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)

Match List - I with List - II.

List - I

(a) 10 km height over earth's surface

(b) 70 km height over earth's surface

(c) 180 km height over earth's surface

(d) 270 km height over earth's surface

List - II

(i) Thermosphere

(ii) Mesosphere

(iii) Stratosphere

(iv) Troposphere