Binomial Theore...

The co-efficient of x in  the expansion of $$(1-2x^3 + 3x^5) \left( 1 + \dfrac{1}{x}\right)^8$$ is :

for $$x \in R,x \ne \, - 1$$ , if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}}$$ 
then $${a_{17}}$$ is equal to :

The co-efficient of $${x^5}$$ in the expansion of $${\left( {1 + x} \right)^{21}} + {\left( {1 + x} \right)^{22}} + ........ + {\left( {1 + x} \right)^{30}}$$ is: 

If $${S_n} = \sum\limits_{r = 0}^n {\dfrac{1}{{^n{C_r}}}\,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {\dfrac{r}{{^n{C_r}}},\,\,then\,\,\dfrac{{{t_n}}}{{{s_n}}} = } } $$ 

In the expansion of $$(1+ax)^n$$, $$n\in N$$, then the coefficient of x and $$x^2$$ are $$8$$ and $$24$$ respectively. Then?

In the expansion of $$(1+x+{x}^{2}+....+{x}^{27}){(1+x+{x}^{2}+....+{x}^{14})}^{2}$$, the coefficient of $${x}^{28}$$ is

The third term from the end in the expansion of $$\left( \dfrac{3x}{5}-\dfrac{5}{2x}\right)^8$$ is

The sum of the binomial coefficients of $${ \left[ 2x+\cfrac { 1 }{ x }  \right]  }^{ n }$$ is equal to $$256$$. The constant term in the expansion is-

If $$\left| x \right| < 1$$ then the coefficient of $${x^n}$$ in expansion of $${\left( {1 + x + {x^2} + {x^3}....} \right)^2}$$ is

$$^{10}C_0 ^2- ^{10}C_1^2 + ^{10}C_2^2- .......- (^{10}C_9) + ( ^{10}C_{10})^2= $$