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 241-250 of 550 questions.
If the roots of \(x^2-14x+k=0\) are equal, what is (k)?
B. (49)
समान मूलों के लिए (D=0), इसलिए (196-4k=0) और (k=49)। समान मूल की शर्त में विवेचक शून्य रखें। / For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
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In \(x^2+kx+49=0\), if the roots are equal and positive, which possible value of (k) is correct?
B. (-14)
समान मूलों के लिए \(k^2=196\) और समान मूल \(-\frac{k}{2}\) होगा। धनात्मक मूल के लिए (k=-14) सही है। / For equal roots, \(k^2=196\), and the equal root is \(-\frac{k}{2}\). For a positive root, (k=-14) is correct.
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In which option is the (x) term absent but the equation is quadratic?
A. \(3x^2-27=0\)
\(3x^2-27=0\) में \(x^2\) पद है और (x) पद अनुपस्थित है। (x) पद न होने पर भी समीकरण द्विघात हो सकता है। / In \(3x^2-27=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without the (x) term.
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If \(6x^2-18x+12=0\) is divided by (6), which simplified equation is obtained?
A. \(x^2-3x+2=0\)
हर पद को (6) से भाग देने पर \(x^2-3x+2=0\) मिलता है। समान अशून्य गुणनखंड से भाग देने पर मूल नहीं बदलते। / Dividing every term by (6) gives \(x^2-3x+2=0\). Dividing by a common nonzero factor does not change the roots.
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Which pair of numbers is useful to identify the factors of \(x^2-13x+42=0\)?
A. (6) और (7)(6) and (7)
\(6\cdot7=42\) और (6+7=13) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-6)(x-7)) बनते हैं। / \(6\cdot7=42\) and (6+7=13). Because the middle term is negative, the factors are ((x-6)(x-7)).
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If the roots of \(x^2+sx+18=0\) are (-3) and (-6), what is the value of (s)?
A. (9)
मूलों का योग (-9) है और \(x^2+sx+18=0\) में योग (-s) होता है। इसलिए (s=9) है। / The sum of roots is (-9), and in \(x^2+sx+18=0\) the sum is (-s). Therefore (s=9).
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A. \(x^2-8x-15=0\)
क्षेत्रफल \(x^2\) है और दिया है \(x^2=8x+15\)। इसलिए \(x^2-8x-15=0\) सही है। / The area is \(x^2\), and it is given that \(x^2=8x+15\). Therefore \(x^2-8x-15=0\) is correct.
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In which perfect square form can \(x^2+12x+36=0\) be written?
A. ((x+6)2=0)
(x-2+12x+36=(x+6)2) होता है। पूर्ण वर्ग पहचानने के लिए मध्य पद (2ab) से मिलाएं। / (x-2+12x+36=(x+6)2). To identify a perfect square, match the middle term with (2ab).
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What is the standard form of ((2x-1)2=3x+5)?
A. \(4x^2-7x-4=0\)
((2x-1)2=4x-2-4x+1) है और सभी पद एक ओर लाने पर \(4x^2-7x-4=0\) मिलता है। वर्ग सूत्र और चिन्ह दोनों ध्यान से लगाएं। / Here ((2x-1)2=4x-2-4x+1), and bringing all terms to one side gives \(4x^2-7x-4=0\). Apply the square identity and signs carefully.
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If (x=-4) is a root of \(x^2+tx-8=0\), what is the value of (t)?
A. (2)
(x=-4) रखने पर (16-4t-8=0) मिलता है, इसलिए (t=2) है। मूल दिया हो तो सीधे प्रतिस्थापन करें। / Putting (x=-4) gives (16-4t-8=0), so (t=2). When a root is given, substitute it directly.
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