The activity of a radioactive material is 2.56 $$\times$$ 10^$$-$$3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 $$\times$$ 10^$$-$$5 Ci ?

A spherical shell of 1 kg mass and radius R is rolling with angular speed $$\omega$$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is $${a \over 3}$$ R²$$\omega$$. The value of a will be :

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0$$^\circ$$C will be :

(Given gas constant R = 8.3 JK^$$-$$1-mol^$$-$$1)

A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :