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 :

Let the system of linear equations

4x + $$\lambda$$y + 2z = 0

2x $$-$$ y + z = 0

$$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R.

has a non-trivial solution. Then which of the following is true?