Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 241-250 of 651 questions.
What is the simplified form of \(2\sqrt{5}+3\sqrt{20}\)?
B. \(8\sqrt{5}\)
\(\sqrt{20}=2\sqrt{5}\), इसलिए \(2\sqrt{5}+6\sqrt{5}=8\sqrt{5}\) है। गुणांक और मूल दोनों ध्यान से देखें। / \(\sqrt{20}=2\sqrt{5}\), so \(2\sqrt{5}+6\sqrt{5}=8\sqrt{5}\). Watch both coefficients and radicals carefully.
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Which option will have a terminating decimal expansion?
D. \(\frac{7}{16}\)
\(\frac{7}{16}\) परिमेय है और हर \(2^4\) है, इसलिए दशमलव सांत होगा। हर के अभाज्य गुणनखंड देखें। / \(\frac{7}{16}\) is rational and the denominator is \(2^4\), so the decimal will terminate. Check prime factors of the denominator.
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If \(a=\sqrt{2}+1\) and \(b=\sqrt{2}-1\), what is (ab)?
A. (1)
(ab=\(\sqrt{2}\)2-12=1) है। संयुग्मी रूप का गुणनफल परिमेय देता है। / (ab=\(\sqrt{2}\)2-12=1). The product of conjugate forms gives a rational result.
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Which is the simplified form of \(\sqrt{2}+\sqrt{32}\)?
B. \(5\sqrt{2}\)
\(\sqrt{32}=4\sqrt{2}\), इसलिए योग \(5\sqrt{2}\) है। समान मूलों को जोड़ने से पहले सरल करें। / \(\sqrt{32}=4\sqrt{2}\), so the sum is \(5\sqrt{2}\). Simplify before adding like radicals.
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What is the value of (\(2\sqrt{3}\)2)?
C. (12)
(\(2\sqrt{3}\)2=4\times3=12) है। गुणांक और मूल दोनों का वर्ग करें। / (\(2\sqrt{3}\)2=4\times3=12). Square both the coefficient and the radical.
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Which option shows correct rationalisation of the denominator?
A. \(\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}\)
हर और अंश को \(\sqrt{7}\) से गुणा करने पर \(\frac{\sqrt{7}}{7}\) मिलता है। परिमेयकरण में मान नहीं बदलना चाहिए। / Multiplying numerator and denominator by \(\sqrt{7}\) gives \(\frac{\sqrt{7}}{7}\). Rationalisation should not change the value.
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If \(r=\sqrt{15}-\sqrt{6}\) and \(s=\sqrt{15}+\sqrt{6}\), what is the value of (rs)?
B. (9)
संयुग्मी गुणन में (rs=\(\sqrt{15}\)2-\(\sqrt{6}\)2=9) होता है। ऐसे प्रश्नों में \(a^2-b^2\) लगाएं। / In conjugate multiplication (rs=\(\sqrt{15}\)2-\(\sqrt{6}\)2=9). Use \(a^2-b^2\) in such questions.
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What is the simplified value of \(\frac{\sqrt{98}+\sqrt{50}}{\sqrt{2}}\)?
A. (12)
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\), इसलिए भाग देने पर (12) मिलता है। पहले अंश को सरल करें। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\), so division gives (12). Simplify the numerator first.
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If \(\sqrt{k}\) lies between (6) and (7), which value of (k) is possible?
C. (43)
क्योंकि (36<43<49), इसलिए \(6<\sqrt{43}<7\)। वर्गमूल की सीमा वर्गों से तय करें। / Since (36<43<49), \(6<\sqrt{43}<7\). Decide bounds of square roots using squares.
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What is the simplified form of (\sqrt{5}\(2\sqrt{5}-3\sqrt{20}\))?
A. (-20)
\(\sqrt{20}=2\sqrt{5}\), इसलिए अंदर \(2\sqrt{5}-6\sqrt{5}=-4\sqrt{5}\) और गुणनफल (-20) है। पहले कोष्ठक सरल करें। / \(\sqrt{20}=2\sqrt{5}\), so inside becomes \(2\sqrt{5}-6\sqrt{5}=-4\sqrt{5}\) and the product is (-20). Simplify the bracket first.
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