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 371-380 of 600 questions.
If each root of \(x^2-6x-16=0\) is decreased by (2), what is the product of the new roots?
A. (-24)
पुराने मूल (8) और (-2) हैं। नए मूल (6) और (-4) होंगे इसलिए गुणनफल (-24) है। / The old roots are (8) and (-2). The new roots are (6) and (-4), so the product is (-24).
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A. \(x^2-12x+27=0\)
पुराने योग (4) और गुणनफल (3) हैं। नए योग (12) और गुणनफल (27) होंगे इसलिए \(x^2-12x+27=0\) है। / The old sum is (4) and product is (3). The new sum is (12) and product is (27), so the equation is \(x^2-12x+27=0\).
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A. (12)
पुराने मूलों का योग (6) है। नया योग (\(\alpha+3\)+\(\beta+3\)=6+6=12) होगा। / The old sum of roots is (6). The new sum is (\(\alpha+3\)+\(\beta+3\)=6+6=12).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-12x+36=0\), what is the value of \(\alpha-\beta\)?
A. (0)
यह ((x-6)2=0) है इसलिए दोनों मूल (6) और (6) हैं। अतः \(\alpha-\beta=0\) है। / This is ((x-6)2=0), so both roots are (6) and (6). Hence \(\alpha-\beta=0\).
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A. (10)
समीकरण के मूल (3) और (-7) हैं। इसलिए (\left|\alpha-\beta\right|=\left|3-(-7)\right|=10) है। / The roots are (3) and (-7). Therefore (\left|\alpha-\beta\right|=\left|3-(-7)\right|=10).
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If the sum of roots is (6) and the sum of their squares is (52), what is the product of roots?
A. (-8)
(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) है। \(52=36-2\alpha\beta\) से \(\alpha\beta=-8\) मिलता है। / (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). From \(52=36-2\alpha\beta\), we get \(\alpha\beta=-8\).
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If the roots of \(x^2-9x+c=0\) are in the ratio (1:2), what is the value of (c)?
A. (18)
मूल (t) और (2t) मानें तो (3t=9) से (t=3) है। मूल (3) और (6) होंगे इसलिए (c=18) है। / Let the roots be (t) and (2t). From (3t=9), (t=3), so the roots are (3) and (6), hence (c=18).
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If roots of \(x^2+px+18=0\) are in the ratio (1:2) and both are negative, what is (p)?
A. (9)
मूल (-3) और (-6) होंगे क्योंकि गुणनफल (18) है। उनका योग (-9) है इसलिए (p=9) है। / The roots are (-3) and (-6) because the product is (18). Their sum is (-9), so (p=9).
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If roots of \(x^2+bx+16=0\) are equal and positive, what is the value of (b)?
A. (-8)
बराबर धनात्मक मूल (4) और (4) होंगे। योग (8) है इसलिए (-b=8) से (b=-8) है। / The equal positive roots are (4) and (4). The sum is (8), so (-b=8) gives (b=-8).
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If the product of roots of \(4x^2-3x+k=0\) equals the sum of roots, what is (k)?
A. (3)
योग \(-\frac{b}{a}=\frac{3}{4}\) और गुणनफल \(\frac{k}{4}\) है। \(\frac{k}{4}=\frac{3}{4}\) से (k=3) है। / The sum is \(-\frac{b}{a}=\frac{3}{4}\) and the product is \(\frac{k}{4}\). From \(\frac{k}{4}=\frac{3}{4}\), (k=3).
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