The speed of light in a material medium is given by :

Which of the following are true statements ?
(A) Electric field due to a single charge is cylindrically symmetric.
(B) Gauss's theorem holds good for any closed surface.
(C) Electric field due to an electric dipole is spherically symmetric.
(D) The field due to a uniformly charged spherical shell is zero at all points inside the shell.
Choose the correct answer from the options given below :

The maximum distance between the transmitting and receiving antenna for a satisfactory communication in LOS mode is 48 Km . If the height of the receiving antenna is 8 (Given radius of earth \(R_e=6400 km\) )

Identify the incorrect statements from the following.
(A) A charged particle of charge e is moving through a magnetic field, work will be done by the magnetic field on the charge.
(B) A conductor with free electrons is placed in a magnetic field. No current is flowing through the conductor. No magnetic force acts on the conductor.
(C) A charged particle is moving perpendicular to the magnetic field. The magnetic force does not change the speed of the particle but changes its direction.
(D) A charged particle is moving in a straight direction without any change of direction. It shows that no magnetic field is there.
Choose the correct answer from the options given below:

Light ray travels from an rarer medium to an denser medium. Which of the following is incorrect if \( (0^{\circ} < i < 90^{\circ}) \).

Three parallel plates (each of area A) are separated by distances \( d_1 \) and \( d_2 \) respectively. The in-between spaces are filled with dielectrics of relative permittivity \( \epsilon_1 \) and \( \epsilon_2 \). The permittivity of free space is \( \epsilon_0 \). The capacitance of the combination is:

A plane electromagnetic wave of frequency 30 MHz travels in free space along the \( x \)-direction.
At a particular point in space and time, \( \vec{E} = 6.3\hat{j} \text{ V/m} \).
The magnetic field \( \vec{B} \) at this point would be:

Read the given passage and answer the question.
ABO blood groups in human beings are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surfaces and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and I. The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles, IA and IB are completely dominant over I.
Select the correct option for number of alleles present in ABO blood groups:

A nucleus with mass number 240 and binding energy per nucleon 7.6 MeV splits into two fragments each of mass number 120 with binding energy per nucleon 8.5 MeV. The amount of energy released in this process will be :

An electric dipole is placed in a non-uniform electric field, such that the dipole moment is parallel to the electric field. The dipole will experience

Isotonic solutions must have the same
(A) Solute
(B) Density
(C) Elevation in boiling point
(D) Depression in freezing point
Choose the correct answer from the options given below :

A charged particle carrying charge \(q = 1 \mu C\) moves in a uniform magnetic field with velocity \(v_1 = 10^6 \text{ m/s}\) at an angle of \(45^\circ\) with the x-axis in the xy-plane and experiences a force \(F_1 = 0.4\sqrt{2} \text{ N}\) along the negative z-axis. When the same particle moves with velocity \(v_2 = 10^6 \text{ m/s}\) along the z-axis, it experiences a force \(F_2\) in the y-direction. Find the magnitude of the magnetic field.

The frequency band of FM broadcast is -