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Chapter 7: Problem 512
Constant term in expansion of \([1+(2 / \mathrm{x})-(2 / \mathrm{x})]^{4}\) is ........ (a) 5 (b) \(-5\) (c) 4 (d) \(-4\)
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Remainder when \(2^{2000}\) is divided by 17 is......... (a) 1 (b) 2 (c) 8 (d) 12
\(\mathrm{R}=(3+\sqrt{5})^{2 \mathrm{n}}\) and \(\mathrm{f}=\mathrm{R}-[\mathrm{R}]\), Where [] is an integer part function then \(\mathrm{R}(1-\mathrm{f})=\) (a) \(2^{2 \mathrm{n}}\) (b) \(4^{2 \mathrm{n}}\) (c) \(8^{2 \mathrm{n}}\) (d) \(1^{2 \mathrm{n}}\)
Let \(\mathrm{x}>-1\) then statement \((1+\mathrm{x})^{\mathrm{n}}>1+\mathrm{n} \mathrm{x}\) is true for (a) \(\forall \mathrm{n} \in \mathrm{N}\) (b) \(\forall n>1\) (c) \(\forall \mathrm{n}>1\) and \(\mathrm{x} \neq 0\) (d) \(\forall \mathrm{n} \in \mathrm{R}\)
If \(\mathrm{x}\) is so small that terms with \(\mathrm{x}^{3}\) and higher powers of \(\mathrm{x}\) may be neglected then \(\left[\left\\{(1+\mathrm{x})^{(3 / 2)}-\\{1+(\mathrm{x} / 2)\\}^{3}\right\\} /\left\\{(1-\mathrm{x})^{(1 / 2)}\right\\}\right]\) may be approximated as \(\ldots \ldots \ldots\) (a) \([(-3) / 8] \mathrm{x}^{2}\) (b) \((1 / 2) \mathrm{x}-(3 / 8) \mathrm{x}^{2}\) (c) \(1-(3 / 8) x^{2}\) (d) \(3 x+(3 / 8) x^{2}\)
coefficients of 5 th, 6 th and 7 th terms are in A. P. for expansion of \((1+\mathrm{x})^{\mathrm{n}}\) then \(\mathrm{n}=\) (a) 7 or 12 (b) \(-7\) or 14 (c) 7 or 14 (d) \(-7\) or 12
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