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 501-510 of 600 questions.
If \(x=\sqrt{13}+\sqrt{5}\), what is the value of \(x^2-18\)?
C. \(2\sqrt{65}\)
\(x^2=13+5+2\sqrt{65}=18+2\sqrt{65}\) है। इसलिए \(x^2-18=2\sqrt{65}\) है। / \(x^2=13+5+2\sqrt{65}=18+2\sqrt{65}\). So \(x^2-18=2\sqrt{65}\).
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Which is the simplified form of \(\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}}\)?
A. \(\frac{9+2\sqrt{14}}{5}\)
संयुग्मी से गुणा करने पर अंश \(9+2\sqrt{14}\) और हर (5) मिलता है। इसलिए सरल रूप \(\frac{9+2\sqrt{14}}{5}\) है। / Multiplying by the conjugate gives numerator \(9+2\sqrt{14}\) and denominator (5). So the simplified form is \(\frac{9+2\sqrt{14}}{5}\).
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If \(a=6+\sqrt{3}\) and \(b=6-\sqrt{3}\), what is the value of \(a^2-b^2\)?
D. \(24\sqrt{3}\)
(a-2-b-2=(a-b)(a+b)) है जहाँ \(a-b=2\sqrt{3}\) और (a+b=12) है। इसलिए मान \(24\sqrt{3}\) है। / (a-2-b-2=(a-b)(a+b)) where \(a-b=2\sqrt{3}\) and (a+b=12). So the value is \(24\sqrt{3}\).
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If \(p=\frac{1}{\sqrt{19}+4}\), what is the simplified form of (p)?
A. \(\frac{\sqrt{19}-4}{3}\)
संयुग्मी से गुणा करने पर हर (19-16=3) बनता है। इसलिए \(p=\frac{\sqrt{19}-4}{3}\) है। / Multiplying by the conjugate makes the denominator (19-16=3). So \(p=\frac{\sqrt{19}-4}{3}\).
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If \(y=\sqrt{12}+\sqrt{27}\), what is the value of \(y^2\)?
B. (75)
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\), इसलिए \(y=5\sqrt{3}\) है। इसका वर्ग (75) है। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so \(y=5\sqrt{3}\). Its square is (75).
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Which is the rationalised form of \(\frac{5}{\sqrt{14}-3}\)?
D. (\frac{5\(\sqrt{14}+3\)}{5})
संयुग्मी से गुणा करने पर हर (14-9=5) बनता है। इसलिए रूप (\frac{5\(\sqrt{14}+3\)}{5}), यानी \(\sqrt{14}+3\), है। / Multiplying by the conjugate makes the denominator (14-9=5). So the form is (\frac{5\(\sqrt{14}+3\)}{5}), that is \(\sqrt{14}+3\).
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If \(s=\sqrt{108}+\sqrt{300}\), what is the value of \(\frac{s}{\sqrt{3}}\)?
C. (16)
\(\sqrt{108}=6\sqrt{3}\) और \(\sqrt{300}=10\sqrt{3}\), इसलिए \(s=16\sqrt{3}\) है। भाग देने पर (16) मिलता है। / \(\sqrt{108}=6\sqrt{3}\) and \(\sqrt{300}=10\sqrt{3}\), so \(s=16\sqrt{3}\). Dividing gives (16).
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What is the value of \(\sqrt{8+\sqrt{11}}\times\sqrt{8+\sqrt{11}}\)?
D. \(8+\sqrt{11}\)
एक ही वर्गमूल को अपने आप से गुणा करने पर अंदर की संख्या मिलती है। इसलिए मान \(8+\sqrt{11}\) है। / Multiplying the same square root by itself gives the number inside. Therefore the value is \(8+\sqrt{11}\).
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If \(A=\sqrt{147}+\sqrt{243}\) and \(B=16\sqrt{3}\), which statement is correct?
C. (A=B)
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{243}=9\sqrt{3}\), इसलिए \(A=16\sqrt{3}\) है। अतः (A=B) है। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{243}=9\sqrt{3}\), so \(A=16\sqrt{3}\). Hence (A=B).
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Which is the simplified form of \(\frac{\sqrt{13}+\sqrt{3}}{\sqrt{13}-\sqrt{3}}\)?
C. \(\frac{8+\sqrt{39}}{5}\)
संयुग्मी से गुणा करने पर अंश \(16+2\sqrt{39}\) और हर (10) मिलता है। इसलिए उत्तर \(\frac{8+\sqrt{39}}{5}\) है। / Multiplying by the conjugate gives numerator \(16+2\sqrt{39}\) and denominator (10). So the answer is \(\frac{8+\sqrt{39}}{5}\).
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