DUET 2021 Question Paper Ph.D in informatics

DU PhD in informatics IIC
Topic:‐ INFO PHD

1) The electrostatic potential V(x,y) in free space in a region where the charge density ρ is zero is given by V(x,y) = 4e2x + f(x) –
3y2. Given that the x‐component of the electric field Ex , and V are zero at the origin, f(x) is:[Question ID = 3622]
1. 3x2 – 4e2x + 8x ​ [Option ID = 14485]
2. 4e2x ‐ 8x [Option ID = 14486]
3. 3x2 – 4e2x + 16x [Option ID = 14487]
4. 3x2 – 4e2x ​ [Option ID = 14488]

2) A solenoid of inductance L and resistance R is connected to a battery, the time taken for the magnetic energy to reach ¼ of
its maximum value is[Question ID = 3623]
1. (L/R)loge(1) [Option ID = 14489]
2. (L/R)loge(2) [Option ID = 14490]
3. (L/R)loge(3) [Option ID = 14491]
4. (L/R)loge(4) [Option ID = 14492]

3) The depth of penetration of electromagnetic wave in a medium having conductivity σ at a frequency of 1 MHz is 25 cm. The
depth of penetration at a frequency of 4 MHz will be[Question ID = 3624]
1. 12.5 cm [Option ID = 14493]
2. 25.0 cm [Option ID = 14494]
3. 50.0 cm [Option ID = 14495]
4. 100.0 cm [Option ID = 14496]

4) A one dimensional harmonic oscillator has Hamiltonian H = ½ p2 + ½ ω2q2. Hamiltonian’s equations of motion are given
by[Question ID = 3625]
1.

[Option ID = 14497]
2.

[Option ID = 14498]
3.

[Option ID = 14499]
4.

[Option ID = 14500]

5) The Hamiltonian of a system is given by H = ½ p2 + p sin(q), which of the following represents the corresponding Lagrangian of
the system[Question ID = 3626]
1. ½ p2 + cos(q) [Option ID = 14501]
2. ½ p2 ​ [Option ID = 14502]
3. ½ p2 + p [Option ID = 14503]
4. ½ p2 ‐ cos (q) [Option ID = 14504]

6) Consider the following statements:

A. Poisson Bracket of two dynamical variables u and v under canonical transformation is invariant.

B. Poisson Bracket of two constants of the motion is also constant of motion.

C. If the Hamiltonian and a quantity G are constants of the motion then must also be a constant.

Choose the correct answer from the options given below:

[Question ID = 3627]
1. Only B

[Option ID = 14505]
2. A and B only

[Option ID = 14506]
3. A, B and C

[Option ID = 14507]
4. Only C

[Option ID = 14508]

7) Electron is moving with velocity 3 x 107 m/sec, the uncertainity in the position of electron is

[Question ID = 3628]
1. 0.0038 ​

[Option ID = 14509]
2. 0.0083 ​

[Option ID = 14510]
3. 0.038 ​

[Option ID = 14511]
4. 0.083 ​

[Option ID = 14512]

8) A particle of mass m trapped in the potential V(x) = 0 for –a £ x £ a and V(x) = ¥ for otherwise. What is the probability of finding the particle between x = 0
and x = a/n when it is in nth state

[Question ID = 3629]
1. n

[Option ID = 14513]
2. 2/n

[Option ID = 14514]
3. 1/n

[Option ID = 14515]
4. 0

[Option ID = 14516]

9) By using the single particle shell model predict the ground state spins of 83Bi209 and 82Pb209[Question ID = 3630]
1. 9/2, 13/2 [Option ID = 14517]
2. 9/2, 7/2 [Option ID = 14518]
3. 11/2, 9/2 [Option ID = 14519]
4. 11/2, 13/2 [Option ID = 14520]

10) To penetrate the Coulomb barrier of a light nucleus, a proton must have a minimum energy of the order of[Question ID =
3631]
1. 1 keV [Option ID = 14521]
2. 1 MeV [Option ID = 14522]
3. 1 GeV [Option ID = 14523]
4. 10 MeV [Option ID = 14524]

11) A microcanonical ensemble represents[Question ID = 3632]
1. A system in contact with a heat reservoir [Option ID = 14525]
2. An isolated system in equilibrium [Option ID = 14526]
3. A system that can exchange particles with its surroundings [Option ID = 14527]
4. A system under constant external pressure [Option ID = 14528]

12) Consider a symmetric elastic collision between a particle of mass m and kinetic energy T and a particle of the same mass at
rest. Relativistically, what is the cosine of the angle between the two particles after the collision?[Question ID = 3633]
1. 1 [Option ID = 14529]
2. T/(T + 4m) [Option ID = 14530]
3. T/(T + 5m) [Option ID = 14531]
4. T/(T + 2m) [Option ID = 14532]

13) The ground state of a quantum system of identical bosons (using the Hartree–Fock approximation and the pseudo potential
interaction model) is described by:[Question ID = 3634]
1. Topological Insulator [Option ID = 14533]
2. Anderson Localization [Option ID = 14534]
3. Bose‐Hubbard Model [Option ID = 14535]
4. Gross‐Pitaevski equation [Option ID = 14536]

14) A relation R on the set A={0 ,1 ,2 ,3} is given as: R={(0,0),(1,1),(1,2),(2,1),(2,2),(3,3)} The relation R is[Question ID =
3635]
1. only reflexive [Option ID = 14537]
2. only symmetric [Option ID = 14538]
3. only transitive [Option ID = 14539]
4. an equivalence relation. [Option ID = 14540]

15)

[Question ID = 3636]

1.

[Option ID = 14541]

2.

[Option ID = 14542]

3.

[Option ID = 14543]

4.

[Option ID = 14544]

16)

[Question ID = 3637]
1.

[Option ID = 14545]
2.

[Option ID = 14546]
3.

[Option ID = 14547]
4.

[Option ID = 14548]

17) Determine the rank of the following matrix

.[Question ID = 3638]
1. 1 [Option ID = 14549]
2. 2 [Option ID = 14550]
3. 3 [Option ID = 14551]
4. 4 [Option ID = 14552]

18) The set of columns in the following matrix

are[Question ID = 3639]
1. Linearly dependent [Option ID = 14553]
2. Linearly independent [Option ID = 14554]
3. Do not form basis [Option ID = 14555]
4.

​ [Option ID = 14556]

19)

[Question ID = 3640]
1.

[Option ID = 14557]
2.

[Option ID = 14558]
3.

[Option ID = 14559]
4.

[Option ID = 14560]

20) Solve the initial value problem

[Question ID = 3641]
1.

[Option ID = 14561]
2.

[Option ID = 14562]
3.

[Option ID = 14563]
4.

[Option ID = 14564]

21) Find the solution of the differential equation

[Question ID = 3642]
1.

[Option ID = 14565]

2.

[Option ID = 14566]
3.

[Option ID = 14567]
4.

[Option ID = 14568]

22) Find a fourth degree polynomial approximation ( a power series about x = 0) to the solution of the initial value problem y" ‐ y
=0 ; y(0) =2 , y'(0)=0.

[Question ID = 3643]
1.

[Option ID = 14569]

2.

[Option ID = 14570]

3.

[Option ID = 14571]

4.

[Option ID = 14572]

23) Find the Laplace transform of the piecewise continuous function,

[Question ID = 3644]
1.

[Option ID = 14573]
2.

[Option ID = 14574]
3.

[Option ID = 14575]
4.

[Option ID = 14576]

24) Find the solution of the initial value problem

[Question ID = 3645]
1.

[Option ID = 14577]
2.

[Option ID = 14578]
3.

[Option ID = 14579]
4.

[Option ID = 14580]

25)

[Question ID = 3646]

1.

[Option ID = 14581]

2.

[Option ID = 14582]

3.

[Option ID = 14583]

4.

[Option ID = 14584]

26)

[Question ID = 3647]
1.

[Option ID = 14585]
2.

[Option ID = 14586]
3.

[Option ID = 14587]
4.

[Option ID = 14588]

27)

[Question ID = 3648]
1.

[Option ID = 14589]
2.

[Option ID = 14590]
3.

[Option ID = 14591]
4.

[Option ID = 14592]

28) A fair dice is rolled 5 times. Find the probability that 1 shows twice, 3 shows twice and 6 shows once.[Question ID = 3649]
1. 0.0019 [Option ID = 14593]
2. 0.0029 [Option ID = 14594]
3. 0.0039 [Option ID = 14595]
4. 0.0049 [Option ID = 14596]

29) A random variable X has the following probability distribution.

‐
X: ‐2 0 1 2 3
1

P(x):0.1K0.22K0.33K

Find K?

[Question ID = 3650]
1.

[Option ID = 14597]
2.

[Option ID = 14598]
3.

[Option ID = 14599]
4.

[Option ID = 14600]

30) In a book of 600 pages, there are 60 typographical errors. Assuming Poisson law for the number of errors per page, find the
probability that a randomly chosen 4 pages will contain no errors.[Question ID = 3651]
1. 0.6703 [Option ID = 14601]
2. 0.7408 [Option ID = 14602]
3. 0.8187 [Option ID = 14603]
4. 0.9048 [Option ID = 14604]

31)

[Question ID = 3652]
1.

[Option ID = 14605]
2.

[Option ID = 14606]
3.

[Option ID = 14607]
4.

[Option ID = 14608]

32)

[Question ID = 3653]
1.

[Option ID = 14609]
2.

[Option ID = 14610]
3.

[Option ID = 14611]
4.

[Option ID = 14612]

33)

[Question ID = 3654]
1.

[Option ID = 14613]
2.

[Option ID = 14614]
3.

[Option ID = 14615]
4.

[Option ID = 14616]

34)

[Question ID = 3655]
1.

[Option ID = 14617]
2.

[Option ID = 14618]
3.

[Option ID = 14619]
4.

[Option ID = 14620]

35)

[Question ID = 3656]
1. Regular Markov chain

[Option ID = 14621]
2. Irregular Markov chain

[Option ID = 14622]
3. Ergodic chain

[Option ID = 14623]
4. Reducible chain

[Option ID = 14624]

36)

[Question ID = 3657]
1.

[Option ID = 14625]
2.

[Option ID = 14626]
3.

[Option ID = 14627]
4.

[Option ID = 14628]

37) Thermal runaway will take place if the quiescent point is such that[Question ID = 3658]
1.

[Option ID = 14629]
2.

[Option ID = 14630]
3.

[Option ID = 14631]
4.

[Option ID = 14632]

38) A small concentration of minority carries is injected into a homogeneous Semiconductor crystal at one point. An electric field

of 10V/cm is applied across the crystal and this moves the minority carries a distance of 1cm in 20µsec. The mobility (in cm2 /v‐
sec) will be[Question ID = 3659]
1. 1,000 [Option ID = 14633]
2. 2,000 [Option ID = 14634]
3. 5,000 [Option ID = 14635]
4. 500,000 [Option ID = 14636]

39) If the differential voltage gain and the common mode voltage gain of a differential amplifier are 48dB and 2dB respectively,
then its common mode rejection ratio is[Question ID = 3660]
1. 23 dB [Option ID = 14637]
2. 25 dB [Option ID = 14638]
3. 46 dB [Option ID = 14639]
4. 50 dB [Option ID = 14640]

40) The density of dynamic RAM is[Question ID = 3661]
1. the same as static RAM [Option ID = 14641]
2. less than that of static RAM [Option ID = 14642]
3. more than that of static RAM [Option ID = 14643]
4. either equal or less than that of static RAM [Option ID = 14644]

41) Choose the correct statements(s) from the following[Question ID = 3662]
1. PROM contains a programmable AND array and a fixed OR array. [Option ID = 14645]
2. PLA contains a fixed AND array and a programmable OR array. [Option ID = 14646]
3. PROM contains a fixed AND array and a programmable OR array. [Option ID = 14647]
4. PLA contains a programmable OR array. [Option ID = 14648]

42) A 10 bit D/A converter given a maximum output of 10.23V. The resolution is[Question ID = 3663]
1. 10 mV [Option ID = 14649]
2. 20 mV [Option ID = 14650]
3. 15 mV [Option ID = 14651]
4. 25 mV [Option ID = 14652]

43) Manchester code is a[Question ID = 3664]
1. Bi‐polar code [Option ID = 14653]
2. non return to zero code [Option ID = 14654]
3. tri‐polar code [Option ID = 14655]
4. uni‐polar code [Option ID = 14656]

44) Bit stuffing refers to[Question ID = 3665]
1. inserting a ‘O' in user data stream to differentiate it with a flag [Option ID = 14657]
2. inserting a ‘0’ in flag stream to avoid ambiguity [Option ID = 14658]
3. appending a nibble to the flag sequence appending a nibble to the user data stream [Option ID = 14659]
4. appending a nibble to the user data stream [Option ID = 14660]

45) Maximum data rate of a channel for a noiseless 3kHz binary channel is[Question ID = 3666]
1. 3000bps [Option ID = 14661]
2. 6000bps [Option ID = 14662]
3. 1500bps [Option ID = 14663]
4. 1000bps [Option ID = 14664]

46) Which of the following is not a standard RS‐232C signal?[Question ID = 3667]
1. RTS [Option ID = 14665]
2. CTS [Option ID = 14666]
3. DSR [Option ID = 14667]
4. VDR [Option ID = 14668]

47) In Ethernet when Manchester encoding is used, the bit rate is[Question ID = 3668]
1. half the baud rate [Option ID = 14669]
2. twice the baud rate [Option ID = 14670]
3. same as the baud rate [Option ID = 14671]
4. thrice the baud rate [Option ID = 14672]

48) The message 11001001 is to be transmitted using the CRC polynomial x3 + 1 to protect it from errors. The message that
should be transmitted is[Question ID = 3669]
1. 11001001000 [Option ID = 14673]
2. 11001001011 [Option ID = 14674]
3. 11001010 [Option ID = 14675]
4. 110010010011 [Option ID = 14676]

49) Which one of the following is not a client‐server application?[Question ID = 3670]
1. Internet chat [Option ID = 14677]
2. Web browsing [Option ID = 14678]
3. E‐mail [Option ID = 14679]
4. Ping [Option ID = 14680]

50) An AM signal and a narrow‐band FM signal with identical carriers, modulating signals and modulation indices of 0.1 are added

together. The resultant signal can be closely approximated by[Question ID = 3671]
1. Broadband FM [Option ID = 14681]
2. SSB with carrier [Option ID = 14682]
3. DSB‐SC [Option ID = 14683]
4. SSB without carrier [Option ID = 14684]