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 381-390 of 600 questions.
If (x-2-4x+(m+4)=0) has no real roots, which condition on (m) is correct?
A. (m>0)
वास्तविक मूल नहीं होने के लिए (D<0) चाहिए। (16-4(m+4)<0) से (m>0) मिलता है। / For no real roots (D<0) is required. From (16-4(m+4)<0), we get (m>0).
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If roots of (x-2-2(m+2)x+(m+2)2=0) are equal, what is true for (m)?
A. हर वास्तविक (m)Every real (m)
समीकरण ((x-(m+2))2=0) बनता है। इसलिए हर वास्तविक (m) के लिए दोनों मूल बराबर होंगे। / The equation becomes ((x-(m+2))2=0). Therefore the roots are equal for every real (m).
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A. (4)
यहां \(\alpha+\beta=9\) और \(\alpha\beta=18\) है। (\(\alpha-2\)\(\beta-2\)=18-2(9)+4=4) है। / Here \(\alpha+\beta=9\) and \(\alpha\beta=18\). (\(\alpha-2\)\(\beta-2\)=18-2(9)+4=4).
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If (3) and (-4) are roots, what is the value of \(\frac{q}{5}\) in \(5x^2+px+q=0\)?
A. (-12)
मूलों का गुणनफल \(\frac{q}{5}\) होता है। (3\cdot(-4)=-12) इसलिए \(\frac{q}{5}=-12\) है। / The product of roots is \(\frac{q}{5}\). Since (3\cdot(-4)=-12), \(\frac{q}{5}=-12\).
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If roots of \(x^2+px+q=0\) are (5) and (-2), what is the value of (p-q)?
A. (7)
योग (3) है इसलिए (p=-3) और गुणनफल (-10) है इसलिए (q=-10)। अतः (p-q=-3-(-10)=7) है। / The sum is (3), so (p=-3), and the product is (-10), so (q=-10). Thus (p-q=-3-(-10)=7).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-6x+2=0\), what is the value of \(\alpha^2+\beta^2\)?
A. (32)
यहां \(\alpha+\beta=6\) और \(\alpha\beta=2\) है। \(\alpha^2+\beta^2=36-4=32\) है। / Here \(\alpha+\beta=6\) and \(\alpha\beta=2\). \(\alpha^2+\beta^2=36-4=32\).
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A. (6)
यहां \(\alpha+\beta=-2\) और \(\alpha\beta=-2\) है। (\alpha-2+\alpha\beta+\beta-2=\(\alpha+\beta\)2-\alpha\beta=6) है। / Here \(\alpha+\beta=-2\) and \(\alpha\beta=-2\). (\alpha-2+\alpha\beta+\beta-2=\(\alpha+\beta\)2-\alpha\beta=6).
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Which can be the roots of (x-2-(2m+3)x+(m+1)(m+2)=0)?
A. (m+1) और (m+2)(m+1) and (m+2)
(m+1+m+2=2m+3) और गुणनफल ((m+1)(m+2)) है। इसलिए मूल (m+1) और (m+2) हो सकते हैं। / (m+1+m+2=2m+3), and the product is ((m+1)(m+2)). Therefore the roots can be (m+1) and (m+2).
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A. (8)
यहां \(\alpha+\beta=10\) और \(\alpha\beta=24\) है। (\(\alpha-2\)\(\beta-2\)=24-20+4=8) है। / Here \(\alpha+\beta=10\) and \(\alpha\beta=24\). (\(\alpha-2\)\(\beta-2\)=24-20+4=8).
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A. (1)
समीकरण के मूल (6) और (7) हैं। इसलिए छोटा मूल (6) और बड़ा मूल (7) है तथा \(\beta-\alpha=1\) है। / The roots are (6) and (7). Thus the smaller root is (6) and the larger root is (7), so \(\beta-\alpha=1\).
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