If a₁, a₂, a₃, ............... a_n are in A.P. and a₁ + a₄ + a₇ + ........... + a₁₆ = 114, then a₁ + a₆ + a₁₁ + a₁₆ is equal to :

Let f(x) = e^x – x and g(x) = x² – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :

$$\mathop {\lim }\limits_{n \to \infty } \left( {{{{{(n + 1)}^{1/3}}} \over {{n^{4/3}}}} + {{{{(n + 2)}^{1/3}}} \over {{n^{4/3}}}} + ....... + {{{{(2n)}^{1/3}}} \over {{n^{4/3}}}}} \right)$$
is equal to :

If the line x – 2y = 12 is tangent to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ at the point $$\left( {3, - {9 \over 2}} \right)$$ , then the length of the latus rectum of the ellipse is :