R S Aggarwal Solutions for Exercise 1: EXERCISE 1

In the expansion of $(x+a{)}^n$, if the sum of odd terms be $P$ and the sum of even terms be $Q$ then $4PQ=$?

If the coefficients of the second, third and fourth terms in the expansion of $(1+x{)}^{2n}$ are in $\mathrm{AP}$, then

If $C$ denotes ${}^{n}C_r$ in the expansion of $(1+x{)}^n,$ then $C_0+C_1+C_2+\dots +C_n=?$

$\left(C_0+C_2+C_4+C_6+\dots \right)=?$

$\left\{\frac{C_1}{C_0}+2\frac{C_2}{C_1}+3\frac{C_3}{C_2}+\dots +n·\frac{C_n}{C_{n-1}}\right\}=?$

$\left[C_1+2C_2+3C_3+\dots +n{C}_n\right]=?$

$\left\{C_0+2C_1+3C_2+\dots +(n+1)C_n\right\}=?$

$\left\{C_0+3C_1+5C_2+\dots +(2n+1)C_n\right\}=?$