Physics - 2018 Past Year Paper - IIT JAM

A current I is flowing through the sides of an equilateral triangle of side a. The magnitude of the magnetic field at the centroid of the triangle is

Two vehicles A and B are approaching an observer O at rest with equal speed as shown in the figure. Both vehicles have identical sirens blowing at a frequency fs . The observer hears these sirens at frequency f_A and f_B, respectively from the two vehicles. Which one of the following is correct?

Three infinite plane sheets carrying uniform charge densities −σ, 2σ, 3σ are placed parallel to the
x-z plane at y = a, 3a, 4a , respectively. The electric field at the point (0, 2a, 0) is 

Two boxes A and B contain an equal number of molecules of the same gas. If the volumes are V_A
and V_B, and λ_A and λ_B denote respective mean free paths, then

Let T_g and T_e be the kinetic energies of the electron in the ground and the third excited states of ahydrogen atom, respectively. According to the Bohr model, the ratio T_g/ T_e is

Which one of the following arrangements of optical components can be used to distinguish between
an unpolarised light and a circularly polarised light?

Which one of the following graphs shows the correct variation of v_o with v_i? Here, v_d is the voltage
drop across the diode and the Op-Amp is assumed to be ideal.

Which one of the figures correctly represents the T-S diagram of a Carnot engine?

The plane of polarisation of a plane polarized light rotates by 60^° after passing through a waveplate. The pass-axis of the wave plate is at an angle α with respect to the plane of polarisation of theincident light. The wave plate and α are

A rectangular loop of dimensions l and w moves with a constant speed of v through a region containing a uniform magnetic field B directed into the paper and extending a distance of 4w. Which of the following figures correctly represents the variation of emf (ε) with the position (x) of the front end of the loop?

The equation of state for one mole of a non-ideal gas is given by PV = A where the coefficients A and B are temperature dependent. If the volume changes from  V₁ to V₂ in an isothermal process, the work done by the gas is

An ideal gas consists of three dimensional polyatomic molecules. The temperature is such that only
one vibrational mode is excited. If R denotes the gas constant, then the specific heat at constant
volume of one mole of the gas at this temperature is

A long solenoid is carrying a time dependent current such that the magnetic field inside has the form  is along the axis of the solenoid. The displacement current at the
point P on a circle of radius r in a plane perpendicular to the axis

Consider an ensemble of thermodynamic systems, each of which is characterized by the samenumber of particles, pressure and temperature. The thermodynamic function describing theensemble is

Given a spherically symmetric charge density ρ(r)  (k being a constant), the electric field for r < R is (take the total charge as Q)

 An infinitely long solenoid, with its axis along  , carries a current I. In addition there is a uniform line charge density λ along the axis. If   is the energy flux, in cylindrical coordinates   then

Consider two waves y₁ = a cos(ωt − kz) and y₂ = a cos[(ω + Δω)t − (k + Δk)z]. The group velocity of the superposed wave will be (Δω ≪ ω and Δk ≪ k)

Consider a convex lens of focal length f. A point object moves towards the lens along its axis between 2f and f. If the speed of the object is V_O, then its image would move with speed V_I. Whichof the following is correct?

A disc of radius R₁ having uniform surface density has a concentric hole of radius R₂ < R₁. If its
mass is M, the principal moments of inertia are 

The function is expanded as a Fourier series of the form 

Which one of the following curves correctly represents (schematically) the solution for the equation 

The mean momentum  of a nucleon in a nucleus of mass number A and atomic number Z depends on A, Z as

The Boolean expressioncan be simplified to

Consider the transformation to a new set of coordinatesfrom rectangular Cartesian coordinates  (x, y), where In the  coordinate system, the area element dxdy is

A particle of mass m is in a one dimensional potential 
At some instant its wave function is given by 
  are the ground and the first excited states, respectively. Identify the correct statement.

A raindrop falls under gravity and captures water molecules from atmosphere. Its mass changes atthe rate λm(t), where λ is a positive constant and m(t) is the instantaneous mass. Assume thatacceleration due to gravity is constant and water molecules are at rest with respect to earth beforecapture. Which of the following statements is correct?

A particle P of mass m is constrained to move on the surface of a cylinder under a force  as
shown in figure (k is the positive constant). Which of the following statements is correct? (Neglect
friction.)

 

Let matrix If det (M) = 0, then

Let f(x) = 3x⁶ − 2x² − 8. Which of the following statements is (are) true?

Two projectiles of identical mass are projected from the ground with same initial angle (α) with respect to earth surface and same initial velocity (u) in the same plane. They collide at the highest point of their trajectories and stick to each other. Which of the following statements is (are) correct?

Two beams of light in the visible range (400 nm - 700 nm) interfere with each other at a point. The optical path difference between them is 5000 nm. Which of the following wavelengths will interfere constructively at the given point?

Which of the following relations is (are) true for thermodynamic variables?

Consider a convex lens of focal length f. The lens is cut along a diameter in two parts. The two lens parts and an object are kept as shown in the figure. The images are formed at following distances from the object:

Let the electric field in some region R be given by   From this we may conclude that

In presence of a magnetic field  and an electric field and an electric field  a particle moves undeflected. Which of the following statements is (are) correct? 

In a pn junction, dopant concentration on the p- side is higher than that on the n-side. Which of the following statements is (are) correct, when the junction is unbiased?

Which of the combinations of crystal structure and their coordination number is (are) correct?

The coefficient of x³ in the Taylor expansion of sin(sin x) around x = 0 is ______. (Specify your answer upto two digits after the decimal point.)

A particle of mass m is moving along the positive x direction under a potential (k and λ are positive constants). If the particle is slightly displaced from its equilibrium position, it oscillates with an angular frequency (ω) __________.
(Specify your answer in units of  as an integer.)

A planet has average density same as that of the earth but it has only 1/8 of the mass of the earth. If the acceleration due to gravity at the surface is g_p and g_e for the planet and earth, respectively, then 

In a grating with grating constant d =a + b, where a is the slit width and b is the separation between the slits, the diffraction pattern has the fourth order missing. The value of b/a is ________.
(Specify your answer as an integer.)

Consider an electromagnetic plane wave where λ is the wavelength, c is the speed of light and b is a constant. The value of b is ________.
(Specify your answer upto two digits after the decimal point.)

Consider a monoatomic ideal gas operating in a closed cycle as shown in the P-V diagram given below. The ratio 
(Specify your answer upto two digits after the decimal point.)

Consider the first order phase transition of the sublimation of zinc. Assume the vapor to be an ideal gas and the molar volume of solid to be negligible. Experimentally, it is found that log₁₀ (p) =where P is the vapor pressure in Pascal, T is in K, C₁ = 6790 K and C₂ = 9. The latent heat of sublimation of zinc from the Clausius - Clapeyron equation is __________ kJ/mole. (R = 8.314 J/mole.K)
(Specify your answer in kJ/mole upto one digit after the decimal point.)

A system of 8 non-interacting electrons is confined by a three dimensional potential   The ground state energy of the system in units of ℏ
is _______________.
(Specify your answer as an integer.)

For the given circuit, value of the base current (I_b) of the npn transistor will be _______ mA. (β is the current gain and assume Op-Amp as ideal.)
(Specify your answer in mA upto two digits after the decimal point.)

The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)

For the following circuit, the collector voltage with respect to ground will be ________V. (Emitter diode voltage is 0.7 V and β_DC of the transistor is large.) (Specify your answer in volts upto one digit after the decimal point.)

A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100 m. The orbital angular momentum of the body is 100 kg m² s^-1. The time period of motion of the body is __________ hours.
(Specify your answer in hours upto two digits after the decimal point.)

The moon moves around the earth in a circular orbit with a period of 27 days. The radius of the earth (R) is 6.4 × 10⁶ m and the acceleration due to gravity on the earth surface is 9.8 ms^-2. If D is the distance of the moon from the center of the earth, the value of D/R will be _____.
(Specify your answer upto one digit after the decimal point.)

A syringe is used to exert 1.5 atmospheric pressure to release water horizontally. The speed of water immediately after ejection is ________. (take 1 atmospheric pressure = 10⁵ Pascal, density of water = 10³ kg m^-3) (Specify your answer in ms^-1 as an integer.)

Consider a slit of width 18 µm which is being illuminated simultaneously with light of orange color (wavelength 600 nm) and of blue color (wavelength 450 nm). The diffraction pattern is observed on a screen kept at a distance in front of the slit. The smallest angle at which only the orange color is observed is θ₁, and the smallest angle at which only the blue color is observed is θ₂. The angular difference θ₂ − θ₁ (in degrees) is _____. (Specify your answers upto two digits after the decimal point.)

A particle of mass m is moving in a circular orbit given by x = R cos(ωt); y = R sin(ωt), as observed in an inertial frame S₁. Another inertial frame S₂ moves with uniform velocity  with respect to S₁. S₁ and S₂ are related by Galilean transformation, such that the origins coincide at t = 0. The magnitude of the angular momentum of the particle at  as observed in S₂ about its origin, is expressed as (mR² ω)x. Then x is _______. (Specify your answer upto two digits after the decimal point.)

Rod R₁ has a rest length 1m and rod R₂ has a rest length of 2m. R₁ and R₂ are moving with respect to the laboratory frame with velocities,respectively. If R₂ has a length of 1m in the rest frame of R₁ v/c is given by ____________________.
(Specify your answer upto two digits after the decimal point.)

Two events E₁ and E₂ take place in an inertial frame S with respective time-space coordinates (in SI units):  and E₂ (t₂ = 0, x₂ = 10⁸ , y₂ = 0, z₂ = 0). Another inertial frame S′ is moving with respect to S with a velocity  The time difference (t′₂− t′₁ )as observed in S′ is ____s.(c = 3×10⁸ ms^-1)
(Specify your answer in seconds upto two digits after the decimal point.)

In the following circuit, the time constant RC is much greater than the period of the input signal. Assume diode as ideal and resistance R to be large. The dc output voltage across resistance R will be _______V.
(Specify your answer in volts upto one digit after the decimal point.)

For a metal, the electron density is 6.4 × 10²⁸ m^-3. The Fermi energy is ________eV. (h = 6.626 × 10^-34 J s , m_e = 9.11 × 10^-31 kg, 1eV = 1.6 × 10^-19 J)
(Specify your answer in electron volts (eV) upto one digit after the decimal point.)