Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 1: KEAM 2018

The sum of the coefficients in the expansion of ${\left(1+2\mathrm{x}-{\mathrm{x}}^2\right)}^{20}$ is

The coefficient of $x^3$ in the expansion of ${\left(1-x+x^2\right)}^5$ is

Remainder when $x=1!+2!+3!+4!+\dots +100!$ is divided by $240,$ is

The remainder when $2^{2003}$ is divided by $17$ is

If $x=3^{100},$ then $x$ has

The third term in the expansion of ${\left(\frac{1}{x}+x^{{\log }_{10}x}\right)}^5,x>1$ is $1000,$ then $x$ equals.

The coefficient of $x^{13}$ in the expansion of ${\left(1-x\right)}^5{\left(1+x+x^2+x^3\right)}^4$ is

If ${}^{n}C_{r-1}=10,{}^{n}C_r=45$ and ${}^{n}C_{r+1}=120,$ then $r$ equals