NTA JEE Main 19th April 2014 Online

A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $$T_0$$. The initial temperature of the sphere is $$3T_0$$. If the specific heat of the material of the sphere varies as $$\alpha T^3$$ per unit mass with the temperature T of the sphere, where $$\alpha$$ is a constant, then the time taken for the sphere to cool down to temperature $$2T_0$$ will be ($$\sigma$$ is Stefan Boltzmann constant)

A monoatomic gas is compressed from a volume of 2 m$$^3$$ to a volume of 1 m$$^3$$ at a constant pressure of 100 N m$$^2$$. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas:

A gas molecule of mass M at the surface of the earth has kinetic energy equivalent to 0 °C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than the radius of the earth. (k$$_B$$ is Boltzmann constant)

A body is in simple harmonic motion with time period $$T = 0.5$$ s and amplitude $$A = 1$$ cm. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

The total length of a sonometer wire fixed between two bridges is 110 cm. Now, two more bridges are placed to divide the length of the wire in the ratio 6 : 3 : 2. If the tension in the wire is 400 N and the mass per unit length of the wire is 0.01 kg m$$^{-1}$$, then the minimum common frequency with which all the three parts can vibrate, is:

The electric field in a region of space is given by, $$\vec{E} = E_0\hat{i} + 2E_0\hat{j}$$ where $$E_0 = 100$$ N C$$^{-1}$$. The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly:

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose relative permittivity varies linearly from $$\epsilon_1$$ at one plate to $$\epsilon_2$$ at the other. The capacitance of the capacitor is:

Four bulbs B$$_1$$, B$$_2$$, B$$_3$$ and B$$_4$$ of 100 W each are connected to 220 V main as shown in the figure. The reading in an ideal ammeter will be:

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field $$B_s$$ inside the superconductor will be such that:

A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 m s$$^{-1}$$ (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is: