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 261-270 of 550 questions.
What is the nature of roots of \(x^2+14x+49=0\)?
B. दो समान वास्तविक मूलTwo equal real roots
यहाँ \(D=14^2-4\cdot1\cdot49=0\) है। इसलिए इस समीकरण के दो समान वास्तविक मूल हैं। / Here \(D=14^2-4\cdot1\cdot49=0\). Therefore the equation has two equal real roots.
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What is the sign of the discriminant of \(4x^2+x+6=0\)?
C. ऋणात्मकNegative
\(D=1^2-4\cdot4\cdot6=1-96=-95\), इसलिए विवेचक ऋणात्मक है। (4ac) की गणना सावधानी से करें। / \(D=1^2-4\cdot4\cdot6=1-96=-95\), so the discriminant is negative. Calculate (4ac) carefully.
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Which option has roots (x=3) and (x=8)?
A. \(x^2-11x+24=0\)
मूल (3) और (8) हों तो गुणनखंड ((x-3)) और ((x-8)) होंगे। इनका गुणन \(x^2-11x+24=0\) देता है। / If the roots are (3) and (8), the factors are ((x-3)) and ((x-8)). Their product gives \(x^2-11x+24=0\).
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If the roots are (-5) and (4), what will be the monic quadratic equation?
A. \(x^2+x-20=0\)
गुणनखंड ((x+5)) और ((x-4)) होंगे। इन्हें गुणा करने पर \(x^2+x-20=0\) मिलता है। / The factors are ((x+5)) and ((x-4)). Multiplying them gives \(x^2+x-20=0\).
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A. \(x^2-9x-36=0\)
वाक्य से \(x^2-9x=36\) बनता है। सभी पद एक ओर लाने पर \(x^2-9x-36=0\) मिलता है। / The statement gives \(x^2-9x=36\). Bringing all terms to one side gives \(x^2-9x-36=0\).
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A. \(2x^2+2x-144=0\)
पूर्णांक (x) और (x+1) होंगे, इसलिए (x-2+(x+1)2=145)। सरल करने पर \(2x^2+2x-144=0\) मिलता है। / The integers are (x) and (x+1), so (x-2+(x+1)2=145). Simplifying gives \(2x^2+2x-144=0\).
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A. \(x^2+7x-120=0\)
लंबाई (x+7) होगी और क्षेत्रफल (x(x+7)=120) होगा। इसलिए \(x^2+7x-120=0\) है। / The length is (x+7), and the area is (x(x+7)=120). Therefore \(x^2+7x-120=0\).
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What are the roots of \(x^2-10x=0\)?
A. (0,10)
(x-2-10x=x(x-10)), इसलिए मूल (0) और (10) हैं। समान गुणनखंड निकालना तेज तरीका है। / (x-2-10x=x(x-10)), so the roots are (0) and (10). Taking the common factor is a quick method.
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What are the roots of \(49x^2-64=0\)?
A. \(x=\pm \frac{8}{7}\)
\(49x^2=64\), इसलिए \(x^2=\frac{64}{49}\) और \(x=\pm\frac{8}{7}\) है। वर्गमूल लेते समय दोनों चिन्ह लें। / \(49x^2=64\), so \(x^2=\frac{64}{49}\) and \(x=\pm\frac{8}{7}\). Take both signs while taking square roots.
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Which factor form can represent \(x^2+11x+30=0\)?
A. ((x+5)(x+6)=0)
\(5\cdot6=30\) और (5+6=11) है। इसलिए सही गुणनखंड ((x+5)(x+6)) हैं। / \(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).
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