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 331-340 of 600 questions.
What is the value of \( \sqrt{12}+\sqrt{75}-\sqrt{48}-\sqrt{27} \)?
A. (0)
क्रमशः \(2\sqrt{3},5\sqrt{3},4\sqrt{3},3\sqrt{3}\) मिलते हैं। (2+5-4-3=0) इसलिए मान (0) है। / They become \(2\sqrt{3},5\sqrt{3},4\sqrt{3},3\sqrt{3}\). Since (2+5-4-3=0), the value is (0).
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If \(x=3-\sqrt{5}\), then \( \frac{1}{x} \) equals what?
A. \( \frac{3+\sqrt{5}}{4} \)
\( \frac{1}{3-\sqrt{5}} \) को संयुग्मी से गुणा करें। हर (9-5=4) और अंश \(3+\sqrt{5}\) होगा। / Multiply \( \frac{1}{3-\sqrt{5}} \) by the conjugate. The denominator is (9-5=4) and the numerator is \(3+\sqrt{5}\).
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If \(a=\sqrt{3}+\sqrt{2}\), what is the value of \(a^2+\frac{1}{a^2}\)?
B. (98)
\(a^2=5+2\sqrt{6}\) और \( \frac{1}{a^2}=5-2\sqrt{6} \)। योग (10) होना चाहिए। / \(a^2=5+2\sqrt{6}\) and \( \frac{1}{a^2}=5-2\sqrt{6} \). The sum should be (10).
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If \(x=\sqrt{5}+2\), what is the value of \(x+\frac{1}{x}\)?
A. \(2\sqrt{5}\)
\( \frac{1}{\sqrt{5}+2}=\sqrt{5}-2 \) है। इसलिए \(x+\frac{1}{x}=\sqrt{5}+2+\sqrt{5}-2=2\sqrt{5}\)। / \( \frac{1}{\sqrt{5}+2}=\sqrt{5}-2 \). Hence \(x+\frac{1}{x}=\sqrt{5}+2+\sqrt{5}-2=2\sqrt{5}\).
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If (x=-7), what is the value of \( \sqrt{x^2}-2x \)?
A. (21)
\( \sqrt{x^2}=|x|=7 \) और (-2x=14) है। इसलिए कुल (21) मिलेगा। / \( \sqrt{x^2}=|x|=7 \) and (-2x=14). Therefore the total is (21).
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What is the correct simplified form of \( |3-\sqrt{20}| \)?
A. \( \sqrt{20}-3 \)
\( \sqrt{20}>3 \) इसलिए \(3-\sqrt{20}\) ऋणात्मक है। निरपेक्ष मान इसे \( \sqrt{20}-3 \) बना देता है। / Since \( \sqrt{20}>3 \), \(3-\sqrt{20}\) is negative. Absolute value changes it to \( \sqrt{20}-3 \).
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What is the simplified form of \( |\sqrt{30}-6| \)?
A. \(6-\sqrt{30}\)
\( \sqrt{30}<6 \) इसलिए \( \sqrt{30}-6 \) ऋणात्मक है। निरपेक्ष मान \(6-\sqrt{30}\) होगा। / Since \( \sqrt{30}<6 \), \( \sqrt{30}-6 \) is negative. The absolute value is \(6-\sqrt{30}\).
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What is the correct statement about \( \sqrt{27}+\sqrt{12} \) and \( \sqrt{75} \)?
A. दोनों बराबर हैंBoth are equal
\( \sqrt{27}+\sqrt{12}=3\sqrt{3}+2\sqrt{3}=5\sqrt{3} \)। \( \sqrt{75}=5\sqrt{3} \) इसलिए दोनों बराबर हैं। / \( \sqrt{27}+\sqrt{12}=3\sqrt{3}+2\sqrt{3}=5\sqrt{3} \). Also \( \sqrt{75}=5\sqrt{3} \), so both are equal.
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Which relation is correct between \( \sqrt{48}+\sqrt{108} \) and \(10\sqrt{3}\)?
A. \( \sqrt{48}+\sqrt{108}=10\sqrt{3} \)
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{108}=6\sqrt{3} \)। योग \(10\sqrt{3}\) है। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{108}=6\sqrt{3} \). Their sum is \(10\sqrt{3}\).
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What is the value of \( \frac{1}{\sqrt{3}-\sqrt{2}}-\frac{1}{\sqrt{3}+\sqrt{2}} \)?
A. \(2\sqrt{2}\)
समान हर (3-2=1) और अंश ( \sqrt{3}+\sqrt{2}-\(\sqrt{3}-\sqrt{2}\)=2\sqrt{2} ) है। / The common denominator is (3-2=1), and the numerator is ( \sqrt{3}+\sqrt{2}-\(\sqrt{3}-\sqrt{2}\)=2\sqrt{2} ).
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