If $$f(x) = \int {{{5{x^8} + 7{x^6}} \over {{{({x^2} + 1 + 2{x^7})}^2}}}dx,(x \ge 0),f(0) = 0} $$ and $$f(1) = {1 \over K}$$, then the value of K is

A square ABCD has all its vertices on the curve x²y² = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is _________.

The number of solutions of the equation

$$|\cot x| = \cot x + {1 \over {\sin x}}$$ in the interval [ 0, 2$$\pi$$ ] is

An oil drop of radius 2 mm with a density 3g cm^$$-$$3 is held stationary under a constant electric field 3.55 $$\times$$ 10⁵ V m^$$-$$1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s²)