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 311-320 of 600 questions.
If \(kx^2-6x+9=0\) has equal roots and \(k\ne0\), what is the value of (k)?
A. (1)
बराबर मूलों के लिए (D=0) होता है। (36-36k=0) से (k=1) है। / For equal roots (D=0). From (36-36k=0), (k=1).
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How many real roots does \(x^2+2x+5=0\) have?
A. (0)
यहां (D=4-20=-16<0) है। इसलिए वास्तविक मूलों की संख्या (0) है। / Here (D=4-20=-16<0). Therefore the number of real roots is (0).
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If roots of (x-2-(a+1)x+a=0) are (1) and (a), why is it correct?
A. योग (a+1) और गुणनफल (a) हैSum is (a+1) and product is (a)
मूल (1) और (a) का योग (a+1) तथा गुणनफल (a) है। इसलिए मोनिक समीकरण (x-2-(a+1)x+a=0) बनता है। / The roots (1) and (a) have sum (a+1) and product (a). Therefore the monic equation is (x-2-(a+1)x+a=0).
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A. (15)
यहां \(\alpha+\beta=6\) और \(\alpha\beta=8\) है। (\(\alpha+1\)\(\beta+1\)=\alpha\beta+\alpha+\beta+1=15) है। / Here \(\alpha+\beta=6\) and \(\alpha\beta=8\). (\(\alpha+1\)\(\beta+1\)=\alpha\beta+\alpha+\beta+1=15).
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A. (-30)
(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)) होता है। यहां \(\alpha\beta=-10\) और \(\alpha+\beta=3\) इसलिए मान (-30) है। / (\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Here \(\alpha\beta=-10\) and \(\alpha+\beta=3\), so the value is (-30).
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A. \(\frac{17}{4}\)
यहां \(\alpha+\beta=\frac{5}{2}\) और \(\alpha\beta=1\) है। (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\(\alpha+\beta\)2-2\alpha\beta}{\(\alpha\beta\)2}=\frac{17}{4}) है। / Here \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=1\). (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\(\alpha+\beta\)2-2\alpha\beta}{\(\alpha\beta\)2}=\frac{17}{4}).
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If the roots of \(x^2+px+16=0\) are equal and both negative, what is the value of (p)?
A. (8)
बराबर मूलों के लिए मूल (-4) और (-4) होंगे क्योंकि गुणनफल (16) है। योग (-8) है इसलिए (-p=-8) से (p=8) है। / For equal roots, the roots are (-4) and (-4) because the product is (16). The sum is (-8), so (-p=-8) gives (p=8).
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If one root of \(x^2+ax+a=0\) is (1), what will be the other root?
A. \(-\frac{1}{2}\)
(x=1) रखने पर (1+2a=0) से \(a=-\frac{1}{2}\) है। गुणनफल (a) है इसलिए दूसरा मूल \(-\frac{1}{2}\) होगा। / Putting (x=1) gives (1+2a=0), so \(a=-\frac{1}{2}\). The product is (a), so the other root is \(-\frac{1}{2}\).
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If the difference of roots of \(x^2-5x+q=0\) is (1), what is the value of (q)?
A. (6)
मूलों का योग (5) और अंतर (1) है इसलिए मूल (3) और (2) हैं। उनका गुणनफल (q=6) है। / The sum of roots is (5) and the difference is (1), so the roots are (3) and (2). Their product is (q=6).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-Sx+P=0\), what is \(\alpha^2+\beta^2\) equal to?
A. \(S^2-2P\)
यहां मूलों का योग (S) और गुणनफल (P) है। इसलिए (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta=S-2-2P) है। / Here the sum of roots is (S) and product is (P). Therefore (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta=S-2-2P).
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