An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol^$$-$$1) needed to meet this energy requirement is ____________ g.

(Use : $$\Delta$$_CH(glucose) = $$-$$2700 kJ mol^$$-$$1)

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)

The Boolean expression $$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$ is equivalent to :

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: