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 541-550 of 600 questions.
What is the value of (\(\sqrt{23}+\sqrt{7}\)\(\sqrt{23}-\sqrt{7}\))?
C. (16)
यह संयुग्मी गुणन है इसलिए मान (23-7=16) है। \(a^2-b^2\) रूप पहचानें। / This is conjugate multiplication so the value is (23-7=16). Identify the \(a^2-b^2\) form.
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What is the rationalised form of \(\frac{5}{\sqrt{29}+2}\)?
B. \(\frac{\sqrt{29}-2}{5}\)
संयुग्मी से गुणा करने पर हर (29-4=25) बनता है। इसलिए रूप \(\frac{\sqrt{29}-2}{5}\) है। / Multiplying by the conjugate makes the denominator (29-4=25). So the form is \(\frac{\sqrt{29}-2}{5}\).
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If \(x=\sqrt{24}+\sqrt{6}\), what is the value of \(x^2\)?
D. (54)
\(\sqrt{24}=2\sqrt{6}\) इसलिए \(x=3\sqrt{6}\) है। इसका वर्ग (54) है। / \(\sqrt{24}=2\sqrt{6}\) so \(x=3\sqrt{6}\). Its square is (54).
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What is the simplified form of \(\sqrt{242}-\sqrt{128}+\sqrt{72}\)?
C. \(9\sqrt{2}\)
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\) है। इसलिए परिणाम \(9\sqrt{2}\) है। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). Therefore the result is \(9\sqrt{2}\).
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If \(q=\sqrt{10}+3\), what is the value of \(q^2-6q\)?
A. (1)
\(q^2=19+6\sqrt{10}\) और \(6q=18+6\sqrt{10}\) है। घटाने पर (1) मिलता है। / \(q^2=19+6\sqrt{10}\) and \(6q=18+6\sqrt{10}\). Subtracting gives (1).
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What is the value of \(\frac{\sqrt{27}+\sqrt{12}}{\sqrt{3}}\)?
B. (5)
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। \(\sqrt{3}\) से भाग देने पर (5) मिलता है। / \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Dividing by \(\sqrt{3}\) gives (5).
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If \(z=\sqrt{31}-\sqrt{22}\), which is the value of \(z^2\)?
D. \(53-2\sqrt{682}\)
(\(\sqrt{31}-\sqrt{22}\)2=31+22-2\sqrt{682}) है। मध्य पद का चिन्ह ऋणात्मक रखें। / (\(\sqrt{31}-\sqrt{22}\)2=31+22-2\sqrt{682}). Keep the middle term negative.
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What is the value of (\(\sqrt{29}+5\)2-\(\sqrt{29}-5\)2)?
B. \(20\sqrt{29}\)
पहचान ((a+b)2-(a-b)2=4ab) लगाएं। यहाँ \(a=\sqrt{29}\) और (b=5), इसलिए मान \(20\sqrt{29}\) है। / Use ((a+b)2-(a-b)2=4ab). Here \(a=\sqrt{29}\) and (b=5), so the value is \(20\sqrt{29}\).
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If \(P=\sqrt{363}+\sqrt{147}-\sqrt{75}\), what is (P) equal to?
C. \(13\sqrt{3}\)
\(\sqrt{363}=11\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। इसलिए \(P=13\sqrt{3}\) है। / \(\sqrt{363}=11\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). Therefore \(P=13\sqrt{3}\).
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What is the rationalised form of \(\frac{9}{\sqrt{26}+\sqrt{17}}\)?
A. \(\sqrt{26}-\sqrt{17}\)
संयुग्मी से गुणा करने पर हर (26-17=9) बनता है। इसलिए उत्तर \(\sqrt{26}-\sqrt{17}\) है। / Multiplying by the conjugate makes the denominator (26-17=9). So the answer is \(\sqrt{26}-\sqrt{17}\).
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