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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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\(\left[\left\\{19^{3}+6^{3}+3(19)(6)(25)\right\\} /\left\\{3^{6}+6(243)(2)+(15)(81)(4)\right.\right.\) \(\left.\left.+(20)(27)(8)+(15)(9)(16)+(6)(3)(32)+2^{6}\right\\}\right]=\) (a) (b) 5 (c) 2 (d) 6
\(\left|\begin{array}{l}\mathrm{n} \\\ 0\end{array}\right|+3\left|\begin{array}{l}\mathrm{n} \\\ 1\end{array}\right|+5\left|\begin{array}{l}\mathrm{n} \\\ 2\end{array}\right|+\ldots+(2 \mathrm{n}+1)\left|\begin{array}{l}\mathrm{n} \\\ \mathrm{n}\end{array}\right|=\ldots ; \mathrm{n} \in \mathrm{N}\) (a) \((\mathrm{n}+2) 2^{\mathrm{n}}\) (b) \((n+1) 2^{n}\) (c) \(\mathrm{n} 2^{\mathrm{n}}\) (d) \((\mathrm{n}+1) 2^{\mathrm{n}+1}\)
In the binomial expansion of \((a-b)^{n}, n \geq 0\), the sum of \(5^{\text {th }}\) and \(6^{\text {th }}\) terms is zero then \((\mathrm{a} / \mathrm{b})=\) (a) \([5 /(\mathrm{n}-4)]\) (b) \([6 /(\mathrm{n}-5)]\) (c) \([(n-5) / 6]\) (d) \([(n-4) / 5]\)
It coefficients of middle terms in expansion of \((1+\lambda \mathrm{x})^{8}\) and \((1-\lambda \mathrm{x})^{6}\) are equal then \(\lambda=\) (a) \((2 / 7)\) (b) \([(-2) / 7]\) (c) \([(-3) / 7]\) (d) None of these
The expansion of \(\left[\mathrm{x}+\sqrt{\left(\mathrm{x}^{3}-1\right)}\right]^{5}+\left[\mathrm{x}-\sqrt{\left(\mathrm{x}^{3}-1\right)}\right]^{5}\) is a polynomial of degree (a) 5 (b) 6 (c) 7 (d) 8
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