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 351-360 of 651 questions.
What is the value of (\(4\sqrt{3}\)2)?
C. (48)
(\(4\sqrt{3}\)2=16\times3=48) है। गुणांक और मूल दोनों का वर्ग करें। / (\(4\sqrt{3}\)2=16\times3=48). Square both the coefficient and the radical.
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If \(a=3+\sqrt{5}\) and \(b=3-\sqrt{5}\), what is the value of \(a^2-b^2\)?
A. \(12\sqrt{5}\)
(a-2-b-2=(a-b)(a+b)), जहाँ \(a-b=2\sqrt{5}\) और (a+b=6) है। इसलिए मान \(12\sqrt{5}\) है। / (a-2-b-2=(a-b)(a+b)), where \(a-b=2\sqrt{5}\) and (a+b=6). So the value is \(12\sqrt{5}\).
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If \(x=\frac{1}{\sqrt{2}+1}\), what is the value of \(x+\sqrt{2}\)?
A. (1)
\(\frac{1}{\sqrt{2}+1}=\sqrt{2}-1\) होता है। इसलिए \(x+\sqrt{2}=2\sqrt{2}-1\) नहीं, बल्कि (\(\sqrt{2}-1\)+\sqrt{2}=2\sqrt{2}-1) है। / \(\frac{1}{\sqrt{2}+1}=\sqrt{2}-1\). So (x+\sqrt{2}=\(\sqrt{2}-1\)+\sqrt{2}=2\sqrt{2}-1).
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Which is the simplified form of \(\frac{2+\sqrt{3}}{2-\sqrt{3}}\)?
A. \(7+4\sqrt{3}\)
हर के संयुग्मी \(2+\sqrt{3}\) से गुणा करने पर हर (1) और अंश (\(2+\sqrt{3}\)2) बनता है। इसलिए उत्तर \(7+4\sqrt{3}\) है। / Multiplying by the conjugate \(2+\sqrt{3}\) makes the denominator (1) and numerator (\(2+\sqrt{3}\)2). So the answer is \(7+4\sqrt{3}\).
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What is the value of \(\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{2}-1}\)?
B. \(2\sqrt{2}\)
पहला पद \(\sqrt{2}-1\) और दूसरा \(\sqrt{2}+1\) बनता है। योग \(2\sqrt{2}\) है। / The first term becomes \(\sqrt{2}-1\) and the second becomes \(\sqrt{2}+1\). Their sum is \(2\sqrt{2}\).
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If \(x=\sqrt{6}+\sqrt{2}\), what is the correct value of \(x^2\)?
A. \(8+4\sqrt{3}\)
\(x^2=6+2+2\sqrt{12}=8+4\sqrt{3}\) है। वर्ग करते समय मध्य पद को सही सरल करें। / \(x^2=6+2+2\sqrt{12}=8+4\sqrt{3}\). Simplify the middle term correctly while squaring.
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If \(a=5+\sqrt{3}\) and \(b=5-\sqrt{3}\), what is the value of \(a^2-b^2\)?
A. \(20\sqrt{3}\)
(a-2-b-2=(a-b)(a+b)), जहाँ \(a-b=2\sqrt{3}\) और (a+b=10) है। इसलिए मान \(20\sqrt{3}\) है। / (a-2-b-2=(a-b)(a+b)), where \(a-b=2\sqrt{3}\) and (a+b=10). So the value is \(20\sqrt{3}\).
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What is \(\sqrt{45}+\sqrt{20}-\sqrt{80}\) equal to?
A. \(\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\), \(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{80}=4\sqrt{5}\) है। इसलिए परिणाम \(\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{20}=2\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\). Therefore the result is \(\sqrt{5}\).
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What type of number is the value of (\(\sqrt{10}+\sqrt{6}\)\(\sqrt{10}-\sqrt{6}\))?
B. परिमेय (4)Rational (4)
संयुग्मी गुणन से (10-6=4) मिलता है। यह परिमेय संख्या है। / Conjugate multiplication gives (10-6=4). It is a rational number.
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What is the simplified form of \(\sqrt{48}+\sqrt{75}-\sqrt{27}\)?
A. \(6\sqrt{3}\)
\(\sqrt{48}=4\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। इसलिए परिणाम \(6\sqrt{3}\) है। / \(\sqrt{48}=4\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). Therefore the result is \(6\sqrt{3}\).
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