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 581-590 of 600 questions.
B. (18)
\(\alpha+\beta=9\) और \(\alpha\beta=n\) है। (81-2n=45) से (n=18) मिलता है। / Here \(\alpha+\beta=9\) and \(\alpha\beta=n\). From (81-2n=45), we get (n=18).
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If the roots of \(7x^2-6x+\lambda=0\) are not real, what is the correct condition on \(\lambda\)?
A. \(\lambda>\frac{9}{7}\)
वास्तविक नहीं होने के लिए (D<0) चाहिए। \(36-28\lambda<0\) से \(\lambda>\frac{9}{7}\) मिलता है। / For non-real roots, (D<0) is required. From \(36-28\lambda<0\), we get \(\lambda>\frac{9}{7}\).
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If the roots of \(x^2-16x+q=0\) are in the ratio (5:3), what is the value of (q)?
C. (60)
जड़ें (5r) और (3r) मानें। (8r=16) से (r=2), इसलिए गुणनफल \(15r^2=60\) है। / Let the roots be (5r) and (3r). From (8r=16), (r=2), so the product is \(15r^2=60\).
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What are the roots of (x-2-(u+2v)x+2uv=0)?
A. (u) और (2v)(u) and (2v)
जड़ों का योग (u+2v) और गुणनफल (2uv) है। ये (u) और (2v) से मेल खाते हैं। / The sum of roots is (u+2v) and the product is (2uv). These match (u) and (2v).
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If \(\alpha,\beta\) are roots of \(x^2-7x+r=0\) and \(\alpha^2\beta+\alpha\beta^2=84\), what is (r)?
B. (12)
(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)) होता है। यहाँ \(\alpha+\beta=7\), इसलिए (7r=84) और (r=12)। / We use (\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Here \(\alpha+\beta=7\), so (7r=84) and (r=12).
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If \(\alpha,\beta\) are roots of \(x^2-5x+1=0\), what is \(\alpha^4+\beta^4\)?
A. (527)
\(\alpha+\beta=5\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=23\), फिर \(\alpha^4+\beta^4=23^2-2=527\)। / Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=23\), then \(\alpha^4+\beta^4=23^2-2=527\).
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If both roots of \(x^2-14x+m=0\) are prime numbers, what is the sum of possible values of (m)?
D. (94)
योग (14) वाली अभाज्य जोड़ियाँ ((3,11)) और ((7,7)) हैं। इसलिए (m=33) या (m=49), और योग (82) है, अतः विकल्पों में कोई सही नहीं है। / The prime pairs with sum (14) are ((3,11)) and ((7,7)). Thus (m=33) or (m=49), and the sum is (82), so none of the options is correct.
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If \(x^2+px+64=0\) has equal and positive roots, what is the value of (p)?
A. (-16)
समान जड़ों के लिए \(p^2-256=0\), इसलिए \(p=\pm16\)। समान जड़ \(-\frac{p}{2}\) धनात्मक होनी चाहिए, अतः (p=-16)। / For equal roots, \(p^2-256=0\), so \(p=\pm16\). The equal root \(-\frac{p}{2}\) must be positive, hence (p=-16).
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If \(\alpha,\beta\) are roots of \(4x^2-20x+9=0\), what is the positive value of \(\alpha-\beta\)?
B. \(\frac{7}{2}\)
\(\alpha+\beta=5\) और \(\alpha\beta=\frac{9}{4}\) है। (\(\alpha-\beta\)2=25-9=16), इसलिए धनात्मक अंतर (4) है, अतः विकल्प (A) सही होना चाहिए। / Here \(\alpha+\beta=5\) and \(\alpha\beta=\frac{9}{4}\). Thus (\(\alpha-\beta\)2=25-9=16), so the positive difference is (4); option (A) should be correct.
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A. (4)
\(\alpha+\beta=5\) और \(\alpha\beta=\frac{9}{4}\) है। (\(\alpha-\beta\)2=25-9=16), इसलिए धनात्मक अंतर (4) है। / Here \(\alpha+\beta=5\) and \(\alpha\beta=\frac{9}{4}\). Since (\(\alpha-\beta\)2=25-9=16), the positive difference is (4).
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