Binomial Theorem

If the coefficient of 4th and 13th terms in the expansion of $$\left(x^2 \, + \, \dfrac{1}{x}\right)^n$$ be equal then find the term which is independent of x. 
Find out the sum  of the coefficient  in the  expansion  of the binomial $$(5p  \, - \, 4q) ^n $$  where  n is  a + ive  integer . 
Express $$\dfrac{14}{-5}$$ as a rational number with numerator $$56$$.
Multiply the binomials.
$$\left( {2x + 5} \right)$$ and $$\left( {4x - 3} \right)$$

If $$ \displaystyle C_{r}=^{n}C_{r} $$ then to evaluate the expansion $$ \displaystyle A=\sum \sum_{0\leq r\leq s\leq n}^{} $$ $$ \displaystyle C_{r}C_{s} $$, We make use of $$ \displaystyle \sum_{r=0}^{n}C_{r}^{2}=^{2n}C_{n} $$ and the expansion of $$ \displaystyle \left ( \sum_{r=0}^{n}C_{r} \right )^{2} $$. On the basis of above information answer the following questions.