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 461-470 of 550 questions.
If the roots of \(x^2-16x+k=0\) are real and distinct, what is the correct condition on (k)?
A. (k<64)
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (256-4k>0), इसलिए (k<64)। / For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
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Which equation has discriminant (-35)?
A. \(x^2+x+9=0\)
\(x^2+x+9=0\) के लिए \(D=1^2-4\cdot1\cdot9=-35\) है। विवेचक में (4ac) पूरा घटाएं। / For \(x^2+x+9=0\), \(D=1^2-4\cdot1\cdot9=-35\). Subtract the full (4ac) in the discriminant.
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If one root of \(x^2+ax+40=0\) is (5), what are the other root and (a)?
A. दूसरा मूल (8), (a=-13)other root (8), (a=-13)
मूलों का गुणनफल (40) है, इसलिए दूसरा मूल (8) होगा। योग (13) है और (-a=13), इसलिए (a=-13)। / The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).
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What is the sum of squares of the roots of \(4x^2+8x+3=0\)?
A. \( \frac{5}{2} \)
(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) होता है। यहाँ ((-2)2-2\cdot\frac{3}{4}=\frac{5}{2})। / (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). Here ((-2)2-2\cdot\frac{3}{4}=\frac{5}{2}).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-14x+48=0\), what is (\(\alpha-6\)\(\beta-6\))?
A. (0)
(\(\alpha-6\)\(\beta-6\)=\alpha\beta-6\(\alpha+\beta\)+36) है। यहाँ (48-84+36=0)। / (\(\alpha-6\)\(\beta-6\)=\alpha\beta-6\(\alpha+\beta\)+36). Here (48-84+36=0).
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What is the standard form of ((x+4)(x+7)+(x-3)(x+6)=88)?
A. \(2x^2+14x-78=0\)
बाईं ओर \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\) है। (88) घटाने पर \(2x^2+14x-78=0\) मिलता है। / The left side is \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\). Subtracting (88) gives \(2x^2+14x-78=0\).
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A. (90)
(2r+5r=21) से (r=3) मिलता है, इसलिए मूल (6) और (15) हैं। स्थिर पद मूलों का गुणनफल (90) होगा। / From (2r+5r=21), we get (r=3), so the roots are (6) and (15). The constant term is the product of roots (90).
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Which statement is correct for \(x^2-10x+29=0\)?
A. वास्तविक मूल नहीं हैंIt has no real roots
यहाँ (D=(-10)2-4\cdot1\cdot29=-16<0) है। इसलिए वास्तविक मूल नहीं होंगे। / Here (D=(-10)2-4\cdot1\cdot29=-16<0). Therefore it has no real roots.
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If one root of (x-2-(m+6)x+6m=0) is (6), what is the other root?
A. (m)
मूलों का गुणनफल (6m) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{6m}{6}=m\) है। / The product of roots is (6m) and one root is (6). Hence the other root is \(\frac{6m}{6}=m\).
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What is the difference between the roots of \(5x^2-22x+24=0\)?
A. \( \frac{2}{5} \)
मूल (2) और \(\frac{12}{5}\) हैं। उनका अंतर \(\frac{12}{5}-2=\frac{2}{5}\) है। / The roots are (2) and \(\frac{12}{5}\). Their difference is \(\frac{12}{5}-2=\frac{2}{5}\).
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