G Tewani Solutions for Chapter: Binomial Theorem, Exercise 1: Exercises

The number of distinct terms in the expansion of ${\left(x+\frac{1}{x}+x^2+\frac{1}{x^2}\right)}^{15}$ is/are (with respect to different powers of $x$)

If $p=(8+3\sqrt{7}{)}^n$ and $f=p-\left[p\right],$ where $[·]$ denotes the greatest integer function, then the value of $p(1-f)$ is equal to

The coefficient of $x^{53}$ in the following expansion $\sum _{m=0}^{100}{}^{100}C_m{\left(x-3\right)}^{100-m}·2^m$ is

Let $f\left(x\right)=a_0+a_{1}x+a_2{x}^2+\dots .+a_n{x}^n+\dots \dots \dots$ and $\frac{f\left(x\right)}{1-x}=b_0+b_{1}x+b_2{x}^2+\dots \dots .+b_n{x}^n+\dots \dots \dots ,$ then

Maximum sum of the coefficients in the expansion of ${\left(1-x\sin \theta +x^2\right)}^n$ is

Value of $\sum _{k=1}^{\infty }\sum _{r=0}^k\frac{1}{3^k}\left({}^{k}C_r\right)$ is

The value of $\sum _{r=1}^{n+1}\left(\sum _{k=1}^n{}^{k}C_{r-1}\right)$ (where $r, k, n\in N$) is equal to

If ${\left(1-x\right)}^{-n}=a_0+a_{1}x+a_2{x}^2+\dots ..+a_r{x}^r+\dots$, then $a_0+a_1+a_2+\dots +a_r$ is equal to