જો ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .... + {C_n}{x^n}$, તો ${C_0}{C_2} + {C_1}{C_3} + {C_2}{C_4} + {C_{n - 2}}{C_n}$= . . .

  • A

    $\frac{{(2n)!}}{{(n + 1)!(n + 2)!}}$

  • B

    $\frac{{(2n)!}}{{(n - 2)!(n + 2)!}}$

  • C

    $\frac{{(2n)!}}{{(n)!(n + 2)!}}$

  • D

    $\frac{{(2n)!}}{{(n - 1)!(n + 2)!}}$

Similar Questions

સંખ્યા $111......1$ ($91$ વખત) એ . . .

બહુપદી $(x-1) (x-2^1) (x-2^2) .... (x-2^{19})$ માં $x^{19}$ નો સહગુણક મેળવો 

${C_0} - {C_1} + {C_2} - {C_3} + ..... + {( - 1)^n}{C_n}$ = . . .

જો ${a_k} = \frac{1}{{k(k + 1)}},$( $k = 1,\,2,\,3,\,4,.....,\,n$), તો ${\left( {\sum\limits_{k = 1}^n {{a_k}} } \right)^2} = $

$\left( \begin{array}{l}30\\0\end{array} \right)\,\left( \begin{array}{l}30\\10\end{array} \right) - \left( \begin{array}{l}30\\1\end{array} \right)\,\left( \begin{array}{l}30\\11\end{array} \right)$ + $\left( \begin{array}{l}30\\2\end{array} \right)\,\left( \begin{array}{l}30\\12\end{array} \right) + ....... + \left( \begin{array}{l}30\\20\end{array} \right)\,\left( \begin{array}{l}30\\30\end{array} \right) = .$ . ..

  • [IIT 2005]