Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 1: BITSAT 2017

Let ${\left(2x^2+3x+4\right)}^{10}=\sum _{r=0}^{20}{a}_r{x}^r$, then the value of $\frac{a_{8}}{a_{12}},$ is

If ${\left(1+x+x^2\right)}^{20}=\sum _{r=0}^{40}{a}_r·x^r$, then $\sum _{r=0}^{39}{\left(-1\right)}^r·a_r·a_{r+1}$ equal to

If the coefficient of $x^3$ and $x^4$ in the expansion of $\left(1+ax+b{x}^2\right){\left(1-2x\right)}^{18}$ in powers of $x$ are both zero, then $\left(a, b\right)$ is equal to

In the expansion of ${\left(1+x+x^3+x^4\right)}^{10}$, the coefficient of $x^4$ is

The coefficient of $x^{-n}$ in ${\left(1+x\right)}^n{\left(1+\frac{1}{x}\right)}^n$ is

The greatest term in the expansion of $\sqrt{3}{\left(1+\frac{1}{\sqrt{3}}\right)}^{20}$ is

The coefficient of $x^5$ in the expansion of ${\left(1+x\right)}^{21}+{\left(1+x\right)}^{22}+\dots +{\left(1+x\right)}^{30}$ is

The value of $\sum _{r=1}^{10}r·\frac{{}^{n}C_r}{{}^{n}C_{r-1}}$ is equal to