A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _________ min. (Round off to the Nearest Integer). [Use : ln 2 = 0.69; ln 10 = 2.3]

The solubility of CdSO₄ in water is 8.0 $$\times$$ 10^$$-$$4 mol L^$$-$$1. Its solubility in 0.01 M H₂SO₄ solution is __________ $$\times$$ 10^$$-$$6 mol L^$$-$$1. (Round off to the Nearest Integer). (Assume that solubility is much less than 0.01 M)

A solute A dimerizes in water. The boiling point of a 2 molal solution of A is 100.52$$^\circ$$C. The percentage association of A is __________. (Round off to the Nearest Integer).

[Use : K_b for water = 0.52 K kg mol^$$-$$1 Boiling point of water = 100$$^\circ$$C]

Let y = y(x) be the solution of the differential equation

$${{dy} \over {dx}} = (y + 1)\left( {(y + 1){e^{{x^2}/2}} - x} \right)$$, 0 < x < 2.1, with y(2) = 0. Then the value of $${{dy} \over {dx}}$$ at x = 1 is equal to :