જો ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .... + {C_n}{x^n}$, તો ${C_0}{C_2} + {C_1}{C_3} + {C_2}{C_4} + {C_{n - 2}}{C_n}$= . . .
$\frac{{(2n)!}}{{(n + 1)!(n + 2)!}}$
$\frac{{(2n)!}}{{(n - 2)!(n + 2)!}}$
$\frac{{(2n)!}}{{(n)!(n + 2)!}}$
$\frac{{(2n)!}}{{(n - 1)!(n + 2)!}}$
જો $(1 + x - 3x^2)^{2145} = a_0 + a_1x + a_2x^2 + .........$ હોય તો $a_0 - a_1 + a_2 - a_3 + ..... $ નો છેલ્લો અંક મેળવો
$\sum\limits_{r - 1}^{11} {(x + r)\,(x + r + 1)\,(x + r + 2)...\,(x + r + 9)}$ ના વિસ્તરણમાં $x^9$ નો સહગુણક મેળવો
જો $(1 + x)(1 + x + x^2)(1 + x + x^2 + x^3)\,\, ......\,\,$$(1 + x + x^2 + ..... + x^{30}) = $$a_0 + a_1x + a_2x^2$ .....$+$ $a_{465}x^{465}$, હોય તો $a_0 + a_2 + a_4 + ......... +$ ની કિમત મેળવો
$\left( {\begin{array}{*{20}{c}}{20}\\0\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\1\end{array}} \right)$$+$$\left( {\begin{array}{*{20}{c}}{20}\\2\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\3\end{array}} \right)$$+…..-……+$$\left( {\begin{array}{*{20}{c}}{20}\\{10}\end{array}} \right)$ નો સરવાળો.
$\sum\limits_{k = 0}^{10} {^{20}{C_k} = } $