For x $$ \in $$ R, x $$ \ne $$ -1,

if (1 + x)²⁰¹⁶ + x(1 + x)²⁰¹⁵ + x²(1 + x)²⁰¹⁴ + . . . . + x²⁰¹⁶ =

$$\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,$$ then a₁₇ is equal to :

If the number of terms in the expansion of $${\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,$$ is 28, then the sum of the coefficients of all the terms in this expansion, is :

The sum of coefficients of integral power of $$x$$ in the binomial expansion $${\left( {1 - 2\sqrt x } \right)^{50}}$$ is :

If the coefficints of $${x^3}$$ and $${x^4}$$ in the expansion of $$\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}$$ in powers of $$x$$ are both zero, then $$\left( {a,\,b} \right)$$ is equal to: