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 491-500 of 600 questions.
What is the square of \(\sqrt{12+\sqrt{35}}\) equal to?
A. \(12+\sqrt{35}\)
वर्गमूल का वर्ग अंदर की संख्या देता है। इसलिए (\left\(\sqrt{12+\sqrt{35}}\right\)2=12+\sqrt{35}) है। / The square of a square root gives the number inside. So (\left\(\sqrt{12+\sqrt{35}}\right\)2=12+\sqrt{35}).
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If \(x=5+\sqrt{24}\), what is the value of \(x^2-10x\)?
A. (-1)
\(x^2=49+10\sqrt{24}\) और \(10x=50+10\sqrt{24}\) है। घटाने पर (-1) मिलता है। / \(x^2=49+10\sqrt{24}\) and \(10x=50+10\sqrt{24}\). Subtracting gives (-1).
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What is the rationalised form of \(\frac{7}{\sqrt{19}-\sqrt{12}}\)?
A. \(\sqrt{19}+\sqrt{12}\)
संयुग्मी से गुणा करने पर हर (19-12=7) बनता है। इसलिए (\frac{7\(\sqrt{19}+\sqrt{12}\)}{7}=\sqrt{19}+\sqrt{12}) है। / Multiplying by the conjugate makes the denominator (19-12=7). So (\frac{7\(\sqrt{19}+\sqrt{12}\)}{7}=\sqrt{19}+\sqrt{12}).
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If \(P=\sqrt{363}-\sqrt{147}+\sqrt{75}\), what is (P) equal to?
B. \(9\sqrt{3}\)
\(\sqrt{363}=11\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। इसलिए \(P=9\sqrt{3}\) है। / \(\sqrt{363}=11\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). Therefore \(P=9\sqrt{3}\).
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If \(t=\sqrt{19}+3\), what is the value of \(t+\frac{10}{t}\)?
A. \(2\sqrt{19}\)
\(\frac{10}{\sqrt{19}+3}=\sqrt{19}-3\) है क्योंकि हर (19-9=10) बनता है। इसलिए योग \(2\sqrt{19}\) है। / \(\frac{10}{\sqrt{19}+3}=\sqrt{19}-3\) because the denominator becomes (19-9=10). So the sum is \(2\sqrt{19}\).
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What is the value of (\(\sqrt{32}+\sqrt{50}\)2)?
A. (162)
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\), इसलिए योग \(9\sqrt{2}\) है। इसका वर्ग (162) है। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\), so the sum is \(9\sqrt{2}\). Its square is (162).
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If \(x=\sqrt{10}+\sqrt{6}\), what is the value of \(x^2-16\)?
B. \(4\sqrt{15}\)
\(x^2=10+6+2\sqrt{60}=16+4\sqrt{15}\) है। इसलिए \(x^2-16=4\sqrt{15}\) है। / \(x^2=10+6+2\sqrt{60}=16+4\sqrt{15}\). So \(x^2-16=4\sqrt{15}\).
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What is the value of \(\frac{1}{\sqrt{12}+\sqrt{5}}+\frac{1}{\sqrt{12}-\sqrt{5}}\)?
C. \(\frac{4\sqrt{3}}{7}\)
दोनों भिन्नों को जोड़ने पर अंश \(2\sqrt{12}\) और हर (12-5=7) मिलता है। इसलिए मान \(\frac{4\sqrt{3}}{7}\) है। / Adding both fractions gives numerator \(2\sqrt{12}\) and denominator (12-5=7). So the value is \(\frac{4\sqrt{3}}{7}\).
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If \(a=\sqrt{18}+\sqrt{8}\) and \(b=\sqrt{18}-\sqrt{8}\), what is the value of \(a^2-b^2\)?
D. (48)
(a-2-b-2=(a-b)(a+b)) है जहाँ \(a-b=2\sqrt{8}\) और \(a+b=2\sqrt{18}\) है। इसलिए मान \(4\sqrt{144}=48\) है। / (a-2-b-2=(a-b)(a+b)), where \(a-b=2\sqrt{8}\) and \(a+b=2\sqrt{18}\). So the value is \(4\sqrt{144}=48\).
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What is the simplified value of \(\frac{\sqrt{243}-\sqrt{108}}{\sqrt{3}}\)?
B. (3)
\(\sqrt{243}=9\sqrt{3}\) और \(\sqrt{108}=6\sqrt{3}\), इसलिए अंश \(3\sqrt{3}\) है। \(\sqrt{3}\) से भाग देने पर (3) मिलता है। / \(\sqrt{243}=9\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so the numerator is \(3\sqrt{3}\). Dividing by \(\sqrt{3}\) gives (3).
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