Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 1: Level 1

The sum of all those terms which are rational numbers in the expansion of ${\left(2^{\frac{1}{3}}+3^{\frac{1}{4}}\right)}^{12}$ is:

If in the expansion of ${\left(x^3-\frac{1}{x^2}\right)}^n$, the sum of coefficients of $x^5$ and $x^{10}$ is $0$, then the coefficient of the third term is

The number of irrational terms in the expansion of ${\left(5^{\frac{1}{6}}+2^{\frac{1}{8}}\right)}^{100}$ is

If the last term in ${\left(\sqrt[3]{2}+\frac{1}{\sqrt{2}}\right)}^n$ is ${\left[\frac{1}{3(9{)}^{1/3}}\right]}^{{\log }_{3}8},$ then the fifth term is

The solution set of ${}^{5}C_{x-1}>2·\left({}^{5}C_x\right)$ is

If the coefficients of ${\left(2r+4\right)}^{\mathrm{th}},{\left(r-2\right)}^{\mathrm{th}}$ terms in the expansion of ${\left(1+x\right)}^{18}$ are equal, then the value of $r$ is

If the constant term, in binomial expansion of ${\left(2x^r+\frac{1}{x^2}\right)}^{10}$ is $180,$ then $r$ is equal to ____________.

The value of the numerically greatest term in the expansion of $(2x+3y{)}^{11}$ when $x=\frac{1}{2}$ and $y=\frac{1}{3}$ is