If A = {x $$ \in $$ R : |x| < 2} and B = {x $$ \in $$ R : |x – 2| $$ \ge $$ 3}; then :

If one end of a focal chord AB of the parabola y² = 8x is at $$A\left( {{1 \over 2}, - 2} \right)$$, then the equation of the tangent to it at B is :

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :

Let a function ƒ : [0, 5] $$ \to $$ R be continuous, ƒ(1) = 3 and F be defined as :

$$F(x) = \int\limits_1^x {{t^2}g(t)dt} $$ , where $$g(t) = \int\limits_1^t {f(u)du} $$

Then for the function F, the point x = 1 is :