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 211-220 of 600 questions.
If \(x^2+kx+25=0\) has equal roots, what are the values of (k)?
A. (k=10) या (k=-10)(k=10) or (k=-10)
यहाँ \(D=k^2-100=0\) है। इसलिए \(k=\pm10\) होगा। / Here \(D=k^2-100=0\). Therefore \(k=\pm10\).
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Which condition is correct for two real and distinct roots of \(x^2-12x+k=0\)?
A. (k<36)
यहाँ (D=144-4k) है। दो असमान वास्तविक मूलों के लिए (D>0), इसलिए (k<36)। / Here (D=144-4k). For two distinct real roots (D>0), so (k<36).
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What condition on (k) gives no real roots in \(x^2+4x+k=0\)?
A. (k>4)
यहाँ (D=16-4k) है। कोई वास्तविक मूल न होने के लिए (D<0), इसलिए (k>4)। / Here (D=16-4k). For no real roots (D<0), so (k>4).
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If \(2x^2-3x+p=0\) has real roots, which condition on (p) is correct?
A. \(p\leq\frac{9}{8}\)
वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(9-8p\geq0\) से \(p\leq\frac{9}{8}\)। / For real roots we need \(D\geq0\). Here \(9-8p\geq0\) gives \(p\leq\frac{9}{8}\).
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If \(3x^2+mx+12=0\) has equal roots, what are the values of (m)?
A. (m=12) या (m=-12)(m=12) or (m=-12)
यहाँ (D=m-2-4(3)(12)=0) है। इससे \(m^2=144\), इसलिए \(m=\pm12\)। / Here (D=m-2-4(3)(12)=0). This gives \(m^2=144\), so \(m=\pm12\).
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If \(kx^2+8x+4=0\) has equal roots and \(k\neq0\), what is the value of (k)?
A. (4)
समान मूलों के लिए (D=0) है। (82-4(k)(4)=0) से (k=4)। / For equal roots (D=0). (82-4(k)(4)=0) gives (k=4).
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Choose the correct condition on (k) for real roots of \(4x^2+4kx+9=0\).
A. \(k\leq-\frac{3}{2}\) या \(k\geq\frac{3}{2}\)\(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\)
यहाँ (D=(4k)2-4(4)(9)=16\(k^2-9\)) है। वास्तविक मूलों के लिए \(k^2\geq9\) यानी \(k\leq-\frac{3}{2}\) या \(k\geq\frac{3}{2}\)। / Here (D=(4k)2-4(4)(9)=16\(k^2-9\)). For real roots \(k^2\geq9\), so \(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\).
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For equal roots in (x-2-2(k+2)x+9=0), what are the values of (k)?
A. (k=1) या (k=-5)(k=1) or (k=-5)
समान मूलों के लिए (4(k+2)2-36=0) है। इससे \(k+2=\pm3\), इसलिए (k=1) या (k=-5)। / For equal roots (4(k+2)2-36=0). Thus \(k+2=\pm3\), so (k=1) or (k=-5).
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What is the interval of (k) for no real roots in (x-2+(k-3)x+4=0)?
A. (-1<k<7)
यहाँ (D=(k-3)2-16) है। (D<0) से (-1<k<7) मिलता है। / Here (D=(k-3)2-16). From (D<0), we get (-1<k<7).
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If (2x-2+(k+1)x+3=0) has two distinct real roots, which condition on (k) is correct?
A. \(k<-1-2\sqrt{6}\) या \(k>-1+2\sqrt{6}\)\(k<-1-2\sqrt{6}\) or \(k>-1+2\sqrt{6}\)
यहाँ (D=(k+1)2-24) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए ((k+1)2>24)। / Here (D=(k+1)2-24). For distinct real roots (D>0), so ((k+1)2>24).
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