The value of $$\cot \left( {\sum\limits_{n = 1}^{19} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{p = 1}^n {2p} } \right)} \right)$$ is :

Two sides of a parallelogram are along the lines, x + y = 3 & x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is :

A helicopter is flying along the curve given by y – x^3/2 = 7, (x $$ \ge $$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -

If  $$\int \, $$x⁵.e^$$-$$4x3 dx = $${1 \over {48}}$$e^$$-$$4x3 f(x) + C, where C is a constant of inegration, then f(x) is equal to -