Chapter 7: Problem 536
\({ }^{10} \mathrm{C}_{1}+{ }^{10} \mathrm{C}_{3}+{ }^{10} \mathrm{C}_{5}+\ldots \ldots \ldots+{ }^{10} \mathrm{C}_{9}=\) (a) 512 (b) 1024 (c) 2048 (d) 1023
Chapter 7: Problem 536
\({ }^{10} \mathrm{C}_{1}+{ }^{10} \mathrm{C}_{3}+{ }^{10} \mathrm{C}_{5}+\ldots \ldots \ldots+{ }^{10} \mathrm{C}_{9}=\) (a) 512 (b) 1024 (c) 2048 (d) 1023
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Get started for free\(\left[(\sqrt{2}+1)^{8}\right]=\ldots \ldots \ldots ;\) where [] is integer part function. (a) 1151 (b) 1152 (c) 1153 (a) 1154
\(\left[(\sqrt{3}+1)^{6}\right]=\ldots \ldots \ldots ;\) where [] is integer part function. (a) 415 (b) 416 (c) 417 (a) 418
\(\mathrm{C}_{0}+2 \mathrm{C}_{1}+3 \mathrm{C}_{2}+\cdots+(\mathrm{n}+1) \mathrm{C}_{\mathrm{n}}\) is \(=\) (a) \((\mathrm{n}+1) 2^{\mathrm{n}-1}\) (b) \((\mathrm{n}+2) 2^{\mathrm{n}-1}\) (c) \((\mathrm{n}+1) 2^{\mathrm{n}}\) (d) \((\mathrm{n}+1) 2^{\mathrm{n}-1}\)
If \(\mathrm{P}\) and \(\mathrm{Q}\) are coefficients of \(\mathrm{x}^{\mathrm{n}}\) in expansion of \((1+\mathrm{x})^{2 \mathrm{n}}\) and \((1+x)^{2 n-1}\) then (a) \(\mathrm{P}=\mathrm{Q}\) (b) \(P=2 Q\) (c) \(2 \mathrm{P}=\mathrm{Q}\) (a) \(P+Q=0\)
\(\left|\begin{array}{c}\mathrm{n}-1 \\\ 1\end{array}\right|+\left|\begin{array}{c}\mathrm{n}-1 \\\ 2\end{array}\right|+\ldots+\left|\begin{array}{l}\mathrm{n}-1 \\\ \mathrm{n}-1\end{array}\right|=\underline{ } ; \mathrm{n}>1\) (a) \(2^{\mathrm{n}}-1\) (b) \(2^{\mathrm{n}-2}\) (c) \(2^{\mathrm{n}-1}-1\) (d) \(2^{\mathrm{n}-1}\)
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