The size of the image of an object, which is at infinity, is formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image

A network of Four capacitors of capacity equal to C₁ = C, C₂ = 2C, C₃ = 3C and C₄ = 4C, are connected to a battery as shown in the figure. The ratio of the charges on C₂ and C₄ is

A rod AD, consisting of three segments AB, BC and CD joined together, is hanging vertically from a fixed support at A. The lengths of the segments are respectively 0.1 m, 0.2 m and 0.15 m. The cross - section of the rod is uniform 10^-4 m². A weight of 10 kg is hung from D. Calculate the displacements of point D if Y_AB = 2.5 x 10¹⁰ N/m², Y_BC = 4 x 10¹⁰ N/m² and Y_CD = 1 x 10¹⁰ N/m². (Neglect the weight of the rod.)

A block of mass m & charge q is released on a long smooth inclined plane. Magnetic field B is constant, uniform, horizontal and out of the plane of paper as shown. Find the time from start when block loses contact with the surface.

A battery of internal resistance 4Ω is connected to the network of resistances as shown in figure. In order that the maximum power can be delivered to the network, the value of R in $$ should be

In the circuit shown in diagram, the equivalent resistance between point A and B is

Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when they are 300 m apart. Graphs given below show their velocities as a function of time as they slow down. The separation between the trains, when both have stopped, is:

A tuning fork sends out waves of wavelength 68.75 cm and 3 m in air and hydrogen gas respectively. If the velocity of sound in air is 330 ms^-1, find the velocity of sound in hydrogen. Also, find the frequency of the tuning fork

A particle executes S.H.M. given by x = 0 · 24 cos (400 t - 0.5) in SI units. Find amplitude

A lens (μ = 1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection from its surface at λ = 4800 Å. Find the minimum thickness of the film which will minimise the intensity of the reflected light. (Assume near normal incidence)