3. IIT-JAM Full-Length-test 03_17-1-2016.pdf

fiziks Institute for CSIR‐UGC JRF/NET, GATE, IIT‐JAM, GRE in PHYSICAL SCIENCES

ALL INDIA TEST SERIES IIT - JAM - 2016 Full Length Test – 03

PHYSICS (PH) TIME: 3 HOURS

MAXIMUM MARKS. 100

Section A: This section contains a total of 30 Multiple Choice Questions (MCQ)

carrying one or two marks each. Each MCQ type question has four choices out of which only one choice is the correct answer. There will be negative marking @

1 rd 2 rd for one marks MCQ and negative marks 3 3

for two marks MCQ for each wrong answer. Section B: This section contains a total of 10 Multiple Select Questions (MSQ) carrying

two marks each. Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices. The candidate gets full credit if he/she selects all the correct answers only and no wrong answers. Section C: This section contains a total of 20 Numerical Answer Type (NAT) questions

carrying one or two marks each. For these NAT type questions, the answer is a signed real number which needs to be entered using the virtual keyboard on the monitor. No choices will be shown for these types of questions. Note: There will be no negative marking for Section B and Section C.

Head office: fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi‐16 Phone: 011‐26865455/+91‐9871145498 Website: http://www.physicsbyfiziks.com

Branch office: Anand Institute of of Mathematics, Mathematics, 28‐B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi‐16


SECTION A

Q1.

Q1 – Q10 (Multiple Choice Questions: One mark each) 1 rd There will be negative marks for each wrong answer 3 If E is energy and n is number density of the ideal gas, then pressure P is given by

1 (a) P = n E 3

Q2.

(b) P =

2 3

n E

(c) P = n E

(d) P =

3 2

n E

In the figure shown all the strings are mass less, and friction is absent everywhere. If g = 10 m / s 2 , then tension T1 , T 2 and T 3 are respectively:

(a) T1 = 10 N, T2 = 10 N, T3 = 10 N

Q3.

T 2

(b) T1 = 10 N , T2 = 20 N, T3 = 30 N

1 kg

(c) T1 = 10 N , T2 = 30 N , T3 = 20 N

T 3

(d) T1 = 10 N, T2 = 20 N, T3 = 10 N

2 kg

2 kg T 1 1 kg

The wave function of free particle is given by ψ ( x) = 4 eikx + 5 e− ikx then current density associated with wave function ψ ( x) is (a) −

Q4.

 k

m

(b)

k

m

(c) −

9k m

(d)

9k m

An electron is accelerated though a potential difference V . If de Broglie wavelength is given by λ =

α V

for nonrelativistic speeds. If λ and V represent numerical values in

angstrom and volt, then the value of α is (a) 1.25

(b) 12.25

(c) 2.50

(d) 22.25

n

Q5.

⎛ 1+ i ⎞ The smallest value of integer n for which ⎜ ⎟ = 1 is i 1 − ⎝ ⎠ (a) 2

(b) 3


(c) 4

(d) 8

Branch office: Anand Institute of Mathematics, 28‐B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi‐16


Q6.

An object is 30 cm from a spherical mirror, along the central axis. The absolute value of lateral magnification is

1 2

. The image produced is inverted. The focal length of the

mirror is (a) −10 cm

(b) +10 cm

(c) −15 cm

(d) +30 cm



Q7.

In a crystallography notation the vector y

(a) [ 2 21] (b) [ 212]

o

(d) ⎡⎣ 212 ⎤⎦

x

z

The particular integral of the differential equation ( D 2 − 4 D + 4) y = x 3 e 2 x is: (a)

Q9.

a

P a / 2

(c) ⎡⎣ 212 ⎤⎦

Q8.

P in the unit cell shown in the figure is

1 20

4

x e

2 x

(b)

1 20

5

2 x

x e

(c)

1 10

4

2 x

x e

(d)

1 10

5

x e

2 x

The magnetic field at a distance R from a long straight wire carrying a steady current I is proportional to (b) I / R 2

(a) IR

Q10.

(c) I 2 / R 2

(d) I / R

The group velocity of electromagnetic waves moving with phase velocity c in a dispersive medium of refractive index μ is given by (a)

(c)

c

⎛ d ω ⎞ ω μ + ⎜ ⎟ d μ ⎠ ⎝ c d μ ⎞ ⎛ ⎜ μ + ω ⎟ d ω ⎠ ⎝

(b)

(d)


c d μ ⎞ ⎛ ⎜ ω + μ ⎟ d ω ⎠ ⎝ c

⎛ d ω ⎞ + μ ω ⎜ ⎟ d μ ⎠ ⎝ Branch office: Anand Institute of Mathematics, 28‐B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi‐16

fiziks Institute for CSIR‐UGC JRF/NET, GATE, IIT‐JAM, GRE in PHYSICAL SCIENCES Q11 – Q30 (Multiple Choice Questions: Two marks each)

2 rd negative marks for each wrong answer 3

There will be

Q11.

The Van der Waal gas P =

RT V −b

−

a V 2

undergoes adiabatic change then value of (a)

Q12.

RT CV (V − b )

(b)

RT CV (b − V )

with specific heat at constant volume C V dT dV

for large volume V is given by

(c)

CV (V − b) RT

(d)

CV (b − V ) RT

For two phase system in equilibrium, P is a function of temperature T . If β s is adiabatic Compressibility then value of specific heat at constant volume C V is given by 2

TV ⎛ dP ⎞ (b) C V = ⎜ ⎟ β s ⎝ dT ⎠

2

TV ⎛ dT ⎞ (d) C V = ⎜ ⎟ β s ⎝ dP ⎠

⎛ dP ⎞ (a) CV = TV β s ⎜ ⎟ ⎝ dT ⎠ ⎛ dT ⎞ (c) CV = TV β s ⎜ ⎟ ⎝ dP ⎠

Q13.

2

A planet of mass m moves in a circular orbit of radius r 0 in the gravitational potential V (r ) = −

k r

(a) 2r 0 km

Q14.

2

, where k is a positive constant. The orbital angular momentum of the planet is (b) 2 r 0 km

A thin uniform circular disc of mass

(c) r 0 km

(d)

r0km

and radius R is rotating in a horizontal plane

about an axis passing through its centre and perpendicular to its plane with an angular velocity

. Another disc of the same dimensions but of mass M / 4 is placed gently on

the first disc coaxially. The angular velocity of the system now is (a) ω / 5

(b) 2ω / 5


(c)

2ω 5

(d)

4ω 5


fiziks Institute for CSIR‐UGC JRF/NET, GATE, IIT‐JAM, GRE in PHYSICAL SCIENCES 

Q15.



There are two stationary fields of force F1 = ayiˆ and F2 = axiˆ + byjˆ , where i and j are the unit vectors of the

and y axes, and a and b are constants.



(a) F 1 is conservative field 

(b) F 2 is conservative field 



(c) Both F 1 and F 2 is conservative field 



(d) Neither F 1 or F 2 is conservative field Q16.

A particle with rest mass 3

is at rest and decays into two particles of equal rest masses

which move along the z axis. Their velocities are given by

10 





ˆ (a) v1 = v 2 = (0.8c ) z 





ˆ (c) v1 = −v 2 = (0.6c ) z

Q17.



ˆ (b) v1 = −v2 = (0.8c ) z 

ˆ; v 2 = (− 0.8c) z ˆ (d) v1 = (0.6c ) z

⎛ 1 1 1⎞ ⎜ ⎟ A = ⎜ 1 1 1⎟ , then which of the following is NOT correct? ⎜ 1 1 1⎟ ⎝ ⎠ (a) The sum of Eigen values are 3 (b) The product of Eigen value is zero (c) All Eigen values are non degenerate. (d) The Eigen values of the given matrices are real.

Q18.

u = x2 − y 2 , v = 2 xy, x = r cos θ , y = r sin θ , then

(a) r 2 Q19.

(b) 4r 2

∂ (u, v) ∂ (r ,θ )

(c) r 3

(d) 4r 3

A half wave plate is introduced between two cross polaroid P1 & P 2 . The optic axis makes an angle of 300 with the pass axis of P 1 . If unpolarized light of intensity I 0 is normally incident on P 1 , then the intensity of light after polaroid P 2 is (a)

I 0

8

(b)

I 0

4


(c)

I 0

2

(d)

3 I 0 8



Q20.

If the quality factor of an underdamped harmonic oscillator of frequency 512 Hz be 8 ×104 . The number of oscillation does the oscillator make in time in which its energy reduced to

1 of its energy in the absence of damping is e

(a) 12840 Q21.

(b) 12740

(c) 12640

(d) 12540

Consider the digital circuit shown below in which the input C is always low (0).

A B

Z

C (Low) The truth table for the circuit can be written as A

B

0

0

0

1

1

0

1

1

Z

The entries in the Z column (vertically) are (a) 1010

Q22.

(b) 0101

(c) 1111

(d) 1011

Atoms are arranged in a three dimensional simple hexagonal structure. If atomic radius is r , then packing fraction of this structure is (a)

π

3 2

(b)

π

3 3


(c)

3π 16

(d)

2π 3 3



Q23.

A periodic function f ( t ) = {1 − t 2 , t ∈ [ −1,1]

is defined as an expansion in a series of sines and cosines as f ( t ) =

a0

2

∞

∞

k =1

k =1

+ ∑ ak cos ( kω t ) + ∑ bk sin ( kω t )

The coefficient ak is

Q24.

4

4 k π 2

(b) ( −1)

k

(c) 0

(d) ( −1)

k +1

(a)

3

Which

one

equation K 1

of dx dt

the

following

curves

gives

2

4 2

k π 2

the

solution

of

the

differential

+ K 2 x = K 3 , where K 1 , K 2 and K 3 are positive constants with initial

conditions x = 0 at t = ∞ ?

(a )

(b )

↑

↑ t

t x ( d )

(c )

↑ t


t



Q25.

The equation of a surface of revolution is

z

3 2 3 2 x + y . The unit normal to the 2 2

=±

2

⎛ 2 ⎞ ,0,2 ⎟ is ⎜ 3 ⎟ ⎝ ⎠

surface at the point A ⎜

Q26.

(a)

3ˆ 2 ˆ i+ k 5 10

(b)

3ˆ 2 ˆ i− k 5 10

(c)

3ˆ 4 ˆ i− k 5 10

(d)

3ˆ 2 ˆ i+ k 10 10

In deep inelastic scattering electrons are scattered off protons to determine if a proton has any internal structure. The energy of the electron for this must be at least of the order of (a) 106 eV

Q27.

(b) 108 eV

(c) 109 eV

(d) 1012 eV

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 ) = 4e 2 x + f ( x) − 3 y 2 . Given that the x-component of the electric field E x, and V are zero at the origin, f(x) is

Q28.

(a) 3 x 2 − 4e 2 x + 8 x

(b) 3 x 2 − 4e 2 x + 16 x

(c) 4e 2 x − 8

(d) 3 x 2 − 4e 2 x

The vector potential

due to a magnetic moment m at a point r is given by A =

m × r r 3

.

If m is directed along the positive z-axis, the x-component of the magnetic field, at the point r , is (a) Q29.

3myz r 5

(b) −

3mxy r 5

(c)

3mxz r 5

(d)

3m( z 2 − xy ) r 5

Consider the interference of two coherent electromagnetic waves whose electric field 



vectors are given by E 1 = iˆ E 0 cos ω t and E 2 = jˆ E 0 cos(ω t + ϕ ) where difference. The intensity of the resulting wave is given by

ε 0

2

is the phase 2

E 2 , where E is the

time average of E 2. The total intensity is (a) 0

(b) ε 0 E 02


(c) ε 0 E 02 sin 2 ϕ

(d) ε 0 E 02 cos 2 ϕ Branch office: Anand Institute of Mathematics, 28‐B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi‐16


Q30.

Consider the Op-Amp circuit shown in figure. If Vi = V1 sin (ω t ) and Vo = V2 sin (ω t + φ ) , then the minimum and maximum values of φ (in radians) are respectively R1 π π (a) − and + 2 2 R1 − V i (b) 0 and + π 2 R + (c) −π and 0 C π (d) − and 0 2

V o

Q31 – Q40 (Multiple Select Type Questions: Two marks each) No negative marking:

Q31.

m gram water at 00 C is mixed with an equal amount of water at 80 0 C , then which of the following statements are correct? (a) The final temperature at equilibrium is 313 K (b) Increase in entropy when temperature of m gram of cold water rises from 273 K to 313 K is 0.1367 m cal g −1 K −1

(c) Decrease in entropy when temperature of m gram of hot water drops from from 353 K to 313 K is 0.1367 m cal g −1 K −1 (d) Total change in entropy is equal to zero. Q32.

A sphere of mass

=

and radius r shown in figure below slips on

a rough horizontal plane. At some instant it has translational velocity v0 and rotational velocity about the centre

v0

2r

. Then

r

v0

2r v0

A

which of the following statements are correct? (a) Angular momentum of the system about center of the sphere is conserved. 1 rv0 (b) Initial Angular momentum of the system about point is 5 6 (c) Initial Angular momentum of the system is rv0 5 6 (d) The velocity when sphere is just starting pure rolling is v0 7 Head office: fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi‐16 Phone: 011‐26865455/+91‐9871145498 Website: http://www.physicsbyfiziks.com



Q33.

Which of the following statements are INCORRECT? (a) Electrons are fermions and photons are bosons and both are distinguishable particle. (b) In any particular quantum state only one indistinguishable particle can be adjusted. (c) The Fermi Dirac distribution at equilibrium temperature T is f ( E ) =

(d)

The

f ( E ) =

Q34.

Bose

Einstein

distribution

at

equilibrium

1 ⎛ E − μ ⎞ exp ⎜ ⎟ +1 kT ⎝ ⎠

temperature

T

is

1 ⎛ E − μ ⎞ exp ⎜ ⎟ −1 ⎝ kT ⎠

Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is 0.73 eV . The workfunction for sodium is 1.82 eV , then which of the following statements are correct? (a) The energy of the photons causing the photoelectric emission E = 2.55 eV (b) The quantum numbers of the two levels involved in the emission of these photons are 4 to 2 (c) The change in the angular momentum of the electron in the hydrogen atom in the above transition is Δ L =

h

2π

(d) The recoil speed of the emitting atom assuming it to be at rest before the transition is v = 0.814 m / s

(Ionization potential of hydrogen is 13.6 eV ) Q35.

2

If f ( x ) = e − x and g ( x ) = x e − x , then which of the following statements are correct? 2

(a) f and g are continuous (b) f is differentiable everywhere but g is not (c) g is differentiable everywhere but f is not (d) f and g are differentiable Head office: fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi‐16 Phone: 011‐26865455/+91‐9871145498 Website: http://www.physicsbyfiziks.com



Q36.

A grating with 15000 lines per inch is illuminated by sodium light having D1 and D2 0

0

lines of wavelength 5890A and 5896A . The grating spectrum is observed on the focal plane of a convex lens of focal length 10 cm . Choose the correct statements for 2 inch wide grating with slit width of 0.0001 cm . (a) Grating is unable to resolve first order peak (b) Grating can resolve 2 nd order peaks (c) To resolve 1 st order peak minimum grating width required is 2.5 inch (d) Can resolve 3 rd order peaks Q37.

A plastic sphere floats in water with 50 percent of its volume submerged. This same sphere floats in glycerin with 40 percent of its volume submerged. Which of the following statements are correct for the density of glycerin ( ρ gl ) and density of sphere

( ρ ) ? sp

Q38.

(a) ρ gl = 1250 kg / m3

(b) ρ gl = 500 kg / m3

(c) ρ sp = 250 kg / m3

(d) ρ sp = 500 kg / m3

For the circuit shown in figure, which of the following statements are correct? R 6.7 Ω

(a) The resonant frequency is 500 kHz (b) The resonant frequency is 400 kHz

VT =100V

C

500 pF

L 203 μ H

(c) Impedance at resonance is 61 k Ω (d) Total r.m.s current at resonance is1.65 mA Q39.

At a surface current, which one of the magnetostatic boundary conditions are correct? (a) Normal component of the magnetic field is continuous. (b) Normal component of the magnetic vector potential is continuous. (c) Tangential component of the magnetic vector potential is continuous. (d) Tangential component of the magnetic vector potential is not continuous.




Q40.

Consider the circuits shown in figures (a) and (b) below

2 K 100 K

1 K 10 K

10V

10.7 V

4V

5V

(a) (b) If the transistors in figures (a) and (b) have current gain ( β dc ) of 40 and 10 respectively. Then which of the following statements are true? (a) Circuit (a) in active region (b) Circuit (a) in saturation region (c) Circuit (b) in active region (d) Circuit (b) in saturation region

Q41–Q50 (Numerical Answer Type Questions: One mark each) No negative marking:

Q41. The front tyre of Car have pressure 2 atm at 300 0 K . If tyre suddenly brusts and γ = 1.40 , then final temperature is ……… 0 K Q42.

Two radioactive materials X 1 and X 2 have decay constants 10λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 to that of X 2 will be 1 / e after a time

1 . Then the value of α is ……… αλ

Q43. An amplifier has a voltage gain of 500 and input impedance 20 k Ω , without any feedback. Now a negative feedback with β = 0.1 is applied. Its input impedance with feedback will be .............k Ω Q44.

The Jupiter’s period of revolution around the Sun is 12 times that of the Earth. Assuming the planetary orbits to be circular, then the ratio of distance between Jupiter and Sun and that between Earth and Sun is ……….




Q45.

The energy dependence of the density of states for a two dimensional non-relativistic electron gas is given by, g ( E ) = CE n , where C is constant. The value of n is………….

Q46.

The ratio of mobility ( μ ) and diffusion coefficient ( D ) for electrons in a semiconductor at temperature T = 1270 C is ……….. Volts

Q47.

In the Expansion of Maclaurin’s series expand of tan x the coefficient of x 3 is given by ………

Q48.

A simple pendulum of length 2.0 m is oscillating in an elevator accelerating upward at a rate of 2 m / sec 2 . The frequency of pendulum is …………. Hz 0

Q49.

The lattice constant of Cu ( FCC ) is 2.5A . Then the volume of its primitive cell 0 ⎛ ⎞ is…………. ⎜ A ⎟ ⎝ ⎠

Q50.

3

The RC series circuit is shown in figure below. The capacitor is initially uncharged. At time t = 0 , the switch S is closed. The voltage across resistor 1sec after the circuit is closed is…………volts

S

R = 2 k Ω

t = 0

110 V


C = 1000 μ F


fiziks Institute for CSIR‐UGC JRF/NET, GATE, IIT‐JAM, GRE in PHYSICAL SCIENCES Q51–Q60 (Numerical Answer Type Questions: Two marks each) No negative marking:

Q51.

The two particles of mass m and 2m undergoes uniform circular motion about each other at a separation R under the influence of their mutual attraction F . The angular velocity is ω radian per second. If R = α

Q52.

F ω 2 m

, then value of α is given by ……………..

If potential in one dimension is given by V ( x) =

x 2

2

−

x4

4

then stable equilibrium point is

at x = ………………. Q53.

In a Young double slit experiment with D = 50 cm and d = 0.1 cm , mica sheets of thickness 6 cm and 7 cm is introduced after 1 st and 2nd slit. The refractive index of mica sheet is 1.58 . Due to introduction of mica sheet, the central fringe get shifted by ……….

Q54.

A horizontal pipe 10 cm in diameter has a smooth reduction to a pipe 5 cm in diameter. If the pressure of the water in the larger pipe is 8 ×104 P a and the pressure in the smaller pipe is 6 ×104 P a , the rate at which water flow through the pipes is ………….. kg /sec .

Q55.

The entropy of a gas containing N particles enclosed in a volume V is given by

⎛ aVE 3 / 2 ⎞ ⎟ , where E is the total energy, a is a constant and k B is the S = Nk B ln⎜⎜ 5/ 2 ⎟ N ⎝ ⎠ Boltzmann constant. The chemical potential μ of the system at a temperature T is given 3 ⎡ ⎛ aVE 2 by −k BT ⎢ln ⎜ 5 ⎢ ⎜ ⎜ ⎢⎣ ⎝ N 2

Q56.

⎤ ⎞ ⎟ − α ⎥ where value of α is given by ………… ⎥ ⎟ ⎟ ⎥⎦ ⎠

Consider a system of eight non-interacting, identical quantum particles of spin

3 2

in a one

dimensional box of length L . The minimum excitation energy of the system is α

π 2  2

2mL2

.

Then the value of α is…………..




Q57.

Liquid 4 He has a normal boiling point of 4.2 K . However, at a pressure of 1 mm of Hg , it boils at 1.2 K . The average latent heat of vaporization of 4 He in this temperature range is …………… J mol −1 . Take R = 8.314 J mol −1 K −1 .

Q58.

A plane electromagnetic wave of intensity 9 W / m2 is incident normally on the surface of a material is partially reflected. Measurements on the standing wave in the region in front of the interface show that the ratio of the electric field amplitude at the maxima and the minima is 5. Then the intensity of the reflected wave is .............W / m 2

Q59.

For the given zener diode network, the maximum value of load resistance R L that will maintain output voltage to 15 V is………… Ω ( V Z = 15 V , I ZM = 32mA ) I

+ 1k Ω

I Z

V i = 50 V

I L

R L

− Q60.

A unit vector nˆ on the y -plane is at an angle of 120 o with respect to iˆ . If b = a / 2 then 



angle between the vectors u = a iˆ + b nˆ and v = anˆ + b iˆ will be...........degree .

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3. IIT-JAM Full-Length-test 03_17-1-2016.pdf

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