Binomial Theore...

In the expansion of $$\left (x + \dfrac {1}{x}\right )^{n}$$, then the coefficient of the term indepenent of x is

The sum of the series $$^{20}C_0 - \,^{20}C_1+\,^{20}C_2-\,^{20}C_3+...+\,^{20}C_{10}$$ is 

If $$T_r=^{2016}C_rx^{2016-r}$$, for $$r=0, 1, ,....2016$$, then $$(T_0 - T_2+T_4....+T_{2016})^2+(T_1-T_3+T_5....T_{2015})^2$$ is equal to - 

If $$C_{0}, C_{1}, C_{2}, ...., C_{n}$$ are binomial coefficients of order $$n$$, then the value of $$\dfrac {C_{1}}{2} + \dfrac {C_{3}}{4} + \dfrac {C_{5}}{6} + .... =$$

The total number of terms in the expansion of $$(x + a)^{47} - (x - a)^{47}$$ after simplification is

Let $$((1 + x) + x^{2})^{9} = a_{0} + a_{1}x + a_{2}x^{2} + ..... + a_{18}x^{18}$$. Then

Let $$n \ge 5$$ and $$b \neq 0$$. In the binomial expansion of $${ \left( a-b \right)  }^{ n }$$, the sum of the 5th and 6th terms is zero then $${ a }/{ b }$$ equals

Given $$(1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+...$$ and that $$a_1^2=2a_2$$ then the value of $$n$$ is-

In the expansion of $${ \left( 3x-\cfrac { 1 }{ { x }^{ 2 } }  \right)  }^{ 10 }$$, the $$5^{th}$$ term from the end is

The coefficient of $$x^{49}$$ in the product $$(x - 1) (x - 2) (x - 3) .... (x - 50)$$ is