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.
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What is the simplified surd form of \( \sqrt{1125} \)?
C. \(15\sqrt{5}\)
\(1125=225\times5\) इसलिए \( \sqrt{1125}=15\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड पहले निकालें। / Since \(1125=225\times5\), \( \sqrt{1125}=15\sqrt{5} \). First take out the largest perfect-square factor.
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What is obtained by simplifying \( \sqrt{1452} \)?
B. \(22\sqrt{3}\)
\(1452=484\times3\) और \( \sqrt{484}=22 \) है। इसलिए सरल रूप \(22\sqrt{3}\) है। / \(1452=484\times3\) and \( \sqrt{484}=22 \). So the simplified form is \(22\sqrt{3}\).
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What is the simplified form of \(5\sqrt{20}-2\sqrt{125}+\sqrt{45}\)?
D. \(3\sqrt{5}\)
\(5\sqrt{20}=10\sqrt{5}\), \(2\sqrt{125}=10\sqrt{5}\), और \( \sqrt{45}=3\sqrt{5} \)। इसलिए परिणाम \(3\sqrt{5}\) है। / \(5\sqrt{20}=10\sqrt{5}\), \(2\sqrt{125}=10\sqrt{5}\), and \( \sqrt{45}=3\sqrt{5} \). Therefore the result is \(3\sqrt{5}\).
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Choose the correct simplified form of \(3\sqrt{75}+4\sqrt{48}-2\sqrt{27}\).
B. \(25\sqrt{3}\)
\(3\sqrt{75}=15\sqrt{3}\), \(4\sqrt{48}=16\sqrt{3}\), और \(2\sqrt{27}=6\sqrt{3}\)। इसलिए \(25\sqrt{3}\) सही है। / \(3\sqrt{75}=15\sqrt{3}\), \(4\sqrt{48}=16\sqrt{3}\), and \(2\sqrt{27}=6\sqrt{3}\). Therefore \(25\sqrt{3}\) is correct.
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What is the value of ( \sqrt{12}\(\sqrt{27}-\sqrt{3}\) )?
A. (12)
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}-\sqrt{3}=2\sqrt{3} \)। गुणनफल \(4\times3=12\) है। / \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}-\sqrt{3}=2\sqrt{3} \). The product is \(4\times3=12\).
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What is the expansion of ( \(4\sqrt{3}+3\sqrt{2}\)2 )?
A. \(66+24\sqrt{6}\)
पहला वर्ग (48) और दूसरा वर्ग (18) है। मध्य पद \(2\times4\sqrt{3}\times3\sqrt{2}=24\sqrt{6}\) है। / The first square is (48) and the second square is (18). The middle term is \(2\times4\sqrt{3}\times3\sqrt{2}=24\sqrt{6}\).
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What is the simplified form of ( \(6\sqrt{5}-\sqrt{7}\)2 )?
A. \(187-12\sqrt{35}\)
( \(6\sqrt{5}\)2=180 ) और ( \(\sqrt{7}\)2=7 ) हैं। मध्य पद \(12\sqrt{35}\) घटेगा। / ( \(6\sqrt{5}\)2=180 ) and ( \(\sqrt{7}\)2=7 ). The middle term \(12\sqrt{35}\) is subtracted.
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What is the value of ( \(3\sqrt{11}+2\sqrt{6}\)\(3\sqrt{11}-2\sqrt{6}\) )?
A. (75)
यह अंतर के वर्ग का रूप है। ( \(3\sqrt{11}\)2-\(2\sqrt{6}\)2=99-24=75 )। / This is a difference of squares. ( \(3\sqrt{11}\)2-\(2\sqrt{6}\)2=99-24=75 ).
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What is the rationalised form of \( \frac{1}{4\sqrt{3}+3\sqrt{5}} \)?
A. \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \)
संयुग्मी से गुणा करने पर हर (48-45=3) आता है। इसलिए रूप \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \) है। / Multiplying by the conjugate gives denominator (48-45=3). So the form is \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \).
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What is the rationalised form of \( \frac{5}{\sqrt{13}-\sqrt{8}} \)?
A. \( \sqrt{13}+\sqrt{8} \)
संयुग्मी से गुणा करने पर हर (13-8=5) आता है। अंश में भी (5) है इसलिए उत्तर \( \sqrt{13}+\sqrt{8} \) है। / Multiplying by the conjugate gives denominator (13-8=5). The numerator also has (5), so the answer is \( \sqrt{13}+\sqrt{8} \).
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