A P Prabhakaran Solutions for Chapter: Binomial Theorem, Exercise 2: SELF EVALUATION TEST

Find the value of $r$ if the coefficients of $(2r+4{)}^{th}$ term and $(r-2{)}^{\mathrm{nd}}$ term in the expansion of $(1+x{)}^{18}$ are equal. 

 Find the middle term in the expansion of ${\left(x+\frac{1}{x}\right)}^{10}$

Find the value of $k$, if  $(\sqrt{3}+1{)}^5+(\sqrt{3}-1{)}^5=k\sqrt{3}$

Find the positive value of $n$ for which the coefficient of $x^2$ in the expansion of $(1+x{)}^n$ is $6$.

 Prove that there is no term involving $x^6$ in the expansion of ${\left(2x^2-\frac{3}{x}\right)}^{11}$.

In the expansion of $(x+y{)}^n$, the coefficients of $4^{th}$ and ${13}^{th}$ terms are equal. Find $n$.

 In the expansion of $(1+x{)}^{m+n}$ where $m$ and $n$ are natural numbers, Prove that the coefficients of $x^m$ and $x^n$ are equal.

Find $a$, $b$ and $n$ in the expansion of $(a+b{)}^n$ if the first three terms of the expansion are $729, 7290$ and $30375$respectively.