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

If the total number of terms in the expansion of $(a-b+2c{)}^n$ is $45,$ then $n=$?

In the expansion of $(x+a{)}^n$, if the sum of odd terms be $P$ and the sum of even terms be $Q$ then $4PQ=$?

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

The middle term in the expansion of ${\left(x-\frac{1}{2y}\right)}^{10}$ 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

If the coefficients of $x^7$ and $x^8$ are equal in the expansion of ${\left(2+\frac{x}{3}\right)}^n$, then $n=$?