Test Report Of Minor Test - 01 - Physics MCQ

# Test Report Of Minor Test - 01 - Physics MCQ

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## 55 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test Report Of Minor Test - 01

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*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 1

### A pair of point charges are placed at a separation d as shown in figure. The value of  along a path C of radius d is  then the value of m is ______ (integer).

Detailed Solution for Test Report Of Minor Test - 01 - Question 1

Test Report Of Minor Test - 01 - Question 2

### A total charge Q is uniformly distributed around a circularting of radius a and infinitesmal thickness. Hie charge density can be written as ( r, φ, z are cylindrical coordinate)

Detailed Solution for Test Report Of Minor Test - 01 - Question 2

must be equal to total charge Q.
only option (b) satisfy this condition.

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Test Report Of Minor Test - 01 - Question 3

### The electric field at any inside point of a charged sphere of radius R is  The potential at r = 2 R is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 3

Test Report Of Minor Test - 01 - Question 4

The electrostatic potential in a certain region is given by V (r) = -αr2 - β . where α and β are two constants and/ * is the distance from die origin. Hie electric flux passing through die sphere of radius? whose centre is at origin is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 4

According Poisson’s equation.

Tlie flux through tlie any closed surface is

Test Report Of Minor Test - 01 - Question 5

An election travelling from a region of potential V1 to higher potential region of potential V2.The change in kinetic energy of the election is proportional to

Detailed Solution for Test Report Of Minor Test - 01 - Question 5

We know that,
Tlie change of kinetic energy = work done
= charge x (change of potential)

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 6

Suppose six equal charges (q) are placed at the comer of a regular hexagonal of side a. Hie dipole moment of this charge distribution with respect to centre of the hexagonal is given by  then the value of α is _______ (an integer)

Detailed Solution for Test Report Of Minor Test - 01 - Question 6

The dipole moment with respect to origin is

Therefore, the value of α is zero.

Test Report Of Minor Test - 01 - Question 7

In a dielectric medium if  is the polarization vector and  is the electric field then in the relation,  is in general a

Detailed Solution for Test Report Of Minor Test - 01 - Question 7

α is in general a tensor quantity of rank 2

Test Report Of Minor Test - 01 - Question 8

A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant then

Detailed Solution for Test Report Of Minor Test - 01 - Question 8

The electrostatic energy of the given charge distribution is

Test Report Of Minor Test - 01 - Question 9

All election have rest mass m and charge -e (e = 1.6 x 10-19c). The classical radius of an electron is given by ( c is the velocity of light).

Detailed Solution for Test Report Of Minor Test - 01 - Question 9

The self electrostatics energy of an electron is given by U =
According to mass energy conservation,

Test Report Of Minor Test - 01 - Question 10

Certain volume current distribution  gives rise to the magnetic vector potential  where k is a constant. The corresponding current distribution  is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 10

And

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 11

The magnetic vector potential at any point in a magnetic field region is given by  The value of the integral  _________. Where c is square  in xy plane. (Answer should be an integer)

Detailed Solution for Test Report Of Minor Test - 01 - Question 11

Test Report Of Minor Test - 01 - Question 12

Consider a rail in the form of a right-angle with one arm along x-axis and the other alog v-axis. A rod placed on the rail slides at a constant velocity  There is a uniform magnetic field   Assuming that the rod stalls from rest at the origin at time t = 0. The induced emf at time t is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 12

Suppose at time t rod cut the rails at (x, 0) and (0,y) points.
x = v0t and y = v0t

Test Report Of Minor Test - 01 - Question 13

In Young double slit experiment, two light sources are placed as shown in figure, the maximum order of visible fringes is

Detailed Solution for Test Report Of Minor Test - 01 - Question 13

The path difference between two waves.

The condition of mth order maxima

For maximum visible fringes,
∴

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 14

Consider a cylindrical wave guide of radius r = 1.5 meter, then the cut-off frequency of TE11 mode is _________ GHz (upto third decimal places)

Detailed Solution for Test Report Of Minor Test - 01 - Question 14

The cut of frequency.

Test Report Of Minor Test - 01 - Question 15

Which of the following statements) is/are TRUE?

Detailed Solution for Test Report Of Minor Test - 01 - Question 15

We know that the phase velocity of a wave can be higher than the speed of light but the group velocity can never be higher than the speed of light (since it refers to the propagation velocity of the particle concerned).

Test Report Of Minor Test - 01 - Question 16

For two operators  the minimum limit of   for any random state will be

Detailed Solution for Test Report Of Minor Test - 01 - Question 16

The expression for the genetic uncertainty principle for any random state ψ is,

Hence, the lower bound is dependent on both the operators and the wavefunction.

Test Report Of Minor Test - 01 - Question 17

Which of the following operators are Hermitian?

Detailed Solution for Test Report Of Minor Test - 01 - Question 17

Since,  is Hermitian  is also Hennitian. [ n is positive integer]

Test Report Of Minor Test - 01 - Question 18

The ground state energy of Li2+ is

Detailed Solution for Test Report Of Minor Test - 01 - Question 18

The nth state energy of a hydrogen like atom having +Ze charge at its nucleus, is
state energy of the hydrogen atom]
For Li, Z = 3
Therefore,

Test Report Of Minor Test - 01 - Question 19

The angular oscillation frequency of the probability distribution function for a wave function

[where ψn(x) is the nth state of a 1-D Harmonic oscillator of classical frequency 'ω' is _______.

Detailed Solution for Test Report Of Minor Test - 01 - Question 19

The energy of the nth state of the 1-D Harmonic oscillator of fr equency ‘ω' is given by

Now. the angular oscillation fr equency of probability density for a superposition of two energy eigenstates having energies En and Em is

Hence, here

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Test Report Of Minor Test - 01 - Question 20

The number of nodes of the radial wave of function of an electron in the 4p state of a hydrogen atom is

Detailed Solution for Test Report Of Minor Test - 01 - Question 20

The number o f radial nodes in a state (n, I) is given by n - l - 1 .[In the case of hydrogen atom]
Here, electron is in 4p state i.e.. n = 4. l = 1
Hence, the number o f nodes in radial wavefimction is 4 - 1 - 1 = 2.

Test Report Of Minor Test - 01 - Question 21

Consider a perturbation of the form

is applied in the 1-D infinite potential well. The first order energy collection to the 1st excited state is

Detailed Solution for Test Report Of Minor Test - 01 - Question 21

First excited state is
Tlierefore,

Test Report Of Minor Test - 01 - Question 22

Two electrons are moving at speeds of 2/5 c and 3/5 c respectively. The ratio of the De-Broglie wave length of the first electron to that of the second electron is.

Detailed Solution for Test Report Of Minor Test - 01 - Question 22

De-Broglie wave length of an electron moving at speed ‘v’ is given by.

[Where m0 is the rest mass]

Test Report Of Minor Test - 01 - Question 23

is a hermitian and  is an anti-hennitian operator. The eigenvalues of the operator  will

Detailed Solution for Test Report Of Minor Test - 01 - Question 23

Hence,  is a hermitian operator.
As we know that the eigenvalues of a hermitian operator are always real.

Test Report Of Minor Test - 01 - Question 24

The commutator  is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 24

We know that,

Test Report Of Minor Test - 01 - Question 25

The first excited state of a 1-D harmonic oscillator of frequency 'ω' is

The expectation value of  in this is

Detailed Solution for Test Report Of Minor Test - 01 - Question 25

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 26

One clay both Shainim Sir and Sandeep Sir decided to perfomi an experiment in CAREER ENDEAVOUR classroom for that Shamim sir placed a dielectiic sphere of radius R and Sandeep sir applied electric field.
They meausrecl the polarization  then Sliamimr sir calculated die surface bound charge and got the result  The value of α is____________________(an integer)

Detailed Solution for Test Report Of Minor Test - 01 - Question 26

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 27

A square loop of side a and centre at origin lies in xy plane. Carries current I in clockwise direction. The magnetic field on the x-axis at distance d from the centre of the square loop is given by ______ (upto second decimal places) (Assume d >> a)

Detailed Solution for Test Report Of Minor Test - 01 - Question 27

As d >> a. so we can treat the square loop as a magnetic dipole of dipolemoment

So. the magnetic field at the distance d on the x-axis is given by

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 28

Two parallel wires are carrying currents I1 and I2. When the currents flow in the same direction the magnetic field at the mid-point between them is 10μT. But if the current flow in the opposite direction then the corresponding field is 40 μT. Then I1/12 is _________________ (upto second decimal places)

Detailed Solution for Test Report Of Minor Test - 01 - Question 28

When current flow in the same direction, the magnetic field at the centre is

When ciurent flow in the same direction.

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 29

The magnetic field for x-polarized plane wave propagating (in a dielectric of refractive index 1.5 along z-direction is given by  The Poynting vector of the wave is _______

Detailed Solution for Test Report Of Minor Test - 01 - Question 29

We have magnetic field EM wave.

According to Maxwell equation.

⇒
Therefore, the Poynting vector

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 30

A He-Ne laser beam (λ = 632.8 nm) at radius has 30 mW power. Considering the beam to the uniform over the cross-section. The magnitude of the electric field associated with this beam is _____________ x 103 V/m. (Upto first decimal places)

Detailed Solution for Test Report Of Minor Test - 01 - Question 30

The intensity,
If E0 is the amplitude of the electric field associated with the wave

Test Report Of Minor Test - 01 - Question 31

Consider a y-polarized electromagnetic wave  incident normally on the interface of a dielectric and a perfect conductor  The resultant electric field in the dielectric is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 31

The transmission coefficient,
And the reflection coefficient.

T herefore, the reflective wave is given by
According to supeiposition principle, the resultant wave in dielectric.

Test Report Of Minor Test - 01 - Question 32

The lower limit of ΔpΔx2 for the ground state of the 1-D infinite potential well of width 'a' that ranges from  is [Note: you need not calculate the exact value of ΔpΔx for the state]

Detailed Solution for Test Report Of Minor Test - 01 - Question 32

Test Report Of Minor Test - 01 - Question 33

An electron in a hydrogen atom starts out in a state  are the ground and the first excited states respectively. The minimum time after which its state will become orthogonal to this initial state, respectively. [ E1 is the ground state energy of the Hydrogen atom]

Detailed Solution for Test Report Of Minor Test - 01 - Question 33

Test Report Of Minor Test - 01 - Question 34

The first born approximation
1. Consists of approximating the scattered wave by a plane wave.
2. Is valid when the average interaction between the incident particles and scattering potential is much larger than the particles kinetic energy.
Which of the above statement(s) is(are) TRUE?

Detailed Solution for Test Report Of Minor Test - 01 - Question 34

Since in first Born-approximation we approximate the scattered wave by a plane wave and also it applies when kinetic energy of incident particles are higher and the scattering potential is comparatively weaker.

Test Report Of Minor Test - 01 - Question 35

If the spin degrees of freedom of a 2-particle system is described by a 24 dimensional Hilbert space. Which of the following could denote the spin of one of the particles involved?

Detailed Solution for Test Report Of Minor Test - 01 - Question 35

The dimensionality of the composite Hilbert space composing of particles of spins S1 and S1 is

The spins of the particles could be

Test Report Of Minor Test - 01 - Question 36

Which of the following expresses the second order energy coll ection to the ground state energy of a mass 'n}' particle in the 1-D infinite potential well of width 'a' when a perturbation of the form  is a constant of appropriate dimensionality] is applied to it.

Detailed Solution for Test Report Of Minor Test - 01 - Question 36

We know that the 2nd order collection to the ith energy state is given by

Here, the collection term will be given by

Test Report Of Minor Test - 01 - Question 37

If 9 non-interacting spin-1/2 particles are placed in a 3-D isotropic harmonic oscillator of frequency ω. the ground state energy of the system will be

Detailed Solution for Test Report Of Minor Test - 01 - Question 37

The energy of a 3-D isotropic harmonic oscillator is given by

Now. the nth level has a p-fold degeneracy, where

The occupation of the electrons in their ground state of the system will be

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 38

The spin state of a particle is represented by  in the  basis. The expectation value of  for this state is ______

Detailed Solution for Test Report Of Minor Test - 01 - Question 38

Therefore,

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Test Report Of Minor Test - 01 - Question 39

Consider a 1 -D potential Well of the form

The minimum energy of the particle for which the transmission co-efficient becomes 1 (The well becomes transparent) is (in units of  _______. (Upto 3 decimal places)

Detailed Solution for Test Report Of Minor Test - 01 - Question 39

The energies En at which the well becomes transparent are :

The lowest value will occur for n = 1

The answer will be 1/16 ≌ 0.063

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 40

The degeneracy level for a state of energy E of a 2-D box of length ‘a ’ is

Detailed Solution for Test Report Of Minor Test - 01 - Question 40

The energy for the (nx, ny) state in a 2-D box is given by

= √5 , √5

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 41

The first excited state energy for a system of 8 non-interacting spin -5/2 particles in the 1-D harmonic oscillator of angular frequency ‘ω' of  is _________ (In units of hω.)

Detailed Solution for Test Report Of Minor Test - 01 - Question 41

For a spin-m fermion (2m -1) number of fermions can occupy an energy state.
In this case,  particles can be in the same energy state.
Hence, ground state is
First excited state occurs when one of the around state particles comes to the n = 1 state.
Hence, number of panicles for first excited state
Energy =

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 42

An energy eigenstate of the hydrogen atom has a wave function.

The value of the azimuthal quantum number associated with this state is______.

Detailed Solution for Test Report Of Minor Test - 01 - Question 42

Any eigenstate of the hydrogen atom can be written as.

Comparing this form with the given wave function, we find,

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Test Report Of Minor Test - 01 - Question 43

A panicle of mass 10-13 gm is having a wavelength of 6000 with a spread of 600 . The minimum time necessary for the panicle to cross a particular point is ____ x 10-12 seconds.

Detailed Solution for Test Report Of Minor Test - 01 - Question 43

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Test Report Of Minor Test - 01 - Question 44

Electrons of energy 10 eV are incident on a potential step of height 13.8 eV. The ratio of the probability of finding the particle within the penetration depth (x0) in the classically forbidden region to, the probability of finding it with in a distance of 2x0 from the origin is _________ .
[Rest mass of electron = 0.51 MeV/c2, hc = 198 MeV . fm]

Detailed Solution for Test Report Of Minor Test - 01 - Question 44

The wave fiinction in the classically forbidden region is given by
Now  penetration depth
The ratio of the probabilities is

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 45

Two particles of spin -3/2 and spin-1 are at rest in a box and total spin is measured to be 5/2 and its total z-component is found to be 3/2. The probability that a measurement of the z-component of spin of the spin-1 particle is found to be zero is _____.

Detailed Solution for Test Report Of Minor Test - 01 - Question 45

Therefore, the probability of finding the sz component of spin-1 particle to be ‘0' is

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 46

If the initial state of a system in a 1-D harmonic oscillator of frequency 'ω' is.

The expectation value of position at

Detailed Solution for Test Report Of Minor Test - 01 - Question 46

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 47

The probability of finding -h/2 upon a measurement of  on a spin -1/2 particle whose spin state is given by
is ______.

Detailed Solution for Test Report Of Minor Test - 01 - Question 47

0.01

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 48

A particle in a 1-D harmonic oscillator of frequency ‘ω' starts out in a state

The probability of finding the energy of the particle to be hω/2 at time ‘t' is ______.

Detailed Solution for Test Report Of Minor Test - 01 - Question 48

The probability of measuring hω/2 energy at time ‘t’ is given by |c0|2.

[Ground state of the 1 -D oscillator]

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 49

The wave function of a particle is represented by,

The average momentum of the particle is______.[in units of πh/a]

Detailed Solution for Test Report Of Minor Test - 01 - Question 49

Since. π(x) is symmetric φ(p) will also have a definite parity and | φ(p)|2 will be an even function.
[since integrand is odd and is integrated over a symmetric interval].

*Answer can only contain numeric values
Test Report Of Minor Test - 01 - Question 50

The wave function of a particle is given by  in a potential of the form V ( x ) = The value of ‘k ’ in units of mα/h2  is ________.

Detailed Solution for Test Report Of Minor Test - 01 - Question 50

Test Report Of Minor Test - 01 - Question 51

Suppose due to some charge distribution the electric field at the point p(r,θ) is
The equation o f field line is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 51

We have
Therefore, the differential equation of electric field line is

⇒
⇒

Test Report Of Minor Test - 01 - Question 52

Consider a uniformly polarized cube of dielectric of side a with uniform polarization  where P0 is a constant as shown in figure . The value of and  over the closed surface S which cuts through the dielec tiic completly enclosing the upper surface are respectively (all the dimension of the rectangle surface are larger than a)

Detailed Solution for Test Report Of Minor Test - 01 - Question 52

The bound surface charge density on the upper surface of dielectric. σb = P0
and volume bound charge density
Now, according to Gauss's law,

and the

Test Report Of Minor Test - 01 - Question 53

Suppose a charge q moving on a ringe of radius R with constant velocity v.the rate of cliange of electric field at the centre of the ring is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 53

Suppose at an y time t particle at P ( R . θ )
The electric field at the centre is

So, the rate o f clianse o f electric field.

Test Report Of Minor Test - 01 - Question 54

A spiral coil of outer radius R and having N(≫1), is placed in a magnetic field 5 = 0.5 cos(314t)z . The emf generated in the coil is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 54

The number of turn per unit length, n = N/R
Therefore, the magnetic flux passing through the cross-section o f radius r to r + d r is given by

∴
∴

Test Report Of Minor Test - 01 - Question 55

Consider an infinitely long air fielled selonoid of radius a.The magnetic field is given by

The induced electric field is given by

Detailed Solution for Test Report Of Minor Test - 01 - Question 55

According to Maxwell's equation,

⇒

⇒
⇒
And for ρ > a

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