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 321-330 of 600 questions.
For which (m) will (mx-2+(m+3)x+3=0) have equal roots and remain quadratic?
A. (m=3)
(D=(m+3)2-12m=(m-3)2) है। (D=0) से (m=3) और \(m\neq0\) भी संतुष्ट है। / (D=(m+3)2-12m=(m-3)2). From (D=0), (m=3), and \(m\neq0\) is also satisfied.
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What is the value of (a) for equal roots of ((a-1)x-2+2ax+(a+3)=0)?
A. \(a=\frac{3}{2}\)
यहाँ (D=(2a)2-4(a-1)(a+3)=4(3-2a)) है। (D=0) से \(a=\frac{3}{2}\)। / Here (D=(2a)2-4(a-1)(a+3)=4(3-2a)). From (D=0), \(a=\frac{3}{2}\).
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What is the correct condition on \(\lambda\) for real roots of (x-2+2\(\lambda-1\)x+\lambda-2+1=0)?
A. \(\lambda\le0\)
यहाँ (D=4\(\lambda-1\)2-4\(\lambda^2+1\)=-8\lambda) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(\lambda\le0\)। / Here (D=4\(\lambda-1\)2-4\(\lambda^2+1\)=-8\lambda). For real roots \(D\ge0\), so \(\lambda\le0\).
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If (x-2-2\(\alpha+2\)x+\alpha-2=0) has real and distinct roots, what is the condition on \(\alpha\)?
A. \(\alpha>-1\)
(D=4\(\alpha+2\)2-4\alpha-2=16\(\alpha+1\)) है। (D>0) से \(\alpha>-1\) मिलता है। / (D=4\(\alpha+2\)2-4\alpha-2=16\(\alpha+1\)). From (D>0), \(\alpha>-1\).
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What is (h) for equal roots of (x-2+(2h-1)x+h-2=0)?
A. \(h=\frac{1}{4}\)
यहाँ (D=(2h-1)2-4h-2=1-4h) है। (D=0) रखने पर \(h=\frac{1}{4}\)। / Here (D=(2h-1)2-4h-2=1-4h). Putting (D=0) gives \(h=\frac{1}{4}\).
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For which (n) will (x-2+(n+2)x+2n=0) have equal roots?
A. (n=2)
(D=(n+2)2-8n=(n-2)2) है। समान मूलों के लिए (D=0), इसलिए (n=2)। / (D=(n+2)2-8n=(n-2)2). For equal roots (D=0), so (n=2).
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What is the condition on (k) for real roots of (4x-2-4(k+1)x+\(k^2+2k\)=0)?
A. सभी वास्तविक (k)All real (k)
यहाँ (D=16(k+1)2-16\(k^2+2k\)=16) है। इसलिए (D>0) हर वास्तविक (k) के लिए है। / Here (D=16(k+1)2-16\(k^2+2k\)=16). Thus (D>0) for every real (k).
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What is the nature of roots of (9x-2-6(k-1)x+(k-1)2=0)?
A. हमेशा वास्तविक और समानAlways real and equal
यहाँ (D=[-6(k-1)]2-4(9)(k-1)2=0) है। अतः हर (k) के लिए मूल वास्तविक और समान हैं। / Here (D=[-6(k-1)]2-4(9)(k-1)2=0). Hence roots are real and equal for every (k).
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Which equation gives real, irrational and distinct roots?
A. \(x^2-10x+23=0\)
पहले समीकरण में (D=100-92=8>0) है और (8) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न हैं। / In the first equation, (D=100-92=8>0), and (8) is not a perfect square. So the roots are real, irrational and distinct.
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If the discriminant of an equation is (D=(m-5)2), when will the roots be equal?
A. (m=5)
समान मूलों के लिए (D=0) चाहिए। ((m-5)2=0) से (m=5) मिलता है। / For equal roots, (D=0) is needed. From ((m-5)2=0), (m=5).
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