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Chapter 1: Problem 21
If \(n(A)=6\) and \(n(B)=4\) then minimum value of \(n(A-B)\) is (a) 2 (b) 7 (c) 6 (d) 4
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If \(\mathrm{f}(\mathrm{x})=[(1-\mathrm{x}) /(1+\mathrm{x})]\) then \(\mathrm{f}(\mathrm{f}(\cos 2 \theta))=\ldots\) (a) \(\tan 2 \theta\) (b) \(\sec 2 \theta\) (c) \(\cos 2 \theta\) (d) \(\cot 2 \theta\)
If \(\mathrm{f}(2 \mathrm{x}+3 \mathrm{y}, 2 \mathrm{x}-3 \mathrm{y})=24 \mathrm{xy}\) then \(\mathrm{f}(\mathrm{x}, \mathrm{y})\) is (a) \(2 \mathrm{xy}\) (b) \(2\left(\mathrm{x}^{2}-\mathrm{y}^{2}\right)\) (c) \(x^{2}-y^{2}\) (d) none of these
If the function \(\mathrm{f}:[1, \infty) \rightarrow[1, \infty)\) is defined by \(\mathrm{f}(\mathrm{x})=2^{\mathrm{X}(\mathrm{x}-1)}\) then \(\mathrm{f}^{-1}(\mathrm{x})\) is (a) \((1 / 3)^{\mathrm{x}}\) (b) \((1 / 2)\left[1+\sqrt{ \left.\left(1+4 \log _{2} \mathrm{x}\right)\right]}\right.\) (c) \(\left.(1 / 2)\left[1-\sqrt{(} 1+4 \log _{2} \mathrm{x}\right)\right]\) (d) \(2^{[1 /\\{x(x-1)\\}]}\)
If \(\mathrm{A}=\\{1,2,3\\}\), then the number of equivalence relation containing \((1,2)\) is (a) 1 (b) 2 (c) 3 (d) 8
\(g: R \rightarrow R, g(x)=3+3 \sqrt{x}\) and \(f(g(x))=2-3 \sqrt{x}+x\) then \(\mathrm{f}(\mathrm{x})=\ldots\) (a) \(x^{3}-x^{2}+x-5\) (b) \(x^{3}-9 x^{2}+26 x-22\) (c) \(x^{3}+9 x^{2}-26 x+5\) (d) \(x^{3}+x^{2}-x+5\)
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