R S Aggarwal Solutions for Exercise 2: EXERCISE 10B

The term independent of $x$ in the expansion ${\left(x-\frac{1}{3x^2}\right)}^9$ is $T_k$. Find the value of $k$.

If the coefficient of the middle term in the expansion $(1+x{)}^{2n}$ is ${}^{2n}C_k$, then find the value of $k$.

Write the coefficient of $x^7{y}^2$ in the expansion of $(x+2y{)}^9$.

If the coefficients $(r-5{)}^{\mathrm{th}}$ and  $(2r-1{)}^{\mathrm{th}}$ terms in the expansion of ${\left(1+x\right)}^{34}$ are equal, find the value of $r$

Write $4^{\text{th }}$ term from the end in the expansion of ${\left(\frac{3}{x^2}-\frac{x^3}{6}\right)}^7$.

Find the coefficient of $x^n$ in the expansion of $(1+x)(1-x{)}^n$.

In the binomial expansion of $(a+b{)}^n,$ the coefficients of $4^{\text{th }}$ and ${13}^{\mathrm{th}}$ terms are equal to each other. Find the value of $n.$

Find the positive value of $m$ for which the coefficient of $x^2$ in the expansion of $(1+x{)}^m$ is $6$.