The sum of coefficients in ${(1 + x - 3{x^2})^{2134}}$ is
$-1$
$1$
$0$
${2^{2134}}$
(b) For, the sum of coefficients, put $x = 1$, to obtain the sum as ${(1 + 1 – 3)^{2134}} = 1$.
If ${C_0},{C_1},{C_2},…….,{C_n}$ are the binomial coefficients, then $2.{C_1} + {2^3}.{C_3} + {2^5}.{C_5} + ….$ equals
If $\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L$, then $L$ is equal to $…..$
In the expansion of ${(1 + x)^{50}},$ the sum of the coefficient of odd powers of $x$ is
Let ${s_1} = \mathop \sum \limits_{j = 1}^{10} j\left( {j – 1} \right)\left( {\begin{array}{*{20}{c}}{10}\\j\end{array}} \right)\;,$$\;{s_2} = \mathop \sum \limits_{j = 1}^{10} j\;\left( {\begin{array}{*{20}{c}}{10}\\j\end{array}} \right)\;and,$${s_3} = \mathop \sum \limits_{j = 1}^{10} {j^2}\left( {\begin{array}{*{20}{c}}{10}\\j\end{array}} \right)\;,\;$
Statement $-1$:${s_3} = 55 \times {2^9}$
Statement $-2$: ${s_1} = 90 \times {2^8}\;$ and ${s_2} = 10 \times {2^8}$
If the Coefficient of $x^{30}$ in the expansion of $\left(1+\frac{1}{x}\right)^6\left(1+x^2\right)^7\left(1-x^3\right)^8 ; x \neq 0$ is $\alpha$, then $|\alpha|$ equals
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