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.
For which value will (x-2-(a+3)x+3a=0) have equal roots?
A. (a=3)
(D=(a+3)2-12a=(a-3)2) है। (D=0) के लिए (a=3) होगा। / (D=(a+3)2-12a=(a-3)2). For (D=0), (a=3).
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What will be the value of (r) for equal roots in (x-2-(r+4)x+4r=0)?
A. (r=4)
यहाँ (D=(r+4)2-16r=(r-4)2) है। समान मूलों के लिए (r=4) होगा। / Here (D=(r+4)2-16r=(r-4)2). For equal roots, (r=4).
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What is the correct condition on (a) for real roots of (x-2+2(a+1)x+a-2+3=0)?
A. \(a\ge1\)
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। यहाँ (D=4[(a+1)2-\(a^2+3\)]=8(a-1)), इसलिए \(a\ge1\)। / For real roots, \(D\ge0\) is required. Here (D=4[(a+1)2-\(a^2+3\)]=8(a-1)), so \(a\ge1\).
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What is (a) for real and equal roots of (x-2-2(a-3)x+a-2-9=0)?
A. (a=3)
(D=4(a-3)2-4\(a^2-9\)=24(3-a)) है। (D=0) से (a=3) मिलता है। / (D=4(a-3)2-4\(a^2-9\)=24(3-a)). From (D=0), (a=3).
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Under which condition will \(x^2-2sx+s+2=0\) have real and distinct roots?
A. (s<-1) या (s>2)(s<-1) or (s>2)
यहाँ (D=4s-2-4(s+2)=4(s-2)(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है। / Here (D=4s-2-4(s+2)=4(s-2)(s+1)). From (D>0), (s<-1) or (s>2).
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In which interval will (t) lie for \(x^2+2tx+t+4=0\) to have no real roots?
A. \(-\frac{3}{2}<t<2\)
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4(t-2)(2t+3)), इसलिए \(-\frac{3}{2}<t<2\)। / For no real roots, (D<0) is required. Here (D=4(t-2)(2t+3)), so \(-\frac{3}{2}<t<2\).
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Why are the roots of (2x-2-(3q+1)x+q=0) always real and distinct?
A. क्योंकि \(D=9q^2-2q+1>0\)Because \(D=9q^2-2q+1>0\)
यहाँ (D=(3q+1)2-8q=9q-2-2q+1) है। इसका अपना विविक्तकर ((-2)2-4(9)(1)<0) और मान सदैव धनात्मक है। / Here (D=(3q+1)2-8q=9q-2-2q+1). Its own discriminant ((-2)2-4(9)(1)<0), so it is always positive.
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What is correct about the real roots of (x-2+2x+\(p^2+2\)=0)?
A. कभी वास्तविक मूल नहीं होंगेIt will never have real roots
यहाँ (D=4-4\(p^2+2\)=-4\(p^2+1\)<0) है। इसलिए किसी भी वास्तविक (p) के लिए वास्तविक मूल नहीं होंगे। / Here (D=4-4\(p^2+2\)=-4\(p^2+1\)<0). So there are no real roots for any real (p).
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If \(x^2-2px+p^2-5p=0\) has real and distinct roots, what is the correct condition on (p)?
A. (p>0)
यहाँ (D=4p-2-4\(p^2-5p\)=20p) है। वास्तविक और भिन्न मूलों के लिए (D>0), अतः (p>0)। / Here (D=4p-2-4\(p^2-5p\)=20p). For real and distinct roots (D>0), hence (p>0).
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What condition on (u) is needed for real roots of \(x^2-2ux+u^2+7u=0\)?
A. \(u\le0\)
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। यहाँ (D=4u-2-4\(u^2+7u\)=-28u), इसलिए \(u\le0\)। / For real roots, \(D\ge0\) is needed. Here (D=4u-2-4\(u^2+7u\)=-28u), so \(u\le0\).
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