Let $(1 + x)^m = C_0 + C_1x + C_2x^2 + C_3x^3 + . . . . . +C_mx^m$, where $C_r ={}^m{C_r}$ and $A = C_1C_3 + C_2C_4+ C_3C_5 + C_4C_6 + . . . . . .. + C_{m-2}C_m$, then which is false
$A \ge {}^{2m}{C_{m - 2}}$
$A < {}^{2m}{C_{m - 2}}$
$A = {}^{2m}{C_{m - 2}} - {}^m{C_2}$
$A < {C^2}_0 + {C^2}_1 + {C^2}_1 + .......{C^2}_m$
$\sum\limits_{k = 0}^{10} {^{20}{C_k} = } $
The coefficient of $x^8$ in the expansion of $(x-1) (x- 2) (x-3)...............(x-10)$ is :
$\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}$ is equal to
Let ${\left( {1 + x + {x^2}} \right)^{20}}\left( {2x + 1} \right) = {a_0} + {a_1}{x^1} + {a_2}{x^2} + ... + {a_{41}}{x^{41}}$ , then $\frac{{{a_0}}}{1} + \frac{{{a_1}}}{2} + .... + \frac{{{a_{41}}}}{{42}}$ is equal to
If $C_r= ^{100}{C_r}$ , then $1.C^2_0 - 2.C^2_1 + 3.C^2_3 - 4.C^2_0 + 5.C^2_4 - .... + 101.C^2_{100}$ is equal to