GATE Physics Mock Test Series - 5 - Physics MCQ

# GATE Physics Mock Test Series - 5 - Physics MCQ

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## 30 Questions MCQ Test GATE Physics Mock Test Series 2025 - GATE Physics Mock Test Series - 5

GATE Physics Mock Test Series - 5 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The GATE Physics Mock Test Series - 5 questions and answers have been prepared according to the Physics exam syllabus.The GATE Physics Mock Test Series - 5 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Physics Mock Test Series - 5 below.
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GATE Physics Mock Test Series - 5 - Question 1

### In the hydrogen atom spectrum, the ratio of the energy for the transition n = 3 → n = 1 to that of n = 4 —>n = 1 is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 1

Ratio of energy of transition n = 3 → n = 1 t o that of n = 4 → n = 1 is

GATE Physics Mock Test Series - 5 - Question 2

### The 32P radio isotope used in leukemia theraphy has t1/2 = 14.26 days, what % of 32P remains after 35 days

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 2

Time t = n x t1/2
35 = n x 14.26
No.of half lives,

= 100 x 0.1824
N = 18.24%

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GATE Physics Mock Test Series - 5 - Question 3

### The wave function ψ of a quantum mechanical system described by a Hamiltonian  can be written as a linear combination of φ1and φ2 which are the eigen functions of H with eigen values E1 and E2 respectively . At t = 0, the system is prepared in the state and then allowed to evolve with time. The wave function at time t =  will be

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 3

So, wavefunction at time

GATE Physics Mock Test Series - 5 - Question 4

An engine absorb heat at a temperature of 1000 K and rejects heat at 600 K. If the engine operates at maximum possible efficiency, the amount of work performed by the engine for 2000 J heat input is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 4

Maximum possible efficiency =
Heat input W = 2000 x 0.4 = 800 J

GATE Physics Mock Test Series - 5 - Question 5

One mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C. What is the change in internal energy?

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 5

Change in internal energy at constant pressure

GATE Physics Mock Test Series - 5 - Question 6

For an assembly of molecules (molar mas = M) at temperature T, the standard deviation of maxweller’s speed is approximately

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 6

Root mean square velocity
Average velocity
standard deviation of the molecular speeds

GATE Physics Mock Test Series - 5 - Question 7

Two uniform thin rods of equal length 2L and masses M1 and M2 are joined together along the length. The moment of inertia of the combined rod of length 4L about an axis passing through the mid point and perpendicular to the length of the rod is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 7

Moment of inertia of uniform rod about an axis passing through the end and perpendicular to the length of rod is

GATE Physics Mock Test Series - 5 - Question 8

A particle is constrained in a one-dimensional box of length 2a with potential

Energy difference between level n = 3 and n = 2 is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 8

Energy of a particle in one dimensional box

Given that n = 2, L = 2a
&
When, n = 3 and I = 2a

GATE Physics Mock Test Series - 5 - Question 9

A person of mass m stands at one end of a plank of mass M and length L. the plank is lying on a smooth horizontal surface, what is distance moves by the plank as the person walks on it to reach the other end.

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 9

In the given system there is no external force acts along the horizontal surface. Then the centre of mass co - ordinate remains same along to horizontal surface.

GATE Physics Mock Test Series - 5 - Question 10

A particle of mass m is located in a unidimensional potential field where the potential energy of the particle depends on the coordinate x as U(x) = U0 (1 - cos a x ) ; U0 and a are constants. Then the period of small oscillations that the particle performs about the equilibrium position.

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 10

U(x) = U0 (1 - cos ax)

F(x) = - U0 a sin ax
∴F(x) = 0

So, x = 0 is stable equilibrium position.
The small force arising due to this small displacement is

So, this is the condition of S.H.M. motion so. A = -ω2 Δx so to compare

GATE Physics Mock Test Series - 5 - Question 11

If the electrostatic potential at point (x,y) is given by V (x,y) = [ 4x + 9y] volts, the electrostatic energy density at that point (in J/m3) is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 11

Given V(x, y) = 4x + 9y

GATE Physics Mock Test Series - 5 - Question 12

A solid sphere of mass m callides head on with identical sphere at rest. If the coefficient of restitution is e. The loss in kinetic energy

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 12

Let u be the velocity of a moving sphere before collision and v1 and v2 be the velocities of the two sphere after collision.

form conservation of momentum we get
mu = mv+ mv2
v1+ v2 = u

Loss in kinetic energy = KEf - KEi

GATE Physics Mock Test Series - 5 - Question 13

An insulated gas jar of mass M which is equal to the molecular mass of the enclosed gas moves with certain K. E. when the jar is stopped, the increment of temperature of the gas is  ΔT. The K .E . of the system before stopping is , where  adiabatic exponent of the gas.

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 13

The disordered K.E. of the gas converts into the internal energy of its. Hence,

K.E. of the system

GATE Physics Mock Test Series - 5 - Question 14

The input in the below circuit to get output one is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 14

The set of input is (1, 1, 1).

GATE Physics Mock Test Series - 5 - Question 15

If the amplitude of a damped - oscillator becomes one - third in 2 minutes, what will be the amplitude of oscillation as compared to initial one after 6 minutes ?

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 15

In case of damped oscillations, amplitude decrease exponentially with time , i.e

GATE Physics Mock Test Series - 5 - Question 16

The relation between angular frequency ω and wave number K for given type of waves is . The wave number K0 for which the phase velocity equals the group velocity is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 16

Dispersion relation

....(1)
Given Vg = Vphase

2w2 = a K + 9b K3
2a K + 6b K3 = a K + 9b K3
a K = 3 b K3

GATE Physics Mock Test Series - 5 - Question 17

A ray of light passes through four transparent media with refractive indices μ123 and u4 as shown in Fig. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 17

The emergent ray will be parallel to the incident ray provided the refractive index of the medium of incidence is the same as the refractive index of the medium of emergence. Thus μ4 = μ1

GATE Physics Mock Test Series - 5 - Question 18

For a pure substance, the slope of the plot of Gibbs free energy (G) against T at constant pressure is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 18

We know gibbs free energy
G = U + PV - TS

= Tds - pdV + pdV + vdP - Tds - sdT
dG = VdP - SdT
(dG)p = -SdT

So, slope of this curve is - S.

GATE Physics Mock Test Series - 5 - Question 19

The space - time coordinates of two events as measured by O are x1= 6 x 104 m,y1 = z1 = Om, t1’ = 2 x 104sec and x2= 12 x 104m, t2= 1 x 10-4sec. What must be the velocity of O’ with respect to O if O’ measures the two events to occur simultaneously ?

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 19

Subtracting two Lorentz transformation.
If the events are simultaneous in the O’ frome of refrence the t1’ = t2

On solving , we obtain,

Therefore , v is in the negative x - direction.

GATE Physics Mock Test Series - 5 - Question 20

are the Pauli matrices. The expression equal to

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 20

We know that the Pauli matrices are given as

GATE Physics Mock Test Series - 5 - Question 21

The electric field component of a plane electromagnetic wave travelling in vacuum is given by The Poynting vector for the wave is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 21

We know that

Poynting vector for the wave

GATE Physics Mock Test Series - 5 - Question 22

The x-y plane is the boundary between free space and a magnetic material with relative permeability μ. The magnetic field in the free space is  The magnetic field in the magnetic material is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 22

According to boundary condition

The magnetic field in the magnetic material is

GATE Physics Mock Test Series - 5 - Question 23

An infinite, conducting slab kept in a horizontal plane carries a uniform charge density σ . Another infinite slab of thickness t, made of a linear dielectric material of dielectric constant K, is kept above the conducting slab. The bound charge density on the upper surface of the dielectric slab is _______ .

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 23

Electric field due to infinite, conducting slab inside the dielectric is
Polarization

GATE Physics Mock Test Series - 5 - Question 24

Two parallel plates of a capacitor, separated by 2 mm, are at a potential difference of 20V. A dielectric sheet of dielectric constant 2 and thickness 1 mm is inserted between the plates. How does the potential difference between the two plates change ?

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 24

Initially the capacitance was given by
Now after introduction of dielectric slab of thickness t and dielectric constant k the capacitances are both are connected series then as in series combination resultant capacitance will be c

Now charge will remain same.
Hence, initially potential  and after introduction of slab

GATE Physics Mock Test Series - 5 - Question 25

If waves in an ocean travel with a phase velocity then what is the group velocity Vg of the ‘wave packet’ of these waves ?

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 25

The phase velocity
where λ wavelength
Phase velocity

Group velocity =

GATE Physics Mock Test Series - 5 - Question 26

A transistor with β = 100 is used in C E configuration.The collector circuit resistance is 1k Ω & Vcc = 20v. Assuming Vbe = 0. Find the value of collector to base resistance such that quiescent collector emitter voltage is 4V.

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 26

Rb = 25 kΩ

GATE Physics Mock Test Series - 5 - Question 27

Calculate the collector current in Voltage divider method with the following data

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 27

GATE Physics Mock Test Series - 5 - Question 28

(110011.11)2 is written in decimal form as

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 28

(110011.11 ) = (1 x 25) + (1 x 24) + (1 x 21) + (1 x 2o) + (1 x 2-1) + (1 x 2-2
= 32 + 16 + 2 + 1 + 0.5 + 0.25 = 51.75

GATE Physics Mock Test Series - 5 - Question 29

A truth table is given as, then the correct logic expression corresponding to it is

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 29

GATE Physics Mock Test Series - 5 - Question 30

In in the Op-amp circuit V0 is given by

Detailed Solution for GATE Physics Mock Test Series - 5 - Question 30

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