JEST last years model paper

I am looking for JEST or Joint Entrance Screening Test is an entrance exam question paper, will you please provide here???

[Arun Vats]

JEST or Joint Entrance Screening Test is an entrance exam held by few Institutes annually for the Ph. D courses in theoretical Computer Science and Physics.

Questions:

Q1 measures the measurement lies from 99.8 to 100.2 cm. Estimate the net error, when takes
measurement 50 times?
(a) 0.2 cm (b) 0.4 cm (c) 0.82 cm (d) 10 cm.

Q 2. If coherent source of light through A,B has wavelength λ such AB = 4λ . If the detector
is moving along the loop of radius R such that R>> AB then if the radius is increased
gradually what effect will it have on the no. of maxima detected by detector D?
(a) increase (b) decrease (c) first increase than decrease (d) none

Q 3. Slit separation = d
Slit width = w
A plane wavefront incident, when will the 3rd maxima will be missing
(a) 3d = 2w (b) 2d = 3w (c) d = 2w
(b)

Q 4 If 2P −1 = Prime no.
(a) P is a odd no. (b) P can composite no. (c) P is necessarily composite no.
(d) P is Prime no.

Q 5. Find the velocity of box
(a) v cosθ (b) v sinθ (c) v tanθ
(b)

Q 1. If a person has a meter scale and he has to measure a length of 50 m. Each time he
measures the measurement lies from 99.8 to 100.2 cm. Estimate the net error, when takes
measurement 50 times?
(a) 0.2 cm (b) 0.4 cm (c) 0.82 cm (d) 10 cm.

Q 2. If coherent source of light through A,B has wavelength λ such AB = 4λ . If the detector
is moving along the loop of radius R such that R>> AB then if the radius is increased
gradually what effect will it have on the no. of maxima detected by detector D?
(a) increase (b) decrease (c) first increase than decrease (d) none

Q 3. Slit separation = d
Slit width = w
A plane wavefront incident, when will the 3rd maxima will be missing
(a) 3d = 2w (b) 2d = 3w (c) d = 2w

Q 4. Find
0
lim
z→
( 2 ) ( 2 )
2
Real z Img z
z
+
(a) i (b) 1 (c)-1 (d) limit do not exist

Q 5. If 2P −1 = Prime no.
(a) P is a odd no. (b) P can composite no. (c) P is necessarily composite no.
(d) P is Prime no.

Q 6. Find the velocity of box
(a) v cosθ (b) v sinθ (c) v tanθ

Q 7. What is the volume of a sphere in 4-dimensional space of unit radius?
(a)
2
16
π
(b) 4
3
π
(c) 4π i

Q 8. A heard ball dropped from a 1 m height and rebounces to 95 cm. Calculate the total
distance travelled by ball?
(a) 1880 cm (b) 2160 cm

Q 9. Evaluate 3
1
2 2 3
z
π i z z i
⎫⎬
+ − ⎭ 􀁶∫
(a) 0, (b) 2π i

Q 10. If EM waveE 􀁇
is filed component along y in with magnitude Eo, travelling along x-axis
with frequency w. represent this
Ans. cos ( ) o E = E Kx − wt yλ

Q 11. If an astronaut knows the maximum and min distance between the moon of a planet and
the planet maximum orbital velocity of moon is know which quantity of the following
can’t be calculated.
A
B
A, B are known
(a) mass of planet (b) mass of moon (c) Time of the orbit (d) semi major axis.

Q 12. If P and q are two distinct prime numbers then how many divisors p2q3 have?

Q 13. represent carnot cycle in T – S diagram

Q 14. If proton and α − particle accelerated by same potential v, find the ratio of debroglie
wavelength ?
(a) 2 2:1 (b) 2:1 (c) 1 : 2 (d) none of these

Q 15. The difference in arithmetic and geometric mean of two positive integer m and n is equal
to 1. Then
2
m and
2
n are
(a) perfect square
(b)

Q 16. Net capacitance
(a) C1 +C2 +C3 (b)
1 2 3
1 1 1
C C C
+ + (c) 2 3
1
2 3
C C C
C C
+
+

Q 17. Two events are taking place at a distance 5 km with a time interval 5μ s. In an inertial
frame. An observer observes two events as simultaneous. Determine the speed of
observer.

Q 18. Find the time taken for blue light λ = 400nm, to cover a distance of 80 km in optical
fiber having refractive .Index = 1.6
Ans. 427 μ sec.

Q 19. Find ( ) 5
1 1
1 2 ...
k
k l
l
= =
ΣΣ + +

Q 20. ( )
3
, 1 cos o
a r E r
r
φ θ θ
⎡ ⎛ ⎞ ⎤ = − ⎢ −⎜ ⎟ ⎥
⎢⎣ ⎝ ⎠ ⎥⎦
(Potential distribution of sphere of change q)
Find the change distribution
(a) 2 o E ∈cosθ (b) cos o ∈E θ

Q 21. A small mass m moving with velocity collides with turnable table get attached after
collision and moves with angular velocity w? find w?

Q 22. Find the solution of given differential equation.
x dy 3y x2
dx
− =
(a) y = x2 + cx2 (b) (c) (d)

Q 23. If x and y both are non-zero then the value of x2 + xy + y2
(a) always +ve (b) always –ve (c) 0 (d) sometimes +ve and sometime –ve

Q 24. ( )
2 3
x 2 3
V = kx + Lx (a potential fn for a particle in a box)
(a) V is oscillatory (b) v is never osicllater (c)

Q 25. Find eigen value and eigen vector
2 2
2 1
⎡ ⎤
⎢ ⎥
⎢⎣ ⎥⎦

Q 26. Then
(a) B Cl F E = E = E (b) B Cl F E = E ≤ E (c) F B Cl E > E > E (d) F B Cl E > E = E

Q 27. A curve moves from origin to a point P(1, 1) then ( 2 2 )
0
P ∫ y′ + yy′ + y dx will be stationary
for
(a) y = x (b) y = x2

Q 28. A proton accelerated by a potential difference of 1000 V and enter into magnetic field B
= 1000 T along a circular path of r = 20 cm. Determine the velocity of proton during
circular motion.
(a) 1 m/s (b) 105m/s (c) 100 m/s (d) none

Q 29. A mass m is attached to a spring with one end to a rigid support and to other end a spring
is connected which is attached to a mass m. having same spring constant calculate the
node frequency.

Q 30. A particle moving with velocity v hits the uniform circular disc at rest with impact
parameter (b < R) afterwards both particles and disc rotates with same angular velocity
ω . then ω in terms of v is,

Q 31. If donors are added to n-type semiconductor then
(i) Electrons increases holes remain constant
(ii) Electrons increases holes decreases
(iii) Electrons increases holes increases
(iv) No effect will takes place.

Q 32. A particle X of mass M at rest decays into a particle A of mass mA and another particle of
zero mass. Determine the energy of A.

Q 33. If B/A decreases with increases atomic number, then what does it indicate about nuclear
number, than what does it indicate about nuclear forces?
(a) charge dependent
(b) Charge independent

Q 34. The spin and parity of 12C and 17O?
(a) 0 , 5
2
+
+ (b) 0 , 5
2
−
+ (c) 1 , 7
2 2
+ +
(d) 0 , 3
2
+
−

Q 35. A charge q drops from rest from height d to infinite grounded conducting plates.
Calculate the time to reach the charge to plates.

1. Black-body radiation, at temperature Ti fills a volume V. The system expands adiabatically
and reversibly to a volume 8V. The final temperature Tf = xTi, where the factor x is equal to
(a) 0.5 (b) 2.8 (c) 0.25 (d) 1
2. A particle of mass m, constrained to move along the x-axis. The potential energy is given
by, V(x)=a + bx +cx2, where a, b and c are positive constants. If the particle is disturbed
slightly from its equilibrium position, then it follows that
(a) it performs simple harmonic motion with period 2 pÖ(m/2c)
(b) it performs simple harmonic motion with period 2 pÖ(ma/2b2)
(c) it moves with constant velocity
(d) it moves with constant acceleration
3. Consider a square ABCD, of side a, with charges +q, -q, +q, -q placed at the vertices, A, B,
C, D respectively in a clockwise manner. The electrostatic potential at some point located
at distances r (where r >> a) is proportional to
(a) a constant (b) 1/r (c) 1/r2 (d) 1/r3
4. The general solution of dy/dx – y = 2ex is (C is an arbitrary constant)
(a) e2x+Cex (b) 2xex+Cex (c) 2xex+C (d) ex2+C
5. As q®0, lim




 +
q
q
sin
) sin 1 ln(
is
(a) ¥ (b) -¥ (c) 1 (d) 0
6. If P^ is the momentum operator, and s^ are the three Pauli spin matrices, the eigenvalues
of (s^.P^) are
(a) px and pz (b) px ± ipy (c) ± |p| (d) ± (px + py +pz)
7. Two parallel infinitely long wires separated by a distance D carry steady currents I1 and I2
(I1 > I2) flowing in the same direction. A positive point charge moves between the wires
parallel to the currents with a speed v at a distance D/2 from either wire. The magnitude of
an electric field that must be turned on to maintain the trajectory of the particle is
proportional to
(a) (I1-I2)v/D (b) (I1+I2)v/D (c) (I1-I2)v2/D2 (d) (I1+I2)v2/D2
8. An ideal gas of non-relativistic fermions in three dimensions is at a temperature of 0 K.
When both the mass of the particles and the number density are doubled, the energy per
particle is multiplied by a factor,
(a) Ö2 (b) 1 (c) 21/3 (d) 1/21/3
9. The rotational part of the Hamiltonian of a diatomic molecule is (1/2 µ1)(Lx
2+Ly
2)
+ (1/2 µ2) Lz
2 where µ1 and µ2 are moments of inertia. If µ1 = 2µ2, the three
lowest energy levels (in units of h2/4 µ2) are given by
(a) 0, 2, 3 (b) 0, 1, 2 (c) 1, 2, 3 (d) 0, 2, 4
10. A particle of mass 1 gm starts from rest and moves under the action of a force of 30
Newtons defined in the rest frame. It will reach 99% the velocity of light in time
(a) 9.9 x 103 sec (b) 7 x 104 sec (c) 0.999 sec (d) 0.7 sec