A mixture of 100 m mol of Ca(OH)₂ and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of OH^– in resulting solution, respectively, are : (Molar mass of Ca (OH)₂, Na₂SO₄ and CaSO₄ are 74, 143 and 136 g mol^–1 , respectively; K_sp of Ca(OH)₂ is 5.5 × 10^–6 )

A process has $$\Delta $$H = 200 J mol^–1 and $$\Delta $$S = 40 JK^–1 mol^–1. Out of the values given below, choose the minimum temperature above which the process will be spontaneous :

If the system of equations

x + y + z = 5

x + 2y + 3z = 9

x + 3y + az = $$\beta $$

has infinitely many solutions, then $$\beta $$ $$-$$ $$\alpha $$ equals -

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -