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 -

Let n $$ \ge $$ 2 be a natural number and $$0 < \theta < {\pi \over 2}.$$ Then $$\int {{{{{\left( {{{\sin }^n}\theta - \sin \theta } \right)}^{1/n}}\cos \theta } \over {{{\sin }^{n + 1}}\theta }}} \,d\theta $$ is equal to - (where C is a constant of integration)