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 381-390 of 600 questions.
If \(q=\sqrt{5}+2\), what is the value of \(q^2-4q\)?
A. (1)
\(q^2=9+4\sqrt{5}\) और \(4q=4\sqrt{5}+8\) है। घटाने पर (1) मिलता है। / \(q^2=9+4\sqrt{5}\) and \(4q=4\sqrt{5}+8\). Subtracting gives (1).
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Which number definitely lies between \(\sqrt{10}\) and \(\sqrt{12}\)?
A. \(\sqrt{11}\)
क्योंकि (10<11<12), इसलिए \(\sqrt{11}\) दोनों के बीच होगा। धनात्मक वर्गमूलों में अंदर की संख्या से तुलना करें। / Since (10<11<12), \(\sqrt{11}\) lies between them. For positive square roots compare the numbers inside.
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If \(A=\sqrt{80}+\sqrt{45}\) and \(B=7\sqrt{5}\), which statement is correct?
A. (A=B)
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\), इसलिए \(A=7\sqrt{5}\) है। अतः (A=B) है। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so \(A=7\sqrt{5}\). Hence (A=B).
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What is the value of \(\frac{\sqrt{125}-\sqrt{20}}{\sqrt{5}}\)?
A. (3)
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\), इसलिए अंश \(3\sqrt{5}\) है। भाग देने पर (3) मिलता है। / \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\), so the numerator is \(3\sqrt{5}\). Dividing gives (3).
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What is the square of \(\sqrt{7+\sqrt{10}}\) equal to?
A. \(7+\sqrt{10}\)
वर्गमूल का वर्ग अंदर की संख्या देता है। इसलिए (\left\(\sqrt{7+\sqrt{10}}\right\)2=7+\sqrt{10}) है। / The square of a square root gives the number inside. So (\left\(\sqrt{7+\sqrt{10}}\right\)2=7+\sqrt{10}).
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If \(x=\sqrt{7}+\sqrt{2}\), what is the value of \(x^2-9\)?
A. \(2\sqrt{14}\)
\(x^2=7+2+2\sqrt{14}=9+2\sqrt{14}\) है। इसलिए \(x^2-9=2\sqrt{14}\) है। / \(x^2=7+2+2\sqrt{14}=9+2\sqrt{14}\). Therefore \(x^2-9=2\sqrt{14}\).
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In which option is the difference of two irrational numbers rational?
A. \(\sqrt{19}-\sqrt{19}\)
\(\sqrt{19}\) और \(\sqrt{19}\) दोनों अपरिमेय हैं और अंतर (0) है। (0) परिमेय संख्या है। / \(\sqrt{19}\) and \(\sqrt{19}\) are both irrational and their difference is (0). (0) is rational.
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What is the value of (\(\sqrt{20}+\sqrt{45}\)\(\sqrt{20}-\sqrt{45}\))?
A. (-25)
यह \(a^2-b^2\) रूप है, इसलिए मान (20-45=-25) है। संयुग्मी गुणन में सीधे वर्गों का अंतर लें। / This is the \(a^2-b^2\) form, so the value is (20-45=-25). In conjugate multiplication take the difference of squares directly.
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If \(c=\sqrt{6}+\sqrt{2}\) and \(d=\sqrt{6}-\sqrt{2}\), which is the correct pair of (cd) and (c-d)?
A. (4), \(2\sqrt{2}\)
(cd=6-2=4) और \(c-d=2\sqrt{2}\) है। संयुग्मी रूप में गुणन और अंतर अलग-अलग निकालें। / (cd=6-2=4) and \(c-d=2\sqrt{2}\). In conjugate forms find the product and difference separately.
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Which is the simplified form of \(\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\)?
B. \(\frac{5+\sqrt{21}}{2}\)
संयुग्मी से गुणा करने पर अंश \(10+2\sqrt{21}\) और हर (4) मिलता है। इसलिए सरल रूप \(\frac{5+\sqrt{21}}{2}\) है। / Multiplying by the conjugate gives numerator \(10+2\sqrt{21}\) and denominator (4). So the simplified form is \(\frac{5+\sqrt{21}}{2}\).
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