Let x, y, z be positive real numbers such that x + y + z = 12 and x³y⁴z⁵ = (0.1) (600)³. Then x³ + y³ + z³is equal to :

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 :

The value of $$\sum\limits_{r = 1}^{15} {{r^2}} \left( {{{{}^{15}{C_r}} \over {{}^{15}{C_{r - 1}}}}} \right)$$ is equal to :

If    $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3},$$ then 'a' is equal to :