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 201-210 of 600 questions.
What is the simplified surd form of \( \sqrt{180} \)?
A. \(6\sqrt{5}\)
\(180=36\times5\) इसलिए \( \sqrt{180}=6\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें। / Since \(180=36\times5\), \( \sqrt{180}=6\sqrt{5} \). Choose the largest perfect-square factor.
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What is obtained by simplifying \( \sqrt{245} \)?
B. \(7\sqrt{5}\)
\(245=49\times5\) इसलिए \( \sqrt{245}=7\sqrt{5} \)। करणी में पूर्ण वर्ग को बाहर निकालें। / Since \(245=49\times5\), \( \sqrt{245}=7\sqrt{5} \). Take the perfect square outside the radical.
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Which is the simplified form of \( \sqrt{288} \)?
C. \(12\sqrt{2}\)
\(288=144\times2\) इसलिए \( \sqrt{288}=12\sqrt{2} \)। पहले सबसे बड़ा पूर्ण वर्ग खोजें। / Since \(288=144\times2\), \( \sqrt{288}=12\sqrt{2} \). First find the largest perfect square.
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What is the simplified form of \(2\sqrt{45}+3\sqrt{20}\)?
A. \(12\sqrt{5}\)
\(2\sqrt{45}=6\sqrt{5}\) और \(3\sqrt{20}=6\sqrt{5}\) है। इसलिए योग \(12\sqrt{5}\) है। / \(2\sqrt{45}=6\sqrt{5}\) and \(3\sqrt{20}=6\sqrt{5}\). So the sum is \(12\sqrt{5}\).
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What is the simplified form of \(4\sqrt{27}-2\sqrt{75}\)?
A. \(2\sqrt{3}\)
\(4\sqrt{27}=12\sqrt{3}\) और \(2\sqrt{75}=10\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलता है। / \(4\sqrt{27}=12\sqrt{3}\) and \(2\sqrt{75}=10\sqrt{3}\). The difference is \(2\sqrt{3}\).
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What is the value of ( \sqrt{5}\(3+\sqrt{5}\) )?
A. \(3\sqrt{5}+5\)
वितरण नियम से \( \sqrt{5}\times3+\sqrt{5}\times\sqrt{5}=3\sqrt{5}+5 \)। समान करणी गुणन में सावधानी रखें। / By distributive law, \( \sqrt{5}\times3+\sqrt{5}\times\sqrt{5}=3\sqrt{5}+5 \). Be careful in surd multiplication.
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What is the expansion of ( \(4+\sqrt{3}\)2 )?
A. \(19+8\sqrt{3}\)
( (a+b)2 ) का प्रयोग करें। यहाँ \(16+8\sqrt{3}+3=19+8\sqrt{3}\) मिलता है। / Use ( (a+b)2 ). Here \(16+8\sqrt{3}+3=19+8\sqrt{3}\).
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What is the simplified form of ( \(6-\sqrt{8}\)2 )?
B. \(44-24\sqrt{2}\)
( \(6-\sqrt{8}\)2=36-12\sqrt{8}+8 ) है। \( \sqrt{8}=2\sqrt{2} \) रखने पर \(44-24\sqrt{2}\) मिलता है। / ( \(6-\sqrt{8}\)2=36-12\sqrt{8}+8 ). Using \( \sqrt{8}=2\sqrt{2} \), it becomes \(44-24\sqrt{2}\).
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What is the value of ( \(5+\sqrt{17}\)\(5-\sqrt{17}\) )?
B. (8)
यह संयुग्मी गुणन है। (52-\(\sqrt{17}\)2=25-17=8) होगा। / This is conjugate multiplication. (52-\(\sqrt{17}\)2=25-17=8).
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What is the value of ( \(2+\sqrt{19}\)\(2-\sqrt{19}\) )?
B. ( -15 )
संयुग्मी गुणन से (22-\(\sqrt{19}\)2=4-19=-15) मिलता है। मध्य पद कट जाते हैं। / Conjugate multiplication gives (22-\(\sqrt{19}\)2=4-19=-15). The middle terms cancel.
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