M L Aggarwal Solutions for Chapter: Binomial Theorem, Exercise 4: CHAPTER TEST

In the expansion of ${\left(x^2-\frac{1}{3x}\right)}^9$, find the coefficient of $x^9$.

In the expansion of ${\left(x^2-\frac{1}{3x}\right)}^9$, find the term independent of $x$.

In the binomial expansion of $(1+x{)}^{10}$, if the coefficients of $(2m+1{)}^{th}$ and $(4m+5{)}^{th}$ terms are equal then, find $m$.

If the coefficients of $4^{th}$ and ${13}^{th}$ terms in the expansion of ${\left(x^2+\frac{1}{x}\right)}^n$ are equal, then find the term which is independent of $x$.

In the expansion of ${\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)}^n$, the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $1: 6$, find $n$.

Find the second term after the middle term in the expansion of ${\left(\frac{x}{2}+\frac{2}{x^2}\right)}^{20}$.

If the coefficients of $r^{th}$, $(r+1{)}^{th}$ and $(r+2{)}^{th}$ terms in the expansion of $(1+x{)}^{14}$ are in $\mathrm{A}.\mathrm{P}.$ find $r$.

If three consecutive coefficients in the expansion of $(1+x{)}^n$ are in the ratio $6: 33: 110$, find $n$.