The area is ((x+8)(x-5)=104). Expanding gives \(x^2+3x-40=104\), so \(x^2+3x-144=0\).
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Two numbers have sum (15) and product (54). They can be roots of which quadratic equation?
A. \(x^2-15x+54=0\)
यदि मूलों का योग (15) और गुणनफल (54) है, तो समीकरण \(x^2-15x+54=0\) होगा। मोनिक रूप का सूत्र याद रखें। / If the sum of roots is (15) and product is (54), the equation is \(x^2-15x+54=0\). Remember the monic form formula.
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If \(\alpha,\beta\) are roots of \(x^2-11x+30=0\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
A. \( \frac{11}{30} \)
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ मान \(\frac{11}{30}\) है। / \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{11}{30}\).
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