A calorimeter of water equivalent 20 g contains 180 g of water at 25^oC. ‘m’ grams of steam at 100^oC is mixed in it till the temperature of the mixure is 31^oC. The value of ‘m’ is close to :
(Latent heat of water = 540 cal g^–1, specific heat of water = 1 cal g^{–1 o}C^–1)

An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $${N \over {20}}$$ ma² where N is an integer. The value of N is _____.

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cms^–1, the speed (in cms^–1) with which image moves at that instant is ____.

A block starts moving up an inclined plane of inclination 30^o with an initial velocity of v₀ . It comes back to its initial position with velocity $${{{v_0}} \over 2}$$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $${I \over {1000}}$$. The nearest integer to I is____.