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 361-370 of 651 questions.
If \(p=\frac{1}{\sqrt{5}+2}\), which is the simplified form of (p)?
A. \(\sqrt{5}-2\)
संयुग्मी \(\sqrt{5}-2\) से गुणा करने पर हर (5-4=1) होता है। इसलिए \(p=\sqrt{5}-2\) है। / Multiplying by the conjugate \(\sqrt{5}-2\) makes the denominator (5-4=1). So \(p=\sqrt{5}-2\).
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What is the value of \(\frac{\sqrt{72}+\sqrt{50}}{\sqrt{2}}\)?
A. (11)
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\), इसलिए अंश \(11\sqrt{2}\) है। \(\sqrt{2}\) से भाग देने पर (11) मिलता है। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\), so the numerator is \(11\sqrt{2}\). Dividing by \(\sqrt{2}\) gives (11).
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How can \(\sqrt{3+\sqrt{5}}\) be identified according to the given statements?
B. यह वास्तविक संख्या है और इसका वर्ग \(3+\sqrt{5}\) हैIt is real and its square is \(3+\sqrt{5}\)
किसी धनात्मक संख्या का वर्गमूल वास्तविक होता है और उसका वर्ग वही संख्या देता है। यहाँ \(3+\sqrt{5}\) धनात्मक है। / The square root of a positive number is real and its square gives the same number. Here \(3+\sqrt{5}\) is positive.
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If \(p=\sqrt{12}-\sqrt{3}\), what is the value of \(p^2\)?
A. (3)
\(\sqrt{12}=2\sqrt{3}\), इसलिए \(p=\sqrt{3}\) है। अतः \(p^2=3\) होगा। / \(\sqrt{12}=2\sqrt{3}\), so \(p=\sqrt{3}\). Therefore \(p^2=3\).
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If \(m=\sqrt{8}+\sqrt{18}\) and \(n=\sqrt{50}\), what is the value of (m-n)?
A. (0)
\(\sqrt{8}=2\sqrt{2}\), \(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। इसलिए (m-n=0) मिलता है। / \(\sqrt{8}=2\sqrt{2}\), \(\sqrt{18}=3\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). Therefore (m-n=0).
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What is the value of (\(\sqrt{5}+\sqrt{2}\)2-\(\sqrt{5}-\sqrt{2}\)2)?
A. \(4\sqrt{10}\)
पहले वर्ग में \(2\sqrt{10}\) जुड़ता है और दूसरे में \(2\sqrt{10}\) घटता है। अंतर \(4\sqrt{10}\) है। / The first square adds \(2\sqrt{10}\) and the second subtracts \(2\sqrt{10}\). The difference is \(4\sqrt{10}\).
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What is the simplified form of \(\frac{3+\sqrt{5}}{3-\sqrt{5}}\)?
A. \(\frac{7+3\sqrt{5}}{2}\)
संयुग्मी से गुणा करने पर हर (9-5=4) और अंश (\(3+\sqrt{5}\)2=14+6\sqrt{5}) मिलता है। इसलिए उत्तर \(\frac{7+3\sqrt{5}}{2}\) है। / Multiplying by the conjugate gives denominator (9-5=4) and numerator (\(3+\sqrt{5}\)2=14+6\sqrt{5}). So the answer is \(\frac{7+3\sqrt{5}}{2}\).
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If \(x=\sqrt{3}+\sqrt{2}\) and \(y=\sqrt{3}-\sqrt{2}\), what is the value of \(\frac{x}{y}\)?
A. \(5+2\sqrt{6}\)
हर का संयुग्मी \(\sqrt{3}+\sqrt{2}\) है और हर (1) बनता है। इसलिए मान (\(\sqrt{3}+\sqrt{2}\)2=5+2\sqrt{6}) है। / The conjugate of the denominator is \(\sqrt{3}+\sqrt{2}\) and the denominator becomes (1). So the value is (\(\sqrt{3}+\sqrt{2}\)2=5+2\sqrt{6}).
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Which option has an irrational value?
C. \(\sqrt{7}+\sqrt{28}\)
\(\sqrt{7}+\sqrt{28}=3\sqrt{7}\) है जो अपरिमेय है। बाकी विकल्पों में मूल हटकर परिमेय मान मिलते हैं। / \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\), which is irrational. In the other options the radicals simplify to rational values.
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If \(r=\sqrt{20}+\sqrt{45}\), what is (r) equal to?
A. \(5\sqrt{5}\)
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। इसलिए \(r=5\sqrt{5}\) है। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Therefore \(r=5\sqrt{5}\).
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