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 521-530 of 600 questions.
If \(x^{4}=5\), what is the value of \(x^{12}-x^{8}\)?
C. (100)
(x^{12}=\(x^{4}\)^{3}=125) और (x^{8}=\(x^{4}\)^{2}=25)। इसलिए अंतर (100) है। / Here (x^{12}=\(x^{4}\)^{3}=125) and (x^{8}=\(x^{4}\)^{2}=25). Therefore, the difference is (100).
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What is the value of (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}})?
A. \(\frac{27}{8}\)
(\left\(\frac{16}{81}\right\)^{\frac{1}{4}}=\frac{2}{3}), इसलिए (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}}=\left\(\frac{2}{3}\right\)^{-3}=\frac{27}{8})। परीक्षा में चौथा मूल पहले निकालें। / Since (\left\(\frac{16}{81}\right\)^{\frac{1}{4}}=\frac{2}{3}), (\left\(\frac{16}{81}\right\)^{-\frac{3}{4}}=\left\(\frac{2}{3}\right\)^{-3}=\frac{27}{8}). In exams, take the fourth root first.
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Which option gives the correct expansion of (\(3\sqrt{5}-2\sqrt{7}\)^{2})?
A. \(73-12\sqrt{35}\)
(\(3\sqrt{5}\)^{2}=45), (\(2\sqrt{7}\)^{2}=28), और मध्य पद \(12\sqrt{35}\) है। इसलिए विस्तार \(73-12\sqrt{35}\) है। / Here (\(3\sqrt{5}\)^{2}=45), (\(2\sqrt{7}\)^{2}=28), and the middle term is \(12\sqrt{35}\). Therefore, the expansion is \(73-12\sqrt{35}\).
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If \(2^{a}=32\) and \(8^{b}=64\), what is the value of \(a^{b}-b^{a}\)?
B. (9)
(a=5) और \(8^{b}=2^{3b}=2^{6}\) से (b=2)। इसलिए \(a^{b}-b^{a}=25-32=-7\), अतः सही मान (-7) है। / We get (a=5), and from \(8^{b}=2^{3b}=2^{6}\), (b=2). Thus \(a^{b}-b^{a}=25-32=-7\), so the correct value is (-7).
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What is the simplified form of (\frac{\(4x^{-1}\)^{2}\(3x^{3}\)^{2}}{12x^{4}})?
A. (12)
अंश \(16x^{-2}\cdot9x^{6}=144x^{4}\) है। \(\frac{144x^{4}}{12x^{4}}=12\) मिलता है। / The numerator is \(16x^{-2}\cdot9x^{6}=144x^{4}\). Thus \(\frac{144x^{4}}{12x^{4}}=12\).
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If \(\frac{10^{k}\cdot1000^{2}}{100}=10^{9}\), what is the value of (k)?
C. (5)
\(1000^{2}=10^{6}\) और \(100=10^{2}\), इसलिए बाएँ पक्ष की घात (k+6-2=k+4) है। (k+4=9) से (k=5)। / Since \(1000^{2}=10^{6}\) and \(100=10^{2}\), the exponent on the left is (k+6-2=k+4). From (k+4=9), (k=5).
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What is the value of \(\frac{\sqrt{108}+\sqrt{75}-\sqrt{12}}{\sqrt{3}}\)?
C. (9)
\(\sqrt{108}=6\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), और \(\sqrt{12}=2\sqrt{3}\)। अंश \(9\sqrt{3}\) है, इसलिए मान (9) है। / Here \(\sqrt{108}=6\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The numerator is \(9\sqrt{3}\), so the value is (9).
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If \(y=5+2\sqrt{6}\), what is the value of \(y+\frac{1}{y}\)?
B. (10)
\(\frac{1}{5+2\sqrt{6}}=5-2\sqrt{6}\), क्योंकि गुणनफल (25-24=1) है। योग (10) मिलता है। / We have \(\frac{1}{5+2\sqrt{6}}=5-2\sqrt{6}\), because the product is (25-24=1). The sum is (10).
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A. \(\frac{z}{xy^{2}}\)
अंदर \(\frac{x^{-2}y^{4}}{z^{-3}}=x^{-2}y^{4}z^{3}\), इसलिए उल्टा \(x^{2}y^{-4}z^{-3}\) है। \(\frac{y^{2}}{x^{3}z^{2}}\) से गुणा करने पर \(\frac{1}{xy^{2}z^{5}}\) मिलता है। / Inside, \(\frac{x^{-2}y^{4}}{z^{-3}}=x^{-2}y^{4}z^{3}\), so its reciprocal is \(x^{2}y^{-4}z^{-3}\). Multiplying by \(\frac{y^{2}}{x^{3}z^{2}}\) gives \(\frac{1}{xy^{2}z^{5}}\).
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What is the value of (\left\(64^{\frac{2}{3}}\right\)\cdot\left\(8^{-\frac{4}{3}}\right\))?
A. (1)
(64^{\frac{2}{3}}=(4)^{2}=16) और (8^{-\frac{4}{3}}=(2)^{-4}=\frac{1}{16})। गुणनफल (1) है। / Here (64^{\frac{2}{3}}=(4)^{2}=16) and (8^{-\frac{4}{3}}=(2)^{-4}=\frac{1}{16}). The product is (1).
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