At 20$$^\circ$$ C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The mole fraction of benzene in the vapour phase at 20$$^\circ$$ above an equimolar mixture of benzene and methyl benzene is _____________ $$\times$$ 10^$$-$$2. (Nearest integer)

Let a be a positive real number such that $$\int_0^a {{e^{x - [x]}}} dx = 10e - 9$$ where [ x ] is the greatest integer less than or equal to x. Then a is equal to:

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

The value of the integral $$\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $$ is equal to: