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

The number of distinct terms in the expansion of ${\left(x+y^2\right)}^{13}+{\left(x^2+y\right)}^{14}$ is

If ${\left(3+a\sqrt{2}\right)}^{100}+{\left(3+b\sqrt{2}\right)}^{100}=7+5\sqrt{2}$, the number of pairs $(\mathrm{a},\mathrm{b})$ for which the equation is true is, $(a, b$ are rational numbers),

The ${14}^{th}$ term from the end in the expansion of $(\sqrt{x}-\sqrt{y}{)}^{17}$ is

The middle term in the expansion of ${\left(x^2-\frac{2}{x}\right)}^{10}$ is

Let the coefficient of $x^n$ in the expansion of $(1+x{)}^{2n}$ be $p$ and the coefficient of $x^n$ in the expansion of $(1+x{)}^{2n-1}$ be $q$, then

If $p$ and $q$ are positive integers, then the coefficients of $x^p$ and $x^q$ in the expansion of $(1+x{)}^{p+q}$ are

The coefficient of $x^n$ in $\frac{1}{\left(1-x\right)\left(1-2x\right)\left(1-3x\right)}$ is 

Total number of terms in the expansion of $(a+b+c{)}^{10}$ is