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 41-50 of 600 questions.
How many real roots does \(x^2+4=0\) have?
C. (0)
क्योंकि \(x^2\ge 0\) होता है इसलिए \(x^2+4\) कभी (0) नहीं बनता। इसलिए कोई वास्तविक मूल नहीं है। / Because \(x^2\ge 0\) so \(x^2+4\) never becomes (0). Therefore it has no real root.
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What are the roots of \(x^2+2x-8=0\)?
B. (2) और (-4)(2) and (-4)
(x-2+2x-8=(x+4)(x-2)) इसलिए मूल (-4) और (2) हैं। गुणनखंड के चिन्ह उलटकर मूल मिलते हैं। / (x-2+2x-8=(x+4)(x-2)) so the roots are (-4) and (2). Roots have opposite signs to the factor constants.
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What are the roots of \(x^2=16\)?
A. (4) और (-4)(4) and (-4)
\(x^2=16\) से \(x=\pm4\) मिलता है। वर्ग समीकरण में धनात्मक और ऋणात्मक दोनों मूल देखें। / From \(x^2=16\) we get \(x=\pm4\). In a square equation check both positive and negative roots.
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If one root is (3) and the product of roots is (12) then what is the other root?
B. (4)
दूसरा मूल \(\frac{12}{3}=4\) होगा। गुणनफल वाले प्रश्न में दिए मूल से भाग दें। / The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.
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If the sum of roots is (5) and one root is (2) then what is the other root?
B. (3)
दूसरा मूल (5-2=3) है। योग में से दिए हुए मूल को घटाएं। / The other root is (5-2=3). Subtract the given root from the sum.
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If the roots of a quadratic equation are reciprocals of each other then what is their product?
B. (1)
यदि मूल (r) और \(\frac{1}{r}\) हों तो गुणनफल (1) होता है। व्युत्क्रम मूलों में गुणनफल तुरंत (1) याद रखें। / If the roots are (r) and \(\frac{1}{r}\) their product is (1). For reciprocal roots remember the product is (1).
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What are the roots of \(2x^2-5x+3=0\)?
A. (1) और \(\frac{3}{2}\)(1) and \(\frac{3}{2}\)
(2x-2-5x+3=(2x-3)(x-1)) इसलिए मूल \(\frac{3}{2}\) और (1) हैं। गुणांक वाले गुणनखंडों में सावधानी रखें। / (2x-2-5x+3=(2x-3)(x-1)) so the roots are \(\frac{3}{2}\) and (1). Be careful with factors that contain coefficients.
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Which of the following equations has one root (0)?
A. \(x^2+5x=0\)
(x-2+5x=x(x+5)) इसलिए (x=0) एक मूल है। अचर पद (0) हो तो शून्य मूल की संभावना देखें। / (x-2+5x=x(x+5)) so (x=0) is one root. If the constant term is (0) check for a zero root.
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If both roots of a monic quadratic equation are (7) and (7) then which equation is it?
A. \(x^2-14x+49=0\)
दोनों मूल (7) होने पर ((x-7)2=0) मिलता है जो \(x^2-14x+49=0\) है। दोहराए मूल से पूर्ण वर्ग बनाएं। / With both roots (7) we get ((x-7)2=0) which is \(x^2-14x+49=0\). Form a perfect square from repeated roots.
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If (x=3) is a root of \(2x^2-7x+k=0\), what will be the value of (k)?
A. (3)
(x=3) रखने पर (18-21+k=0) इसलिए (k=3) मिलता है। ऐसे प्रश्नों में दिए हुए मूल को सीधे समीकरण में रखें। / Putting (x=3) gives (18-21+k=0), so (k=3). In such questions substitute the given root directly into the equation.
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