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 600 questions.
What is the value of (\(3\sqrt{2}\)2)?
C. (18)
(\(3\sqrt{2}\)2=9\times2=18) है। गुणांक और मूल दोनों का वर्ग करें। / (\(3\sqrt{2}\)2=9\times2=18). Square both the coefficient and the radical.
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If \(u=\sqrt{23}+4\) and \(v=\sqrt{23}-4\), what is the value of (uv)?
A. (7)
संयुग्मी गुणन में (uv=\(\sqrt{23}\)2-42=7) होता है। ऐसे प्रश्नों में \(a^2-b^2\) लगाएं। / In conjugate multiplication (uv=\(\sqrt{23}\)2-42=7). Use \(a^2-b^2\) in such questions.
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What is the simplified value of \(\frac{\sqrt{150}+\sqrt{54}}{\sqrt{6}}\)?
B. (8)
\(\sqrt{150}=5\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\), इसलिए भाग देने पर (8) मिलता है। पहले अंश को समान मूल में बदलें। / \(\sqrt{150}=5\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\), so division gives (8). First convert the numerator into like radicals.
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If \(\sqrt{k}\) lies between (7) and (8), which value of (k) is possible?
C. (57)
क्योंकि (49<57<64), इसलिए \(7<\sqrt{57}<8\)। वर्गमूल की सीमा वर्गों से तय करें। / Since (49<57<64), \(7<\sqrt{57}<8\). Decide square-root bounds using squares.
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What is the simplified form of (\sqrt{10}\(3\sqrt{10}-2\sqrt{40}\))?
B. (-10)
\(\sqrt{40}=2\sqrt{10}\), इसलिए कोष्ठक \(-\sqrt{10}\) और गुणनफल (-10) है। पहले कोष्ठक को सरल करें। / \(\sqrt{40}=2\sqrt{10}\), so the bracket is \(-\sqrt{10}\) and the product is (-10). Simplify the bracket first.
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Which option is the correct rationalised form of \(\frac{6}{\sqrt{19}}\)?
C. \(\frac{6\sqrt{19}}{19}\)
अंश और हर को \(\sqrt{19}\) से गुणा करने पर \(\frac{6\sqrt{19}}{19}\) मिलता है। परिमेयकरण में हर से मूल हटता है। / Multiplying numerator and denominator by \(\sqrt{19}\) gives \(\frac{6\sqrt{19}}{19}\). Rationalisation removes the radical from the denominator.
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Which statement is correct about \(\sqrt{12}+\sqrt{108}\) and \(8\sqrt{3}\)?
C. दोनों बराबर हैंBoth are equal
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{108}=6\sqrt{3}\), इसलिए योग \(8\sqrt{3}\) है। तुलना से पहले सरल रूप निकालें। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so the sum is \(8\sqrt{3}\). Find simplified forms before comparing.
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If the side of a square is \(2\sqrt{7}\) units, what will be its area?
C. (28) वर्ग इकाई(28) square units
क्षेत्रफल (\(2\sqrt{7}\)2=28) वर्ग इकाई है। अपरिमेय भुजा का क्षेत्रफल परिमेय हो सकता है। / The area is (\(2\sqrt{7}\)2=28) square units. A square with irrational side can have rational area.
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What type of number is the decimal \(5.12012001200012\ldots\)?
C. अपरिमेयIrrational
इसमें निश्चित दोहराने वाला खंड नहीं है इसलिए यह अपरिमेय है। असांत अनावर्ती दशमलव को पहचानना जरूरी है। / It has no fixed repeating block, so it is irrational. Identifying non-terminating non-repeating decimals is important.
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What is the rationalised form of \(\frac{1}{5+\sqrt{6}}\)?
A. \(\frac{5-\sqrt{6}}{19}\)
संयुग्मी से गुणा करने पर हर (25-6=19) बनता है। इसलिए परिमेयकृत रूप \(\frac{5-\sqrt{6}}{19}\) है। / Multiplying by the conjugate makes the denominator (25-6=19). So the rationalised form is \(\frac{5-\sqrt{6}}{19}\).
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