Two soap bubbles of radii x and y coalesce to constitute a bubble of radius z is equal
to

A particle of mass m is located in a one dimensional potential field where potential
energy is given by:
V(x) = A(1 – cos px), where A and p are constants. The period of small oscillations of the particle is

The period of oscillation of a simple pendulum of length l suspended from the roof of
a vehicle, which moves without friction down an inclined plane of inclination a, is given by

A diver at a depth of 12 m in water $\\mu=\\dfrac{4}{3}$ sees the sky in a cone of semiverticale
angle :

A particle performs a uniform circular motion with an angular momentum L. If the frequency of
the particle s motion is doubled and its KE is halved, the angular momentum becomes

A radioactive substance has a half-life of 60 minutes. During 3 hour, the fraction of atoms that
have decayed would be

A convex lens of focal length 30 cm produces 5 times magnified real image of an
object. What is the object distance ?

The frequency of oscillation of current in the inductance is

1.56 X $10^5$J of heat is conducted through a 2 $m^2$ wall of 12 cm thick in one hour.
Temperature difference between the two sides of the wall is 20 °C.
The thermal conductivity of the material of the wall is (in W $m^{-1} K^{-1}$)

A stone of relative density K is released from rest on the surface of a lake. If viscous
effects are ignored, the stone sinks in water with an acceleration of