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#1 Super Moderator Join Date: Jun 2011 Can you please give me the Joint Entrance Screening Test PhD entrance exam modal question papers as it is very urgent for me?

As you want to get the Joint Entrance Screening Test PhD entrance exam modal question papers so here is the information of the same for you:

Some content of the file has been given here:

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.

For more detailed information I am uploading PDF files which are free to download:
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Last edited by Aakashd; May 31st, 2019 at 01:18 PM.

#2
 Unregistered Guest Re: Joint Entrance Screening Test PhD entrance exam modal question papers

Hello sir I am Srishti and I am preparing for Joint Entrance Screening Test PhD entrance exam so can you please provide me the modal question papers of this paper subject??
#3
 Super Moderator Join Date: Jun 2013 Re: Joint Entrance Screening Test PhD entrance exam modal question papers

Joint Entrance Screening Test is conducted on a joint basis by many institutes for admission in to the PhD courses.
The discipline in which PhD is offered is mainly Physics and theoretical Computer Science.

And therefore I am providing you here both the subjects papers of this exam that are:

Physics
Theoretical Computer Science

JEST Physics Paper

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

JEST Theoretical Computer Paper

1. Select the correct alternative in each of the following:
(a) Let a and b be positive integers such that a > b and a2 - b2 is a prime number.
Then a2 - b2 is equal to
(A) a - b (B) a + b (C) a × b (D) none of the above
(b) When is the following statement true? (A [ B) \ C = A \ C
(A) If ¯ A \ B \ C = _ (B) If A \ B \ C = _ (C) always (D) never
(c) If a fair die (with 6 faces) is cast twice, what is the probability that the two
numbers obtained di_er by 2?
(A) 1/12 (B) 1/6 (C) 2/9 (D) 1/2
(d) T(n) = T(n/2) + 2; T(1) = 1. When n is a power of 2, the correct expression for T(n)
is:
(A) 2(log n + 1) (B) 2 log n (C) log n + 1 (D) 2 log n + 1

2. Consider the following function, defined by a recursive program:
function AP(x,y: integer) returns integer;
if x = 0 then return y+1
else if y = 0 then return AP(x-1,1)
else return AP(x-1, AP(x,y-1))
(a) Show that on all nonnegative arguments x and y, the function AP terminates.
(b) Show that for any x, AP(x, y) > y.

3. How many subsets of even cardinality does an n-element set have ? Justify answer.

4. A tournament is a directed graph in which there is exactly one directed edge between
every pair of vertices. Let Tn be a tournament on n vertices.
(a) Use induction to prove the following statement:
Tn has a directed hamiltonian path (a directed path that visits all vertices).
(b) Describe an algorithm that finds a directed hamiltonian path in a given tournament.
Do not write whole programs; pseudocode, or a simple description of the
steps in the algorithm, will suffice. What is the worst case time complexity of
your algorithm?

5. Describe two different data structures to represent a graph. For each such
representation, specify a simple property about the graph that can be more
efficiently checked in that representation than in the other representation. Indicate
the worst case time required for verifying both of your properties in either
representation.

6. Two gamblers have an argument. The first one claims that if a fair coin is tossed
repeatedly, getting two consecutive heads is very unlikely. The second, naturally,
is denying this. They decide to settle this by an actual trial; if, within n coin
tosses, no two consecutive heads turn up, the first gambler wins.
(a) What value of n should the second gambler insist on to have more than a 50%
chance of winning?
(b) In general, let P(n) denote the probability that two consecutive heads show up
within n trials. Write a recurrence relation for P(n).
(c) Implicit in the second gambler’s stand is the claim that for all sufficiently large n,
there is a good chance of getting two consecutive heads in n trials; i.e. P(n) > 1/2.
In the first part of this question, one such n has been demonstrated. What
happens for larger values of n? Is it true that P(n) only increases with n? Justify
your answer.

7. Consider the following program:
function mu(a,b:integer) returns integer;
var i,y: integer;
begin
---------P----------
i = 0; y = 0;
while (i < a) do
begin --------Q------------
y := y + b ;
i = i + 1
end
return y
end
Write a condition P such that the program terminates, and a condition Q which is
true whenever program execution reaches the place marked Q above.
__________________
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#4
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