Embibe Experts Solutions for Exercise 7: Assignment

The positive value of $a$ so that the coefficients of $x^5$ is equal to that of $x^{15}$ in the expansion of ${\left(x^2+\frac{a}{x^3}\right)}^{10}$ is:

The sum of the coefficients of all the even powers of $x$ in the expansion of ${\left(2x^2-3x+1\right)}^{11}$ is

The term independent of $x$ in the expansion of ${\left(x-\frac{1}{x}\right)}^4{\left(x+\frac{1}{x}\right)}^3$ is

If the second, third and fourth terms in the expansion of $(x+y{)}^n$ be $135,30$ and $\frac{10}{3}$ respectively, then

$\sum _{r=0}^6{\left(-1\right)}^r\left(\begin{array}{c}16\\ r\end{array}\right)$ is divisible by

The maximum value of ${}^{n}C_r$ is obtained when $r$ is equal to:

The value of the expression $C_0^2-C_1^2+C_2^2-\dots \dots .+(-1{)}^n{C}_n^2$ is

The number ${101}^{100}-1$ is divisible by