If $n$ is an integer greater than $1$,then $a - ^nC_1(a - 1) + ^nC_2(a - 2) + \dots + (-1)^n(a - n) = $

In the expansion of $(x + a)^n$,the sum of odd terms is $P$ and the sum of even terms is $Q$. Then the value of $(P^2 - Q^2)$ is:

If $\sum_{r=1}^{30} \frac{r^2({}^{30}C_r)^2}{{}^{30}C_{r-1}} = \alpha \times 2^{29}$,then $\alpha$ is equal to

If $\sum\limits_{K = 1}^{12} {12K \cdot {^{12}C_K} \cdot {^{11}C_{K - 1}}} $ is equal to $\frac{{12 \times 21 \times 19 \times 17 \times \dots \times 3}}{{11!}} \times {2^{12}} \times p$,then $p$ is:

If $n$ is a positive integer greater than $1$,then $3({ }^n C_0) - 8({ }^n C_1) + 13({ }^n C_2) - 18({ }^n C_3) + \ldots$ up to $(n+1)$ terms $=$

$C_0 C_r + C_1 C_{r+1} + C_2 C_{r+2} + \dots + C_{n-r} C_n =$