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 341-350 of 600 questions.
When will the roots of (x-2-(a+b)x+ab=0) be equal?
A. (a=b)
यहाँ (D=(a+b)2-4ab=(a-b)2) है। समान मूलों के लिए (D=0), अतः (a=b)। / Here (D=(a+b)2-4ab=(a-b)2). For equal roots (D=0), hence (a=b).
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If \(a\neq b\), what will be the nature of roots of (x-2-(a+b)x+ab=0)?
A. वास्तविक और भिन्नReal and distinct
इसका (D=(a-b)2) है। \(a\neq b\) होने पर (D>0), इसलिए मूल वास्तविक और भिन्न हैं। / Its (D=(a-b)2). When \(a\neq b\), (D>0), so the roots are real and distinct.
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What is the nature of roots of (x-2+2(a+1)x+a-2+2a+5=0)?
A. वास्तविक मूल नहींNo real roots
यहाँ (D=4(a+1)2-4\(a^2+2a+5\)=-16<0) है। इसलिए वास्तविक मूल नहीं होंगे। / Here (D=4(a+1)2-4\(a^2+2a+5\)=-16<0). So there will be no real roots.
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If \(x^2-2mx+3m=0\) has real and equal roots, which values of (m) are obtained?
A. (m=0) या (m=3)(m=0) or (m=3)
(D=4m-2-12m=4m(m-3)) है। (D=0) से (m=0) या (m=3) मिलता है। / (D=4m-2-12m=4m(m-3)). From (D=0), (m=0) or (m=3).
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What condition on (m) gives real and distinct roots for \(x^2-2mx+3m=0\)?
A. (m<0) या (m>3)(m<0) or (m>3)
यहाँ (D=4m(m-3)) है। (D>0) से (m<0) या (m>3) मिलता है। / Here (D=4m(m-3)). From (D>0), (m<0) or (m>3).
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Which interval is correct for \(x^2-2mx+3m=0\) to have no real roots?
A. (0<m<3)
वास्तविक मूल न होने के लिए (D<0) चाहिए। (D=4m(m-3)<0) से (0<m<3) मिलता है। / For no real roots, (D<0) is needed. From (D=4m(m-3)<0), we get (0<m<3).
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If \(x^2+2kx+k^2-4k+8=0\) has real roots, what is the condition on (k)?
A. \(k\ge2\)
यहाँ (D=4k-2-4\(k^2-4k+8\)=16(k-2)) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(k\ge2\)। / Here (D=4k-2-4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
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If \(x^2+2kx+k^2-4k+8=0\) has real and equal roots, what is the value of (k)?
A. (k=2)
समान मूलों के लिए (D=0) चाहिए। (16(k-2)=0) से (k=2) मिलता है। / For equal roots, (D=0) is required. From (16(k-2)=0), we get (k=2).
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What will be the value of (k) for real and equal roots of ((k-2)x-2-2(k+1)x+k=0)?
A. \(k=-\frac{1}{4}\)
यहाँ (D=4(k+1)2-4(k-2)k=16k+4) है। समान मूलों के लिए (D=0), इसलिए \(k=-\frac{1}{4}\)। / Here (D=4(k+1)2-4(k-2)k=16k+4). For equal roots (D=0), so \(k=-\frac{1}{4}\).
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In which interval will (a) lie for (x-2+2(a-2)x+2a+5=0) to have no real roots?
A. \(3-\sqrt{10}<a<3+\sqrt{10}\)
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4\(a^2-6a-1\)), इसलिए \(3-\sqrt{10}<a<3+\sqrt{10}\)। / For no real roots, (D<0) is required. Here (D=4\(a^2-6a-1\)), so \(3-\sqrt{10}<a<3+\sqrt{10}\).
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