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 151-160 of 600 questions.
What is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?
A. \(2^2\)
समान आधार में घातें (3-5+4=2) जुड़ती हैं। इसलिए सरल रूप \(2^2\) है। / For the same base, exponents add as (3-5+4=2). Hence the simplified form is \(2^2\).
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What is the simplified form of \(\frac{3^2\cdot3^{-4}}{3^{-3}}\)?
B. \(3^1\)
घातों को (2-4-(-3)=1) करें। ऋणात्मक घात घटाते समय चिह्न बदलता है। / Combine the exponents as (2-4-(-3)=1). The sign changes when subtracting a negative exponent.
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If \(x\neq0\), what is the simplified form of (\frac{\(x^3\)2\cdot x^{-4}}{x})?
A. (x)
पहले (\(x^3\)2=x-6), फिर घात (6-4-1=1) है। इसलिए उत्तर (x) है। / First (\(x^3\)2=x-6), then the exponent is (6-4-1=1). So the answer is (x).
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What is the simplified form of (\left\(\frac{2^3\cdot5^3}{10^2}\right\))?
A. (10)
क्योंकि (23\cdot53=(10)3), इसलिए \(\frac{10^3}{10^2}=10\)। समान घात वाले गुणकों को पहले जोड़ें। / Since (23\cdot53=(10)3), \(\frac{10^3}{10^2}=10\). Combine equal powers first.
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What is the value of \(\frac{16^2}{2^5}\)?
A. \(2^3\)
(162=\(2^4\)2=28) होता है। इसलिए \(\frac{2^8}{2^5}=2^3\) है। / (162=\(2^4\)2=28). Therefore \(\frac{2^8}{2^5}=2^3\).
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What is the value of ((0.2)^{-2})?
C. (25)
\(0.2=\frac{1}{5}\), इसलिए ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25)। दशमलव को भिन्न में बदलना आसान होता है। / \(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.
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What is the value of (\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\))?
A. (1)
(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2=\frac{4}{9}) है। इसलिए \(\frac{4}{9}\cdot\frac{9}{4}=1\) है। / (\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2=\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).
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If (a=2), what is the value of \(a^3+a^{-1}\)?
B. \(\frac{17}{2}\)
\(2^3=8\) और \(2^{-1}=\frac{1}{2}\) है। इसलिए योग \(8+\frac{1}{2}=\frac{17}{2}\) है। / \(2^3=8\) and \(2^{-1}=\frac{1}{2}\). Thus the sum is \(8+\frac{1}{2}=\frac{17}{2}\).
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What is the correct simplified form of (\(x^2y^3\)2)?
A. \(x^4y^6\)
बाहरी घात दोनों कारकों की घातों से गुणा होती है। इसलिए (\(x^2y^3\)2=x-4y-6) है। / The outside exponent multiplies the exponents of both factors. Hence (\(x^2y^3\)2=x-4y-6).
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What is the simplified form of (\frac{\(2x^3\)2}{4x-2}) if \(x\neq0\)?
B. \(x^4\)
(\(2x^3\)2=4x-6) होता है। फिर \(\frac{4x^6}{4x^2}=x^4\) है। / (\(2x^3\)2=4x-6). Then \(\frac{4x^6}{4x^2}=x^4\).
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