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 591-600 of 600 questions.
What is the value of (\(\sqrt{125}+\sqrt{320}\)2)?
A. (845)
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{320}=8\sqrt{5}\), इसलिए योग \(13\sqrt{5}\) है। इसका वर्ग (845) है। / \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{320}=8\sqrt{5}\), so the sum is \(13\sqrt{5}\). Its square is (845).
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If \(w=\sqrt{18}+\sqrt{13}\), what is the value of \(w^2-31\)?
B. \(2\sqrt{234}\)
\(w^2=18+13+2\sqrt{234}=31+2\sqrt{234}\) है। इसलिए \(w^2-31=2\sqrt{234}\) है। / \(w^2=18+13+2\sqrt{234}=31+2\sqrt{234}\). So \(w^2-31=2\sqrt{234}\).
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If \(x=\sqrt{22}+\sqrt{10}\), what is the value of \(x^2-32\)?
A. \(2\sqrt{220}\)
\(x^2=22+10+2\sqrt{220}=32+2\sqrt{220}\) है। इसलिए \(x^2-32=2\sqrt{220}\) है। / \(x^2=22+10+2\sqrt{220}=32+2\sqrt{220}\). So \(x^2-32=2\sqrt{220}\).
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Which is the simplified form of \(\frac{\sqrt{31}+\sqrt{19}}{\sqrt{31}-\sqrt{19}}\)?
A. \(\frac{25+\sqrt{589}}{6}\)
संयुग्मी से गुणा करने पर अंश \(50+2\sqrt{589}\) और हर (12) मिलता है। सरल रूप \(\frac{25+\sqrt{589}}{6}\) है। / Multiplying by the conjugate gives numerator \(50+2\sqrt{589}\) and denominator (12). The simplified form is \(\frac{25+\sqrt{589}}{6}\).
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If \(a=8+\sqrt{7}\) and \(b=8-\sqrt{7}\), what is the value of \(a^2-b^2\)?
B. \(32\sqrt{7}\)
\(a-b=2\sqrt{7}\) और (a+b=16) है। इसलिए \(a^2-b^2=32\sqrt{7}\) है। / \(a-b=2\sqrt{7}\) and (a+b=16). Therefore \(a^2-b^2=32\sqrt{7}\).
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What is the simplified form of \(\sqrt{726}-\sqrt{486}+\sqrt{150}\)?
A. \(7\sqrt{6}\)
\(\sqrt{726}=11\sqrt{6}\), \(\sqrt{486}=9\sqrt{6}\) और \(\sqrt{150}=5\sqrt{6}\) है। इसलिए परिणाम \(7\sqrt{6}\) है। / \(\sqrt{726}=11\sqrt{6}\), \(\sqrt{486}=9\sqrt{6}\), and \(\sqrt{150}=5\sqrt{6}\). Therefore the result is \(7\sqrt{6}\).
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Which is the rationalised form of \(\frac{12}{\sqrt{43}-\sqrt{31}}\)?
C. \(\sqrt{43}+\sqrt{31}\)
संयुग्मी से गुणा करने पर हर (43-31=12) बनता है। इसलिए उत्तर \(\sqrt{43}+\sqrt{31}\) है। / Multiplying by the conjugate makes the denominator (43-31=12). So the answer is \(\sqrt{43}+\sqrt{31}\).
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If \(q=\sqrt{15}+4\), what is the value of \(q^2-8q\)?
A. (-1)
\(q^2=31+8\sqrt{15}\) और \(8q=32+8\sqrt{15}\) है। घटाने पर (-1) मिलता है। / \(q^2=31+8\sqrt{15}\) and \(8q=32+8\sqrt{15}\). Subtracting gives (-1).
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B. (24)
क्षेत्रफल (\(\sqrt{41}+\sqrt{17}\)\(\sqrt{41}-\sqrt{17}\)=41-17=24) है। संयुग्मी आयामों से परिमेय क्षेत्रफल मिलता है। / Area is (\(\sqrt{41}+\sqrt{17}\)\(\sqrt{41}-\sqrt{17}\)=41-17=24). Conjugate dimensions give rational area.
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In which option is the quotient of two irrational numbers rational?
A. \(\frac{\sqrt{75}}{\sqrt{3}}\)
\(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\) है जो परिमेय है। भाग के बाद पूर्ण वर्ग बनने की जाँच करें। / \(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\), which is rational. Check whether division forms a perfect square.
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