Question Paper Name: Physical Science 28th May 2019 Shift1 Set1
Subject Name: Physical Science
Creation Date: 2019-05-28 15:19:43
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Duration: 180
Total Marks: 100
Display Marks: Yes
Share Answer Key With Delivery Engine: Yes
Actual Answer Key: Yes
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Physical Science
Group Number: 1
Group Id: 128206104
Group Maximum Duration: 0
Group Minimum Duration: 120
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Revisit allowed for view?: No
Revisit allowed for edit?: No
Break time: 0
Group Marks: 100
PART A
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Section Id: 12820
Section Number: 1
Section type: Online
Mandatory or Optional: Mandatory
Number of Questions: 8
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Number of Questions to be attempted: 8
Section Marks: 40
Display Number Panel: Yes
Group All Questions: No
Sub-Section Number: 1
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Sub-Section Id: 128206258
Question Shuffling Allowed: Yes
Question Number: 1 Question Id: 1282065533 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
Consider the quantum mechanical motion of a free particle of mass m in a one-dimensional box of length L. What is the expectation value of its kinetic energy in the state with wave function ?(x) = Cx(L-x) where C is a constant of normalization?
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(A) (h²)/(mL²)
(B) (5h²)/(4p²mL²)
(C) (2h²)/(3p²mL²)
(D) (4h²)/(3p²mL²)
Options:
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12820621871. A
12820621872. B
12820621873. C
12820621874. D
Question Number: 2 Question Id: 1282065534 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 5 Wrong Marks: 0
Consider a system of three interacting spins S1, S2 and S3 - each of which can have values +1 and -1. The Hamiltonian is given by H = -J(S1S2 + S2S3 + S1S3). If T is the temperature and kB is the Boltzmann constant, define ß = 1/kBT. What is the thermally averaged value of (S1 S2+S3)?
(A) (exp(4ßJ)-1)/(exp(4ßJ)+3)
(B) exp(3ßJ)/(exp(3ßJ)+2)
(C) (exp(3ßJ)+3)/(exp(3ßJ)+5)
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(D) exp(4ßJ)/(exp(4ßJ)+5)
Options:
12820621875. A
12820621876. B
12820621877. C
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12820621878. D
Question Number: 3 Question Id: 1282065535 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
Consider an infinite wire bent into the shape of a hairpin i.e. a semicircle of radius 1 cm connecting two semi-infinite wires(as shown in the figure) and carrying a current of 1.5 A. What is the strength of the magnetic field at the centre of the semicircle in the unit of Tesla?
(A) 1.3 x 10-7
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(B) 2.9 x 10-5
(C) 7.7 x 10-5
(D) 4.6 x 106
Options:
12820621879. A
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12820621880. B
12820621881. C
12820621882. D
Question Number: 4 Question Id: 1282065536 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
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Atwood's machine shown here the pulley of negligible mass is suspended from a spring balance with a spring constant of 2000 N/m. Two bodies, of mass 1 kg and 3 kg, are hanging from the two ends of the massless and frictionless rope passing over the pulley. When the two masses starts moving under the effect of gravity how much will the spring stretch from its length in the absence of any force?
(A) 1.0 cm
(B) 0.5 cm
(C) 2.0 cm
(D) 1.5 cm
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Options:
12820621883. A
12820621884. B
12820621885. C
12820621886. D
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Question Number: 5 Question Id: 1282065537 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
What is the integral of the function f(z) = 1/ (z² -z) in the complex plane around the circle of radius 2 with the origin at its centre (The direction of integration is positive)?
(A) 0
(B) 2ip
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(C) -2ip
(D) 4p
Options:
12820621887. A
12820621888. B
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12820621889. C
12820621890. D
Question Number: 6 Question Id: 1282065538 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
Consider the differential equation d² y/dx² + 3 dy/dx + 2y = 0. If, at x=0, y= 0 and dy/dx = 1, what is the value of y at x = 1?
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(A) -1.4
(B) 0.56
(C) 0.23
(D) 0.37
Options:
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12820621891. A
12820621892. B
12820621893. C
12820621894. D
Question Number: 7 Question Id: 1282065539 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 5 Wrong Marks: 0
Two waves are superimposed to produce a resultant wave represented by y = a sin (?t-kx) + a sin (?'t-k'x) with k>k' and ?>?', where k and ? are wave vector and frequency respectively. What will be their phase velocity (v) and how it is related with group velocity (u) and phase velocity (v)
(A) (?+?')/(k-k') and u = v-k(dv/dk)
(B) (?+?')/(k+k') and u = v + k(dv/dk)
(C) (?-?')/(k+k') and u = v + k(du/dk)
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(D) (?-?')/(k-k') and u = v-k(du/dk)
Options:
12820621895. A
12820621896. B
12820621897. C
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12820621898. D
Question Number: 8 Question Id: 1282065540 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 5 Wrong Marks: 0
A particle of mass m starts from rest at xo (xo>0) in an attractive inverse cubic force field F = -k/x³ (k>0). How does the time taken depend on xo?
(A) x04
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(B) x02
(C) x0
(D) x03
Options:
12820621899. A
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12820621900. B
12820621901. C
12820621902. D
PART B
Section Id: 128206157
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Section Number: 2
Number of Questions: 20
Number of Questions to be attempted: 20
Section Marks: 60
Display Number Panel: Yes
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Group All Questions: No
Sub-Section Number: 1
Sub-Section Id: 128206259
Question Shuffling Allowed: Yes
Question Number: 9 Question Id: 1282065541 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 3 Wrong Marks: 0
The ground state energy of a neutral lithium atom is -203.2 eV. If the first ionization energy of lithium is 5.39 eV, what is its second ionization energy?
(A) 122.4 eV
(B) 75.4 eV
(C) 197.8 eV
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(D) 192.4 eV
Options:
12820621903. A
12820621904. B
12820621905. C
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12820621906. D
Question Number: 10 Question Id: 1282065542 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
Consider a 100 g block of a very good insulator. If Q1 and Q2 denote the amount of energy required to raise the temperature of this block from 2 K to 4 K, and from 4 K to 6 K, respectively, what is the ratio Q2/Q1?
(A) 4.3
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(B) 2.7
(C) 1.0
(D) 1.7
Options:
12820621907. A
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Question Number: 11 Question Id: 1282065543 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
At the bottom of the conduction band of a semiconductor, Corresponding to the wave-vector ko, the band structure is given by E(k)= A |k - kol 2 where A is a constant. If a magnetic field B is applied on a sample of this semiconductor what will be the cyclotron frequency ?c (m is mass of electron in free space)?
(A) peBA/2h2
(B) eB/m
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(C) eB/2m
(D) 8p2AEB/h2
Options:
12820621911. A
12820621912. B
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12820621913. C
12820621914. D
Question Number: 12 Question Id: 1282065544 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
A 10 V unregulated DC power source is used to make a 6 V regulated power supply using a 6 V Zener diode. The maximum current that can be passed through the diode is 100 mA. Then the value of the series resistance Rz and its wattage are:
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(A) 30 ohm and 0.3 W
(B) 50 ohm and 0.5 W
(C) 60 ohm and 0.6 W
(D) 40 ohm and 0.4 W
Options:
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12820621915. A
12820621916. B
Question Number: 13 Question Id: 1282065545 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
The potential energy of an isotropic harmonic oscillator in three dimensions is given by V(x,y,z) = (1/2)k(x² +y² +z²) where k is a positive constant. The degeneracy factor for the third excited energy level is:
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(A) 10
(B) 7
(C) 6
(D) 3
Options:
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12820621919. A
12820621920. B
12820621921. C
12820621922. D
Question Number: 14 Question Id: 1282065546 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 3 Wrong Marks: 0
The speed of a particle increases from 0.6c to 0.8c, where c is the speed of light in vacuum. In this process the kinetic energy increases by a factor of:
(A) 1.8
(B) 2.7
(C) 1.3
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(D) 3.6
Options:
12820621923. A
12820621924. B
12820621925. C
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12820621926. D
Question Number: 15 Question Id: 1282065547 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
A metal surface with a work function is illuminated by light of wavelength 500 nm. What is the absolute value of the negative potential (with respect to the electrode emitting the photoelectrons) that has to be applied to the anode so that there is no photocurrent?
(A) 1.9 V
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(B) 0.4 V
(C) 3.8 V
(D) 0.6V
Options:
12820621927. A
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12820621928. B
12820621929. C
12820621930. D
Question Number: 16 Question Id: 1282065548 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
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In a two body central force problem the initial position and velocity of one of the particles, of mass 1 kg, are given by (0,0,2) m and (1.6,1.6,0) m/s. For the other particle, of mass 2 kg, the initial position and velocity vectors are (2,0,0) m and (0,2,1) m/s. During the motion the relative position vector always lies in a plane. Which of the following vectors are perpendicular to this plane?
(A) (3,2,-2)
(B) (-2,2,3)
(C) (2,3,2)
(D) (-3,3,2)
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Options:
12820621931. A
12820621932. B
12820621933. C
12820621934. D
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Question Number: 17 Question Id: 1282065549 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
Positronium is a bound state of an electron and a positron. What is the energy required to excite it from the ground state to the first excited state?
(A) 5.1 eV
(B) 10.2 eV
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(C) 2.55 eV
(D) 20.4 eV
Options:
12820621935. A
12820621936. B
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12820621937. C
12820621938. D
Question Number: 18 Question Id: 1282065550 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
In a Penning trap a static potential difference is applied between two electrodes in an evacuated region to produce the potential field V(x,y,z) = c(a z² - x²- y²), where c and a are constants. What must be the value of a?
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(A) 1
(B) -1
(C) 0
(D) 2
Options:
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12820621939. A
12820621940. B
12820621941. C
12820621942. D
Question Number: 19 Question Id: 1282065551 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 3 Wrong Marks: 0
A system of three identical non-interacting bosons each particle can occupy one of three single-particle energy states of energy E, 2E and 3E. What is the number of energy eigenstates for the combined system of three particles?
(A)10
(B) 27
(C) 3
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(D) 1
Options:
12820621943. A
12820621944. B
12820621945. C
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12820621946. D
Question Number: 20 Question Id: 1282065552 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
A satellite of mass 60 kg is going around a planet in an elliptical orbit with an angular momentum of 5 x 1012 kg-m²/s. If the time taken to go once around the orbit is 2 hrs, the area of the orbit is:
(A) 2 x 109 km²
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(B) 5 x 108 km²
(C) 3 x 108 km²
(D) 9 × 107 km²
Options:
12820621947. A
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12820621948. B
12820621949. C
12820621950. D
Question Number: 21 Question Id: 1282065553 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
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A series LCR circuit has L = 300 mH, R= 2 ohm and C = 20 µF. It is driven by a voltage of the form V(t) = V0cos(?t). What is the value of ? at which the amplitude is maximum in the resonance curve of this circuit (in radians/s)?
(A) 1.2
(B) 4.0
(C) 2.3
(D) 6.7
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Options:
12820621951. A
12820621952. B
12820621953. C
12820621954. D
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Question Number: 22 Question Id: 1282065554 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
What is the total translational kinetic energy of all the air molecules in a room of dimensions 3m x 5m x 5m at standard temperature and pressure?
(A) 1.1 × 107 J
(B) 2.9 × 106 J
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(C) 6.5 × 103 J
(D) 3.4 × 105 J
Options:
12820621955. A
12820621956. B
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12820621957. C
12820621958. D
Question Number: 23 Question Id: 1282065555 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
What is the minimum kinetic energy of an electron moving in water so that it may emit Cerenkov radiation?
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(A) 0.68 Mev
(B) 0.38 MeV
(C) 0.51 MeV
(D) 0.26 MeV
Options:
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12820621959. A
12820621960. B
12820621961. C
12820621962. D
Question Number: 24 Question Id: 1282065556 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
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Correct Marks: 3 Wrong Marks: 0
For a n x n square matrix A for which A² equals the n x n identity matrix I, the value of exp(ipA) is:
(A)-I
(B) - A
(C) I+ iA
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(D) - I+iA
Options:
12820621963. A
12820621964. B
12820621965. C
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12820621966. D
Question Number: 25 Question Id: 1282065557 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
An ion is injected into a region of space with a uniform magnetic field of strength 104 Tesla with a speed of 107 m/s and at an angle of 60° with the direction of the magnetic field. The resulting motion is helical. How much does it move along the axis of this helix during each full rotation around the axis?
(A) 540 m
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(B) 3300 m
(C) 8200 m
(D) 15400 m
Options:
12820621967. A
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12820621968. B
12820621969. C
12820621970. D
Question Number: 26 Question Id: 1282065558 Question Type: MCQ Option Shuffling: No Display Question Number: Yes Single Line Question Option: No Option Orientation: Vertical
Correct Marks: 3 Wrong Marks: 0
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The normalized wave function of the electron in a hydrogen atom is given to be ?(r) = C ?1,0,0(r) + (3/5) ?2,1,-1(r) where C is a suitable constant of normalization and ?n,l,m(r) denotes a normalized energy eigen function of the electron in the hydrogen atom in the standard notation. What is the expectation value of the energy of the electron for this state in the unit of eV?
(A) -12.8
(B) -14.2
(C) -7.6
(D) -9.9
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Options:
128
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