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 361-370 of 600 questions.
How many real roots does \(x^2+4x+13=0\) have?
A. (0)
यहां (D=16-52=-36<0) है। इसलिए वास्तविक मूलों की संख्या (0) है। / Here (D=16-52=-36<0). Therefore the number of real roots is (0).
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If roots of (x-2-(a+2)x+2a=0) are (2) and (a), which reason is correct?
A. योग (a+2) और गुणनफल (2a) हैSum is (a+2) and product is (2a)
मूल (2) और (a) का योग (a+2) तथा गुणनफल (2a) है। इसलिए दिया गया मोनिक समीकरण सही बनता है। / The roots (2) and (a) have sum (a+2) and product (2a). Therefore the given monic equation is correct.
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A. (32)
यहां \(\alpha+\beta=8\) और \(\alpha\beta=12\) है। (\(\alpha+2\)\(\beta+2\)=12+2(8)+4=32) है। / Here \(\alpha+\beta=8\) and \(\alpha\beta=12\). (\(\alpha+2\)\(\beta+2\)=12+2(8)+4=32).
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A. (-84)
(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)) होता है। यहां \(\alpha\beta=-21\) और \(\alpha+\beta=4\) इसलिए मान (-84) है। / (\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Here \(\alpha\beta=-21\) and \(\alpha+\beta=4\), so the value is (-84).
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A. \(\frac{7}{4}\)
यहां \(\alpha+\beta=\frac{8}{3}\) और \(\alpha\beta=\frac{4}{3}\) है। मान (\frac{\(\alpha+\beta\)2-2\alpha\beta}{\(\alpha\beta\)2}=\frac{7}{4}) है। / Here \(\alpha+\beta=\frac{8}{3}\) and \(\alpha\beta=\frac{4}{3}\). The value is (\frac{\(\alpha+\beta\)2-2\alpha\beta}{\(\alpha\beta\)2}=\frac{7}{4}).
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If the roots of \(x^2+px+25=0\) are equal and both negative, what is the value of (p)?
A. (10)
बराबर ऋणात्मक मूल (-5) और (-5) होंगे क्योंकि गुणनफल (25) है। योग (-10) है इसलिए (p=10) है। / The equal negative roots are (-5) and (-5) because the product is (25). The sum is (-10), so (p=10).
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If one root of \(x^2+ax+a=0\) is (2), what will be the other root?
A. \(-\frac{2}{3}\)
(x=2) रखने पर (4+3a=0) से \(a=-\frac{4}{3}\) है। गुणनफल (a) है इसलिए दूसरा मूल \(-\frac{2}{3}\) होगा। / Putting (x=2) gives (4+3a=0), so \(a=-\frac{4}{3}\). The product is (a), so the other root is \(-\frac{2}{3}\).
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If the difference of roots of \(x^2-7x+q=0\) is (1), what is the value of (q)?
A. (12)
मूलों का योग (7) और अंतर (1) है इसलिए मूल (4) और (3) हैं। उनका गुणनफल (q=12) है। / The sum of roots is (7) and the difference is (1), so the roots are (4) and (3). Their product is (q=12).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-Sx+P=0\), what is (\(\alpha-\beta\)2) equal to?
A. \(S^2-4P\)
यहां मूलों का योग (S) और गुणनफल (P) है। इसलिए (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta=S-2-4P) है। / Here the sum of roots is (S) and product is (P). Therefore (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta=S-2-4P).
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A. \(x^2-8x-9=0\)
पुराने मूल (8) और (-2) हैं। नए मूल (9) और (-1) होंगे इसलिए समीकरण \(x^2-8x-9=0\) है। / The old roots are (8) and (-2). The new roots are (9) and (-1), so the equation is \(x^2-8x-9=0\).
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