GATE Physics Mock Test Series - 8 - Physics MCQ

The eigenvalues of the matrix A  are

Two events, separated by a (spatial) distance 9 x 10⁹ m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 10⁸ m/s) is

The commutator [x², p²] is

Consider three polarizers P₁ ,P₂ and P₃ placed along an axis as shown in the figure

The pass axis of P₁ and P₃ are at right angles to each other while the pass axis of P₂ makes an angle θ with that of P₁ . A beam of unpolarized light of intensity l₀ is incident on P₁ as shown . The intensity of light emerging from P₃ is

A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT  Neglecting radiation loss, the amplitude of oscillation after the field is switched off is

A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V_∞= 20v. Assuming V_be = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v

The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effective-basewidth caused by___

A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is

A particle of mass m is in a potential given by

where a and r₀ are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is

A planet of mass m moves in a circular orbit of radius r₀ in the gravitational potential V(r) =  where k is a positive constant. The orbital angular momentum of the planet is

The solution of the differential equation

subject to the boundary conditions y(0) = 1 and y(∞) = 0, is

In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I₀ and I₀, respectively. The intensities of the individual waves are

Identify the CORRECT statement for the following vectors 

Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E_D and E_F are conduction band, valence band, impurity level and Fermi level, respectively.

A pendulum suspended from the ceiling of the train is at rest. What will be the time period of pendulum if the train accelerates at 10 m/s² (Take g = 10 m/s²)

A rod of proper length l₀ oriented parallel to the x-axis moves with speed 2c/3 along the x-axis in the. S-frame, where c is the speed of the light in free space. The observer is also moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod as measured by the observer is

Given  is a constant vector and r is the position vector. The value of   where C is a circle of unit radius centered at origin is _____ .

A system has two energy levels with energies ε and 2ε. The lower is 4-fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is

A spherical conductor of radius a is placed in a uniform electric field  the potential at a point  for r > a, is given by

where r is the distance of P from the centre O of the sphere and q is the angle OP makes with the z-axis.

The charge density on the sphere at q = 30° is

The solution of the differential equation for  subject to the initial conditions  is

A particle of mass m is confined in the potential

Let the wave function of the particle be given by

where y₀ and y₁ are the eigen functions of the ground state and the first excited state respectively. The expectation value of the energy is

Two magnetic dipoles of magnitude m each placed in a plane as shown. The energy of interaction is given by

A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r₀ and angular speed w₀ by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass

For the BJT circuit shown, assume that the β of the transistor is very large and V_BE = 0.7V. The mode of operation of the BJT is ___

If for a silicon n-p-n transistor, the base-to-emitter voltage (V_BE) is 0.7V and the collector-to-base voltage (V_CB) is 0.2V. then the transistor is operating in the___

Assuming V_CEsat = 0.2V and β= 50. the minimum base current (l_B) required to drive the transistor in the given figure to saturation is___

In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is