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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

DU PhD in Physics
Topic: PHY PHD S2
1) A small mass m with a charge q is attached to a spring of spring constant k and allowed to oscillate with amplitude A.
Assuming that the amplitude of the oscillations and the speed of the mass is small, the time averaged power radiated by the
system in Gaussian units is
[Question ID = 1426]
1.
[Option ID = 5698]
2.
[Option ID = 5699]
3.
[Option ID = 5700]
4. None of these
[Option ID = 5701]
Correct Answer :
[Option ID = 5698]
2) A sphere of radius a made of a material of dielectric constant
has a uniform charge density
. Assuming V = 0, the
potential V0 at the center of the sphere is
[Question ID = 1427]
1.
[Option ID = 5702]
2.
[Option ID = 5703]
3.
[Option ID = 5704]
4.
[Option ID = 5705]
Correct Answer :
[Option ID = 5702]
3) In the planetary model of the hydrogen atom, the time taken for the electron of charge and mass m in the first Bohr
orbit
=
to spiral into the nucleus is given by
[Question ID = 1428]
1.

---

[Option ID = 5706]
2.
[Option ID = 5707]
3.
[Option ID = 5708]
4. None of these
[Option ID = 5709]
Correct Answer :
[Option ID = 5706]
4) A particle of mass m and charge q is accelerated from rest in a uniform electric field E =
for a time . Assuming
relativistic motion, the speed of the particle at time is given by
[Question ID = 1429]
1.
[Option ID = 5710]
2.
[Option ID = 5711]
3.
[Option ID = 5712]
4.
[Option ID = 5713]
Correct Answer :
[Option ID = 5710]
5) A circular air filled parallel plate capacitor of radius and separation has an electric field
which varies as .
Ignoring edge effects, the magnitude of the magnetic field is given by
[Question ID = 1430]
1.
[Option ID = 5714]
2.
[Option ID = 5715]
3.
[Option ID = 5716]
4.
[Option ID = 5717]
Correct Answer :
[Option ID = 5714]

---

6) The firstorder correction to the ground state energy of an isotropic 3dimensional harmonic oscillator with the
perturbation
is
[Question ID = 1431]
1. 0
[Option ID = 5718]
2.
[Option ID = 5719]
3.
[Option ID = 5720]
4.
[Option ID = 5721]
Correct Answer :
0
[Option ID = 5718]
7) Consider a particle of mass m constrained in the segment a x a and subject to the repulsive potential
. Consider V (x) as a perturbation and calculate the 1 order correction
st
and
to the energies
of the ground and first excited states
[Question ID = 1432]
1.
[Option ID = 5722]
2.
[Option ID = 5723]
3.
[Option ID = 5724]
4.
[Option ID = 5725]
Correct Answer :
[Option ID = 5722]
8) If the scattering amplitude
, the total crosssection
is
[Question ID = 1433]
1.
[Option ID = 5726]
2.
[Option ID = 5727]
3.
[Option ID = 5728]
4. 0
[Option ID = 5729]
Correct Answer :

---

[Option ID = 5726]
9) Find the first order probability of transition of a harmonic oscillator to go from its ground state |0 > to the first exited state |1 >
for a timedependent perturbation
,
, for
late time, and
.
is therefore equal to
[Question ID = 1434]
1. 0
[Option ID = 5730]
2.
[Option ID = 5731]
3. 1
[Option ID = 5732]
4.
[Option ID = 5733]
Correct Answer :
0
[Option ID = 5730]
10) The angle between two (hkl) planes corresponding to (100) and (110) is
[Question ID = 1435]
1. 45?
[Option ID = 5734]
2. 60?
[Option ID = 5735]
3. 30?
[Option ID = 5736]
4. 15?
[Option ID = 5737]
Correct Answer :
45?
[Option ID = 5734]
11) The Madelung constant of a one dimensional crystal consisting of alternate positive and negative ions with interatomic
distance R is given by the expression = 2 ln2. The Madelung constant for a divalent ion can be expressed as:
[Question ID = 1436]
1. = 8 ln2 [Option ID = 5738]
2. = 4 ln2 [Option ID = 5739]
3. = ln2 [Option ID = 5740]
4. 0 [Option ID = 5741]
Correct Answer :
= 8 ln2 [Option ID = 5738]
12) The total scattering amplitude of reflection from (h,k,l) plane is given by the expression
. Where (u , v
j
, w
j
)
j
represent the coordinates of the jth atom. The allowed reflections for
(h,k,l) values for a FCC structure are
[Question ID = 1437]
1. all odd or all even
[Option ID = 5742]
2. all odd
[Option ID = 5743]
3. all even
[Option ID = 5744]
4. zero
[Option ID = 5745]
Correct Answer :
all odd or all even
[Option ID = 5742]

---

13) A one dimensional lattice chain consists of periodic arrangement of atoms with lattice spacing `a'. Each atom is
represented by the potential
. the energy gaps between the bands in the nearly free electron approximation
is
[Question ID = 1438]
1. 2V0
[Option ID = 5746]
2. V0
[Option ID = 5747]
3. V /2
0
[Option ID = 5748]
4.
[Option ID = 5749]
Correct Answer :
2V0
[Option ID = 5746]
14) If an AC current of frequency 1 GHz is observed through a Josephson junction, then the applied dc voltage is, (Given h
= 6.625 x 10
)
34
[Question ID = 1439]
1. 2.07 ?V [Option ID = 5750]
2. 3.8 ?V [Option ID = 5751]
3. 1 ?V [Option ID = 5752]
4. 5.48 ?V [Option ID = 5753]
Correct Answer :
2.07 ?V [Option ID = 5750]
15) Suppose that Newton's theory of gravitation is modified for short range. In this modified theory the potential energy
between two masses
and
are given by,
Where a is a constant and other symbols have their usual physical significance. For short distances
calculate the force
between
and
.
[Question ID = 1440]
1.
[Option ID = 5754]
2.
[Option ID = 5755]
3.
[Option ID = 5756]
4.
[Option ID = 5757]
Correct Answer :
[Option ID = 5754]
16) A statistical system is composed of two ultrarelativistic particles moving in a segment of length L. The Hamiltonian of
the system is given by,
Where, p and
1
p
2 are the momenta of the particles and c is the speed of light in vacuum. The volume of phase space
enclosed by the surface of constant energy E is given by,
[Question ID = 1441]
1.
[Option ID = 5758]

---

2.
[Option ID = 5759]
3.
[Option ID = 5760]
4.
[Option ID = 5761]
Correct Answer :
[Option ID = 5758]
17) Consider an ensemble of N distinguishable particles distributed in two energy levels and , with number of particles in
them N+ and N , respectively in equilibrium. The ensemble is isolated and has a fixed energy E at temperature T given by,
, where kB is the Boltzmann Constant.
If
, find out the temperature at which
.
[Given,
]
[Question ID = 1442]
1. +2K
[Option ID = 5762]
2. 2K
[Option ID = 5763]
3. +1K
[Option ID = 5764]
4. 4K
[Option ID = 5765]
Correct Answer :
+2K
[Option ID = 5762]
18) Primary advantage of a crystal oscillator is that
[Question ID = 1443]
1. it can oscillate at any frequency [Option ID = 5766]
2. it gives a high output voltage [Option ID = 5767]
3. its frequency of oscillation remains almost constant [Option ID = 5768]
4. it gives a constant a d.c. output voltage [Option ID = 5769]
Correct Answer :
its frequency of oscillation remains almost constant [Option ID = 5768]
19) In the spectrum of a frequencymodulated wave
[Question ID = 1444]
1. the carrier frequency disappears when the modulationindex is large [Option ID = 5770]
2. the amplitude of any sideband depends on the modulationindex [Option ID = 5771]
3. the total number of sidebands depends on the modulationindex [Option ID = 5772]
4. the carrier frequency cannot disappear [Option ID = 5773]
Correct Answer :
the amplitude of any sideband depends on the modulationindex [Option ID = 5771]
20) The largest value of output voltage from an 8bit digitaltoanalog converter that produces 1.0 V for a digital input of
00110010 is
[Question ID = 1445]
1. 5.1 V [Option ID = 5774]
2. 10.2 V [Option ID = 5775]
3. 20.4 V [Option ID = 5776]
4. 2.5 V [Option ID = 5777]
Correct Answer :
5.1 V [Option ID = 5774]

---

21) Which of the following statement is NOT correct for a Depletion type nchannel MOSFET
[Question ID = 1446]
1. Channel width can be increased [Option ID = 5778]
2. Channel width can be decreased [Option ID = 5779]
3. Can work with both positive and negative gate bias [Option ID = 5780]
4. Initially the channel between drain and source is completely blocked by a pregion [Option ID = 5781]
Correct Answer :
Initially the channel between drain and source is completely blocked by a pregion [Option ID = 5781]
22) If an inverter is placed between the inputs of an SR FlipFlop, the resulting FlipFlop is a
[Question ID = 1447]
1. DFlip Flop [Option ID = 5782]
2. JK Flip Flop [Option ID = 5783]
3. Master Slave Flip Flop [Option ID = 5784]
4. Remains a SR FlipFlop [Option ID = 5785]
Correct Answer :
DFlip Flop [Option ID = 5782]
23) The Carnot engines X and Y are operating in series. The first engine X receives heat at 1200 K and rejects to a
reservoir at temperature T. The second engine Y receives the heat rejected by X, and thereafter reejects to a heat
reservoir at 300 K. Calculate the temperature (in Kelvin) for the situation, when the work output of the two engines is
equal.
[Question ID = 1448]
1. 750 K [Option ID = 5786]
2. 600 K [Option ID = 5787]
3. 0 K [Option ID = 5788]
4. 450 K [Option ID = 5789]
Correct Answer :
750 K [Option ID = 5786]
24) The quantum mechanical energy states of an atom are described by the energy states such as 0 and at the thermal
equilibrium temperature T. Now the system has partition function Q such that its total internal energy will be:
[Question ID = 1449]
1.
[Option ID = 5790]
2.
[Option ID = 5791]
3.
[Option ID = 5792]
4.
[Option ID = 5793]
Correct Answer :
[Option ID = 5790]
25) 1 Kg of water at 273 K is brought in contact with a heat reservoir at 373 K. Now after the transfer of heat to the heat reservoir,
there is a change of entropy in the system when the water reaches 373 K. What is the change in entropy.
[Given specific heat
cal/KgK]
[Question ID = 1450]
1.

---

[Option ID = 5794]
2.
[Option ID = 5795]
3.
[Option ID = 5796]
4. None of these
[Option ID = 5797]
Correct Answer :
[Option ID = 5795]
26) Roughing vacuum range is
[Question ID = 1451]
1.
mbar
[Option ID = 5798]
2.
mbar
[Option ID = 5799]
3.
mbar
[Option ID = 5800]
4.
mbar
[Option ID = 5801]
Correct Answer :
mbar
[Option ID = 5800]
27) Pirani gauge works in pressure range of
[Question ID = 1452]
1.
Torr
[Option ID = 5802]
2.
Torr
[Option ID = 5803]
3.
Torr
[Option ID = 5804]
4.
Torr
[Option ID = 5805]
Correct Answer :
Torr
[Option ID = 5803]
28) 3 Isospin (I) of elementary particle
is
[Question ID = 1453]
1.
[Option ID = 5806]
2.
[Option ID = 5807]
3. 1
[Option ID = 5808]
4. 0
[Option ID = 5809]

---

Correct Answer :
0
[Option ID = 5809]
29) Which one of the following particle has a strangeness quantum number 1 ?
[Question ID = 1454]
1.
+ [Option ID = 5810]
2.
0 [Option ID = 5811]
3. K
+ [Option ID = 5812]
4. [Option ID = 5813]
Correct Answer :
K
+ [Option ID = 5812]
30) Hypercharge (Y) of elementary particle
is
[Question ID = 1455]
1. 0
[Option ID = 5814]
2. +1
[Option ID = 5815]
3. 1
[Option ID = 5816]
4. 2
[Option ID = 5817]
Correct Answer :
+1
[Option ID = 5815]
31) Quark structure of elementary particle
is
[Question ID = 1456]
1. uus
[Option ID = 5818]
2. uds
[Option ID = 5819]
3. sds
[Option ID = 5820]
4. sus
[Option ID = 5821]
Correct Answer :
uus
[Option ID = 5818]
32) Total number of down quarks in
are
[Question ID = 1457]
1. 9
[Option ID = 5822]
2. 10
[Option ID = 5823]
3. 11
[Option ID = 5824]
4. 12
[Option ID = 5825]
Correct Answer :
11
[Option ID = 5824]
33) If the probability that a problem will be solved by three students is 1/2, 1/3 and 1/6, then what is the probability that
the problem will be solved?

---

[Question ID = 1458]
1. 13/18,
[Option ID = 5826]
2. 1/36
[Option ID = 5827]
3. 1/18
[Option ID = 5828]
4. none of these
[Option ID = 5829]
Correct Answer :
13/18,
[Option ID = 5826]
34) Find the eigenvalues of 4A +3A+2I, where I is the identity matrix and
1
[Question ID = 1459]
1. 9,15
[Option ID = 5830]
2. 9,36
[Option ID = 5831]
3. 7,28
[Option ID = 5832]
4. None of these
[Option ID = 5833]
Correct Answer :
9,15
[Option ID = 5830]
35) If
and
then
is
[Question ID = 1460]
1. u
[Option ID = 5834]
2. 2u
[Option ID = 5835]
3. 4u
[Option ID = 5836]
4. 5u
[Option ID = 5837]
Correct Answer :
5u
[Option ID = 5837]
36) The value of complex integral
with the closed contour
is
[Question ID = 1461]
1.
[Option ID = 5838]
2.
[Option ID = 5839]
3. 3
[Option ID = 5840]
4.
[Option ID = 5841]

---

Correct Answer :
[Option ID = 5838]
37) The Fourier transform of
is
[Question ID = 1462]
1.
[Option ID = 5842]
2.
[Option ID = 5843]
3.
[Option ID = 5844]
4. None of these
[Option ID = 5845]
Correct Answer :
[Option ID = 5842]
38) Given the operator
, where the commutator
, as well as two constant vector and ,
then the commutator
is equal to,
[Question ID = 1463]
1.
[Option ID = 5846]
2.
[Option ID = 5847]
3.
[Option ID = 5848]
4.
[Option ID = 5849]
Correct Answer :
[Option ID = 5846]
39) For
, the series
is equal to:
[Question ID = 1464]
1.
[Option ID = 5850]
2.
[Option ID = 5851]
3.

---

[Option ID = 5852]
4.
[Option ID = 5853]
Correct Answer :
[Option ID = 5850]
40) The integral,
is equal to,
[Question ID = 1465]
1. 1
[Option ID = 5854]
2.
[Option ID = 5855]
3. +1
[Option ID = 5856]
4.
[Option ID = 5857]
Correct Answer :
1
[Option ID = 5854]
41) The solution of the differential equation,
is given by, A being an arbitrary constant,
[Question ID = 1466]
1.
[Option ID = 5858]
2.
[Option ID = 5859]
3.
[Option ID = 5860]
4.
[Option ID = 5861]
Correct Answer :
[Option ID = 5858]
42) If
but
then,
[Question ID = 1467]
1.
[Option ID = 5862]
2.
[Option ID = 5863]
3.
[Option ID = 5864]
4.
[Option ID = 5865]
Correct Answer :
[Option ID = 5862]
43)
equals to:

---

[Question ID = 1468]
1.
[Option ID = 5866]
2.
[Option ID = 5867]
3.
[Option ID = 5868]
4.
[Option ID = 5869]
Correct Answer :
[Option ID = 5866]
44) The entropy S of a thermodynamic system as a function of energy E is given by the following graph
If TA, TB and TC are the temperatures for the phases A, B, and C respectively, then
[Question ID = 1469]
1.
[Option ID = 5870]
2.
[Option ID = 5871]
3.
[Option ID = 5872]
4.
[Option ID = 5873]
Correct Answer :
[Option ID = 5870]
45) If the halflife of radium is about 1600 years, then for a given ball of pure radium weighing 4 gm now, what would be
the amount of time required to have only 0.125 gm of radium to be left,
[Question ID = 1470]
1. 9600 yrs [Option ID = 5874]
2. 4800 yrs [Option ID = 5875]
3. 7200 yrs [Option ID = 5876]
4. 8000 yrs [Option ID = 5877]
Correct Answer :
8000 yrs [Option ID = 5877]
46) The Hamiltonian for a 1dimensional system is given to be
, where and are positive real numbers,
respectively. The phase space trajectory in the position momentum
plane is given by,
[Question ID = 1471]
1. An ellipse
[Option ID = 5878]
2. A straight line with a positive slope
[Option ID = 5879]
3. A parabola
[Option ID = 5880]

---

4. A straight line with a negative slope
[Option ID = 5881]
Correct Answer :
A straight line with a negative slope
[Option ID = 5881]
47) The Lagrangian for a system is given by
, where and are positive real numbers. The
constant b is also a positive real number. The equation of motion that follows from this Lagrangian is
[Question ID = 1472]
1.
[Option ID = 5882]
2.
[Option ID = 5883]
3.
[Option ID = 5884]
4.
[Option ID = 5885]
Correct Answer :
[Option ID = 5885]
48) The Hamiltonian of a system is given by,
where a and b are positive constants. The corresponding Lagrangian is
[Question ID = 1473]
1.
[Option ID = 5886]
2.
[Option ID = 5887]
3.
[Option ID = 5888]
4.
[Option ID = 5889]
Correct Answer :
[Option ID = 5889]
49) Consider the transformation,


,
where,
,
, , and
are real constants. This transformation is:
[Question ID = 1474]
1. Always canonical as it is a linear transformation.
[Option ID = 5890]
2. Never a canonical transformation since it is linear.
[Option ID = 5891]
3.
[Option ID = 5892]
4. A canonical transformation if
[Option ID = 5893]
Correct Answer :

---

A canonical transformation if
[Option ID = 5893]
50) A freeparticle moving in 1dimension is described by the wavefunction,
,
which of the following options is correct?
[Question ID = 1475]
1.
is an eigenstate of the momentum operator
[Option ID = 5894]
2.
is not a solution of the Schrodinger equation, but is an eigenstate of the Hamiltonian.
[Option ID = 5895]
3.
is an eigenstate of the momentum operator as well as an eigenstate of the Hamiltonian.
[Option ID = 5896]
4.
is a solution of the Schlrodinger equation and is an eigenstate of the Hamiltonian.
[Option ID = 5897]
Correct Answer :
is a solution of the Schlrodinger equation and is an eigenstate of the Hamiltonian.
[Option ID = 5897]

---