Physics - 2016 Past Year Paper - IIT JAM MCQ

Consider a particle of mass m following a trajectory given by x = x₀ cos ω₁t and y = y₀ sin ω₂t,
where x₀, y₀, ω₁, and ω₂ are constants of appropriate dimensions. The force on the particle is

Which one of the following points represent the complex number 

The eigenvalues of the matrix representing the following pair of linear equations

x+iy=0

ix+y = 0 
are

The solution of the Boolean equation 

A spherical closed container with smooth inner wall contains a monoatomic ideal gas. If the collisions between the wall and the atoms are elastic, then the Maxwell speed-distribution function    for the atoms is best represented by:

Two sinusoidal signals of frequencies ω_x and ω_y having same amplitude are applied to x- and ychannels of a cathode ray oscilloscope (CRO), respectively. The following stationary figure will be observed when

The phase difference (δ) between input and output voltage for the following circuits (i) and (ii)

will be

For the given set of equations:

x +y = 1

y + z = 1

x + z = 1,

which one of the following statements is correct?

The tangent line to the curve x² + cy+ 5 = 0 at (1, 1) is represented by

In the following RC circuit, the capacitor was charged in two different ways.
(i) The capacitor was first charged to 5V by moving the toggle switch to position P and then it
was charged to 10V by moving the toggle switch to position Q.
(ii) The capacitor was directly charged to 10V, by keeping the toggle switch at position Q.
Assuming the capacitor to be ideal, which one of the following statements is correct?

If a constant voltage +V is applied to the input of the following OPAMP circuit for a time t, then the output voltage V_o will approach

Light travelling between two points takes a path for which

In the following RC network, for an input signal frequency    and the phase angle ψ between v₀ and v₁ respectively are 

Consider a free electron (e) and a photon (ph) both having 10 eV of energy. If λ and P represent wavelength and momentum respectively, then
(mass of electron = 9.1 x 10^-31 kg; speed of light = 3 x 10⁸ m/s)

For an ideal gas, which one of the following T-S diagrams is valid?

If U. F, H and G represent internal energy, Helmholtz free energy, enthalpy, and Gibbs free energy respectively, then which one of the following is a correct thermodynamic relation?

A train passes through a station with a constant speed. A stationary observer at the station platformmeasures the tone of the train whistle as 484 Hz when it approaches the station and 442 Hz when itleaves the station. If the sound velocity in air is 330 m/s, then the tone of the whistle and the speedof the train are

The minimum length of a plane mirror to see the entire full-length image of an object is half of the object’s height. Suppose δ is the distance between eye and top of the head of a person of height h. The person will be able to see his entire full-length image with a mirror of height h/2 fixed on the wall

A particle is moving in a plane with a constant radial velocity of 12 m/s and constant angular velocity of 2 rad/s. When the particle is at a distance r = 8 m from the origin, the magnitude of the instantaneous velocity of the particle in m/s is

A cylindrical rod of length L has a mass density distribution given by    where x is measured from one end of the rod and ρ₀ is a constant of appropriate dimensions. The center of mass of the rod is

A particle travels in a medium along a horizontal linear path. The initial velocity of the particle is v0 and the viscous force acting on it is proportional to its instantaneous velocity. In the absence of any other forces, which one of the following figures correctly represents the velocity of the particle as a function of time?

A lightly damped harmonic oscillator with natural frequency ω₀ is driven by a periodic force of frequency ω. The amplitude of oscillation is maximum when

A block of mass 0.38 kg is kept at rest on a frictionless surface and attached to a wall with a spring of negligible mass. A bullet weighing 0.02 kg moving with a speed of 200 m/s hits the block at time t = 0 and gets stuck to it. The displacement of the block (in metre) with respect to the equilibrium position is given by

(Spring constant = 640 N/m.)

One mole of an ideal gas with average molecular speed v₀ is kept in a container of fixed volume. If the temperature of the gas is increased such that the average speed gets doubled, then

An arbitrarily shaped conductor encloses a charge q and is surrounded by a conducting hollow sphere as shown in the figure. Four different regions of space, 1, 2, 3, and 4, are indicated in the figure. Which one of the following statements is correct?

Consider a small bar magnet undergoing simple harmonic motion (SHM) along the x-axis. A coilwhose plane is perpendicular to the x-axis is placed such that the magnet passes in and out of itduring its motion. Which one of the following statements is correct? Neglect damping effects.

An incompressible, non-viscous fluid is injected into a conical pipe at its orifice as schematically shown in the figure. The pressure at the orifice of area A0 is P0. Neglecting the effect of gravity and assuming streamline flow, which one of the following plots correctly predicts the pressure along axis of the cone?