STAGE-1- TEST- PAPERS-4 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
Time : 2.00 Hr Max. Marks : 184
GENERAL INSTRUCTIONS
1. There are 40 questions in this paper.
2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero Mark
if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
3. For each question in Section II, you will be awarded 5 Marks if you give all correct answers and zero Mark
if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
4. For each question in Section III, you will be awarded 6 Marks if you give the correct answer and zero Mark
will be awarded in all other cases.
5. For each question in Section IV, you will be awarded 5 Marks if you give the correct answer and zero Mark
if no answer is given. In all other cases, minus two (–2) Marks will be awarded.
6. For each question in Section V, you will be awarded 6 Marks if you give all correct answers. No negative Mark will be awarded for an incorrectly answered question.
SECTION - I
Single Correct Choice Type
This section contains 12 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A solid sphere of radius R has moment of inertia about its geometrical axis. If it is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to , then the value of r is equal to :
(A) R (B) R
(C) R (D) R
2. System shown in figure is in equilibrium and at rest. The spring and string are massless Now the string is cut. The acceleration of mass 2m and m just after the string is cut will be :
(A) g/2 upwards , g downwards (B) g upwards, g/ 2 downwards
(C) g upwards , 2g downwards (D) 2g upwards , g downwards
3. A massless rod BD is suspended by two identical massless strings AB and CD of equal lengths. A block of mass ‘m’ is suspended at point P such that BP is equal to ‘x’, if the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of x is :
(A) l/5 (B) l/4
(C) 4l/5 (D) 3l/4
4. A point object is placed at distance of 20 cm from a thin plano-con- vex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at :
(A) 60 cm to the left of the system. (B) 60 cm to the right of the system.
(C) 12 cm to the left of the system. (D) 12 cm to the right of the system.
5. Half life of a radioactive substance 'A' is 4 days. The probability that a nucleus will decay in two half lives is:
(A)
1 (B) 3
4 4
(C)
1 (D) 1
2
6. The graph between object distance u and image distance v for a lens is given below. The focal length of the lens is :
(A) 5 ± 0.1 (B) 5 ± 0.05
(C) 0.5 ± 0.1 (D) 0.5 ± 0.05
7. Two bars of radius '2r' and 'r' are kept in contact as shown. An electric current is passed through the bars. Which one of the following is correct?
(A) Heat produced in bar (2) is 4 times the heat produced in bar (1)
(B) Electric field in both halves is equal
(C) Current density across AB is double that of across BC.
(D) Potential difference across AB is 4 times that of across BC.
42𝑙
8. A student performs an experiment for determination of g 2 , l 1m, and he commits an error of l.
For T he takes the time of n oscillations with the stop watch of least count T and he commits a human error of 0.1sec. For which of the following data, the measurement of g will be most accurate ?
(A) L = 0.5, T = 0.1, n = 20 (B) L = 0.5, T = 0.1, n = 50
(C) L = 0.5, T = 0.01, n = 20 (D) L = 0.1, T = 0.05, n = 50
9. A double star system consists of two stars A and B which have time period TA and TB. Radius RA and RB and mass MA and MB. Choose the correct option.
(A) If TA > TB then RA > RB (B) If TA > TB then MA > MB
T 2 R 3
(C) A
TB
A
RB
(D) TA
= TB
10. Find the time constant for the given RC circuits in correct order :
R = 1 , R = 2 , C = 4 F, C = 2 F
(A) 18,4, 8/9 (B) 18, 8/9, 4
(C) 4,18, 8/9 (D) 4,8/9, 18
11. A biconvex lens of focal length f forms a circular image of radius r of the sun in focal plane. Then which option is correct :
(A) r2 f
(B) r2 f2
(C) If lower half part is covered by black sheet, then area of the image is equal to r2/2
(D) if f is doubled, intensity will increase
12. The number of circular divisions on the shown screw gauge is 50. It moves 0.5 mm on main scale for one complete rotation. Main scale reading is 2. The diameter of the ball is :
(A) 2.25 mm (B) 2.20 mm
(C) 1.20 mm (D) 1.25 mm
SECTION - II
Multiple Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
13. The graph between 1/ and stopping potential (V) of three metals having work functions , and in an experiment of photoelectric effect is plotted
1 2 3
as shown in the figure. Which of the following statement(s) is/are correct ? [Here is the wavelength of the incident ray].
(A) Ratio of work functions : : = 1 : 2 : 4.
(B) Ratio of work functions
: :
= 4 : 2 : 1.
(C) tan is directly proportional to hc/e, where h is Planck’s constant and c is the speed of light.
(D) The violet colour light can eject photoelectrons from metals 2 and 3.
14. A field line is shown in the figure. This field cannot represent
(A) Magnetic field (B) Electrostatic field
(C) Induced electric field (D) Gravitational field of a mass at rest
15. A solid sphere is in pure rolling motion on an inclined surface having inclination .
(A) frictional force acting on sphere is f = mg cos .
(B) f is dissipative force.
(C) friction will increase its angular velocity and decreases its linear velocity.
(D) If decreases, friction will decrease.
16. In a dark room with ambient temperature T0, a black body is kept at a temperature T. Keeping the tempera- ture of the black body constant (at T), sun rays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct ?
(A) The quantity of radiation absorbed by the black body in unit time will increase.
(B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in an unit time will increase.
(C) Black body radiates more energy in unit time in the visible spectrum.
(D) The reflected energy in unit time by the black body remains same.
17. For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that :
q
V = 40R0
for r R0 and V =
q 40r
for r R .
Then which option(s) are correct :
(A) Total charge within 2R0 is q. (B) Total electrostatic energy for r R0 is zero.
(C) At r = R0 electric field is discontinuous. (D) There will be no charge anywhere except at r = R0
18. Which of the following statement is correct in the given figure.
(A) net force on the loop is zero
(B) net torque on the loop is zero
(C) loop will rotate clockwise about axis OO’ when seen from O
(D) loop will rotate anticlockwise about OO’ when seen from O
19. Function x = Asin2t + B cos2t + C sint cost represents SHM
(A) for any value of A,B and C (except C = 0) (B) If A = – B,C = 2B, amplitude = B
(C) If A = B ; C = 0 (D) If A = B ; C = 2B, amplitude = |B|
20. A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and KA, KB and KC are kinetic energies of the ball at A,B and C respec
tively, then :
(A) hA > hC ; KB > KC (B) hA > hC ; KC > KA
(C) hA = hC ; KB = KC (D) hA < hC ; KB > KC
SECTION - III
Subjective Type
This section contains 4 subjective problems. Circle their correct answers.
21. A plate of mass M of dimensions (a × b) is hinged along one edge. The plate is maintained in horizontal position by colliding a ball of mass m, per unit area, elastically 100 times per second this ball is striking on the right half shaded region of the plate as shown in figure. Find the required speed of the ball (ball is colliding in only half part of the plate as shown). (It is given M = 3 kg, m = 0.01
kg, b = 2 m, a = 1 m, g = 10 m/s2)
22. A circular disc is kept on a smooth horizontal plane with its plane parallel to horizontal plane. A groove is made in the disc along the diameter as shown in the figure. The coefficient of friction between block of mass m placed inside the groove and the surface of the groove is 2/5 and sin37º = 3/5. The linear accel- eration of the disc is 25 m/s2 towards left. The acceleration of block with respect to the frame of reference of the disc is :
23. In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Find the final temperature of the mixture (in kelvin).
Given, Lfusion = 80 cal/g = 336 J/g, Lvaporization = 540 cal/g = 2268 J/g, Sice = 2100 J/kg K = 0.5 cal/gK and Swater = 4200 J/kg K = 1 cal/gK
24. f the wavelength of the nth line of Lyman series is equal to the de-Broglie wavelength of electron in initial orbit of a hydrogen like element (z = 11). Find the value of n.
SECTION - IV
Paragraph Type
This section contains 4 Paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for Question Nos. 25 to 27
Two plane harmonic sound waves are expressed by the equations. y (x, t) = A cos (0.5 x – 100 t)
y (x, t) = A cos (0.46 x – 92 t) (All parameters are in MKS) :
25. How many times does an observer hear maximum intensity in one second ? (A) 4 (B) 10
(C) 6 (D) 8
26. What is the speed of the sound ?
(A) 200 m/s (B) 180 m/s
(C) 192 m/s (D) 96 m/s
27. At x = 0 how many times the amplitude of y1 + y2 is zero in one second at x = 0 ? (A) 192 (B) 48
(C) 100 (D) 96
Paragraph for Question Nos. 28 to 30
A wooden cylinder of diameter 4r, height H and density /3 is kept on a hole of diameter 2r of a tank, filled with liquid of density as shown in the figure.
28. If level of the liquid starts decreasing slowly when the level of liquid is at a height h1 above the cylinder the block starts moving up. At what value of h1, will the block rise :
4H
(A) 9
5H
(B) 9
5H
(C) 3
(D) Remains same
29. The block in the above question is maintained at the position by external means and the level of liquid is lowered. The height h2 when this external force reduces to zero is -
4H
(A) 9
5H
(B) 9
2H
(C) Remains same (D) 3
30. If height h2 of water level is further decreased, then
(A) cylinder will not move up and remains at its original position
(B) for h2 = H/3, cylinder again starts moving up
(C) for h2 = H/4, cylinder again starts moving up
(D) for h2 = H/5 cylinder again starts moving up
Paragraph for Question Nos. 31 to 33
Modern trains are based on Maglev technology in which trains are magnetically elevated, which runs its EDS Maglev system.
There are coils on both sides of wheels. Due to motion of train current induces in the coil of track which elevate it. This is in accordance with Lenz’s law. If trains lower down then due to Lenz’s law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force due to gravity.
The advantage of maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.
Disadvantage of maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it elevated and as it moves forward according to Lenz law there is an electromagnetic drag force.
31. What is the advantage of this system ?
(A) No friction hence no power consumption (B) No electric power is used
(C) Gravitation force is zero (D) Electrostatic force draws the train
32. What is the disadvantage of this system ?
(A) Train experiences upward force according to Lenz’s law
(B) Friction force create a drag on the train
(C) Retardation
(D) By Lenz’s law train experience a drag
33. Which force causes the train to elevate up ?
(A) Electrostatic force (B) Time varying electric field
(C) Magnetic force (D) Induced electric field
Paragraph for Question Nos. 34 to 36 The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch S1 while keeping switch S2 open. The capacitor can be connected in series with an inductor ‘L’ by closing switch S2 and opening S1.
34. Initially, the capacitor was uncharged. Now, switch S1 is closed and S2 is kept open. If time constant of this circuit is , then
(A) after time interval , charge on the capacitor is CV/2
(B) after time interval 2, charge on the capacitor is CV(1 – e–2)
(C) the work done by the voltage source will be half of the heat dissipated when the capacitor is fully charged
(D) after time interval 2, charge on the capacitor is CV(1 – e–1)
35. After the capacitor gets fully charged, S1 is opened and S2 is closed so that the inductor is connected in series with the capacitor. Then,
(A) at t = 0, energy stored in the circuit is purely in the form of magnetic energy
(B) at any time t > 0, current in the circuit is in the same direction
(C) at t > 0, there is no exchange of energy between the inductor and capacitor
(D) at any time t > 0, instantaneous current in the circuit may V
36. If the total charge stored in the LC circuit is Q , then for t 0
t
(A) the charge on the capacitor is Q = Q cos
0 2
LC
t
(B) the charge on the capacitor is Q = Q0
cos
d2Q
LC
(C) the charge on the capacitor is Q = –LC
(D) the charge on the capacitor is Q = –
dt2
d2Q dt2
SECTION - V
Matrix - Type
This section contains 4 questions. Each question has four statements (A, B, C and D) given in Column-I and four statements (p,q,r and s) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s and D-q then the answer should be written as : A p,r ; B p, s ; C r, s ; D q.
37. Match the matrix for the given process :
Column Ι Column ΙΙ
(A) Process J K (p) w > 0
(B) Proc11K ess K L
3PJ0
000 vLM2(0m) (q) w < 0
(C) Process L M (r) Q > 0
(D) Process M J (s) Q < 0
38. Match the matrix
Column Ι Column ΙΙ
(A) Fission (p) Converts some matter into energy
(B) Fusion (q) In atoms of high atomic number only
(C) - decay (r) In atoms of low atomic number only
(D) Exothermic nuclear reaction (s) Involves weak nuclear forces
39. Match the matrix
Column Ι Column ΙΙ
(A) Dielectric ring uniformly charged (p) Time independent electrostatic field out of system
(B) Dielectric ring uniformly charged rotating (q) Magnetic field with constant angular velocity
(C) Constant current in ring i0 (r) Induced electric field
(D) A ring carrying current i = i0
cost (s) Magnetic moment
40. A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths fe and f0, respectively. Then :
Column Ι Column ΙΙ
(A) Intensity of light received by lens (p) Radius of aperture (R)
(B) Angular magnification (q) Dispersion of lens
(C) Length of telescope (r) focal length f0, fe
(D) Sharpness of image (s) spherical aberration
A nswers
1. (A) 2. (A) 3. (A) 4. (C) 5. (B)
6. (B) 7. (A) 8. (D) 9. (D) 10. (D)
11. (B)
(D) 12. (C) 13. (A), (C) 14. (B), (D) 15. ( C ) ,
16. (A), (B), (C), (D) (B) 17. (A), (B), (C), (D) 18. (A), (C) 19. (B), (D) 20. ( A ) ,
21. 10 m/s 22. 10 m/s2 23. 273 K. 24. n = 24 25. (A)
26. (A) 27. (C) 28. (C) 29. (A) 30. (A)
31. (A) 32. (A) 33. (D) 34. (B) 35. (D)
36. (C)
37. (A) (s); (B) (p) and (r); (C) (r); (D) (q) and (s).
38. (A) (p) and (q); (B) (p) and (r); (C) (p) and (s); (D) (p), (q) and (r)
39. (A) (p) ; (B) (p), (q), (s) ; (C) (q), (s) ; (D) (q), (r), (s).
40. (A) (p); (B) (r); (C) (r); (D) (p), (q), (s).
1. Mass of disc and mass of sphere are same, moment of inertia about given axis are also same. So equate them i.e.
2/5 MR2 = 1/2 Mr2 + Mr2
2/5 MR2 = 3/2 Mr2
4 2R
r2 = 15 R2 r = 15
2. Just after cut, spring applies same upward force as before cut so net force on each block Fnet = ma.
After string is cut, FBD of m
3mg
a = mg = g
m
FBD of 2m (when string is cut tension in the spring takes finite time to become zero. However tension in the string immediately become zero.)
2mg
3mg 2mg g
a = 2m = 2
3. Frequency of first harmonic in AB = f1 , Frequency of second harmonic in CD = f2 f1 = f2 (given)
= or T
= 4T2
....(i)
Equate torques due to T1 and T2 about O for rotational equilibrium.
T x = T (L – x)
1 2
For translational equilibrium, T1 + T2 = mg
From (i) and (iii),
4mg mg
T1 = 5 and T2 = 5
Put these values in (ii).
4mg
5
× x =
mg L
5 (L – x) or 4x = L – x or x = 5
4. Focal length of equivalent mirror when a lens is silvered at a surface is
1 2 1
f f𝑙 fm
Here the mirror is a plane (surface) mirror.
f =
1
2 1 2
15
or f = cm
f 15 15 2
Positive focal length means a converging mirror. For mirror: As per sign convention
u = – 20 cm, f = 15
cm,
1 1 1
1 1 1
2 v u f
or 1 1 1
v u f
v 20 15 / 2
1 1 2 3 8 1
v 20 15 60 12
or v = – 12 cm
Image is formed at 12 cm to the left of lens.
Note - There are three stages of formation of final image
(i) Lens forms the image of object at A.
(ii) acts as virtual object for mirrored surface.
(iii) , the image formed by mirror acts as virtual object for lens. The lens forms the final image.
5. After two half lives
1 th
4
fraction of nuclei will remain undecayed. Or,
3 th
4
fraction will decay. Hence, the
3
probability that a nucleus decays in two half lives is 4 .
6. Using lens formula and data given in graph.
1 = 1 – 1
f v u
...(1)
1 1
f = 10
1
– 10
f = + 5
By differentiating eq. (1)
f v u =
1 v +
1 f
u + +
1(0.1)
=
1(0.1)
+
f 2 V 2 u2
V 2 u2
52 102
102
f =
0.2 25 =
100
0.2 0.05
4
so, f = 5 ± 0.05 Ans.
7. Current flowing through both the bars is equal. Now, the heat produced is given by :
H = 2 Rt
1
or H R ( R ,
RAB 1 )
r 2
or HAB RAB = 1
RBC 4
HBC RBC 4
g
8. =
L 2 T
g L T
In option (d) error in g is minimum and number of repetition of measurement are maximum. In this case the error in g is minimum.
9. A
rA C rB B
com
A B
GmAmB
(rA rB )2
= mArA
42
2
A
= mB rB
42
2
B
mArA mBrB
2 2
A B
As C is com m r
= mBrB
hence TA
= TB
10. = R .C
= (2 + 1) (2 + 4) = 18 s =
2 1. 2 4
= 8 s =
2 1
. (4 + 2) = 4 s.
1 2 2 1 2 4 9 3 2 1
11. r = f tan Hence, r2 f2.
12. Zero error =
5 0.5
50
= 0.05 mm
Actual measurement
0.5
= 2 × 0.5 mm + 25 × 50
– 0.05 mm
= 1 mm + 0.25 mm – 0.05 mm = 1.20 mm.
13.
hc = eV V =
hc
e c
For plate 1 : Plate 2 Plate 3
1
hc = 0.001
2 = 0.002
hc
3 = 0.004
hc
: : = 1 : 2 : 4
For plate 2, threshold wavelength
hc
= =
hc 1000
= = 500 nm
2 0.002 hc 2
For plate 3, threshold wavelength
hc
= =
hc 1000
= = 250 nm
3 0.004 hc 4
Since violet colour light is 400 nm, so < for plate 2.
So, violet colour light will eject photo–electrons from plate 2 and not from plate 3.
14. Electrostatic and gravitational fields do not form closed lines.
15.
necessary torque for rolling = fr, (frictional force provides this torque) as mg sin – f = ma
but a = r mg sin – f = mr
as = fr = = fr/
mg sin – f = mr ( fr
= 5f/2
2mr 2
mg sin = 7f 2
thus torque due to friction increases angular velocity, but friction acts up the incline hence decreases linear
2
velocity. f = 7 mg sin
As decreases, sin decreases. Hence magnitude of friction decreases.
16. As black body is an infinite sink which absorbs all radiations and good absorber is a good emitter.
Its radiates more energy in visible part though its reflected energy in unit time will be constant.
17. This is the variation of potential of hollow sphere with the distance from the centre and the total charge within the sphere will be q.
As no electric field is developed within it so electrostatic energy for r R0 is zero.
And the total charge resides over its surface and also at r = R0 electric field is discontinuous.
18. Magnetic force on wire BC would be perpendicular to the plane of the loop along the outward direction and on wire DA the magnetic force would be along the inward normal, so net force on the wire loop is zero and torque on the loop would be along the clockwise sense as seen from O.
(1 cos 2t)
19. As x = A 2
(1 cos 2t) C
+ B 2 + 2
sin 2t
x = B + B sin 2t (its linear part shifts the mean position
of the particle the coefficient sin 2 t is its amplitude.) x
20. As total mechanical energy at points A,B and C will be constant
max = B
E = E = E
C
mgh + K
A
= KB
= mgh + KC
K > K
(mghA + KA
= KB)
and KB > KC (mghC + KC = KB)
KC K A
Also hA – hC = mg
when mghA + KA = mghC + KC
if hA
> hC
K > K
(if LHS is positive then RHS have to be positive)
21. As collision is elastic
dP b
F = dt
n x a x 2mV
2
Equating the torque about hinge side we have,
a b 3b b
torque about hinge = n ×
Substituting the given values we get,
V = 10 m/s
22. N = mg N = ma sin370
macos 370 N2 N1
× (2mv)
4 = Mg × 2
a = = 10 m/s2 .
m
23. Q = 0
Heat lost by steam to convert into 0ºC water HL = 0.005 × 540 + 0.05 × 10 × 1
= 27 + 5 = 32 kcal
Heat required by ice to change into 0º C water
Hg = 0.45 ×
1 × 20 + 0.45 × 80 = 4.5 + 36.00 = 40.5 kcal
2
Thus, final temperature of mixture is 0ºC = 273 K
24.
= RZ2 1 2 =
= mv = mvr =
(n 1)h
(n 1)
n 1
(h / mv) h hr
r0 (n 1)2
2hr
1
= 2r
1
Putting, r =
Z
(n 1)Z 1 1 1
= RZ2 1 (n 1)2 =
2r (n 1)2
(n +1) – (n 1) =
2r ZR
= 2 11 0.53 1010 1.1 107
0 0
1000
= 2 12.1 0.53
= 24.8 (n + 1) = 25 n = 24
25.
2f1 100
f1 = 50
2f = 92 f = 46
beat frequency = 50 – 48 = 4
2
26.
= 0.5 =
2
0.5
= 4 Speed v = f = 50 × 4 = 200
27. At x = 0,
y = y1
+ y2
= 2A cos 96 t cos 4 t
For y = 0, cos 96 t = 0 or cos 4 t = 0
96 t = (2n + 1) (/2) or 4t = (2m + 1) /2
For 0 < t < 1 –
1 < n < 95.5 or –
2
1 < m < 3.5
2
Here n and m are integers, therefore net amplitude becomes zero 100 times.
28. A1 A2 A3
= r2 = area of base of cylinder in air
= 3r2 = area of base of cylinder in water
= 4r2 = cross-section area of cylinder
Equating the forces, we get
(P + gh )A + gH A = (P )A + [P + g(h + H)]A
a 1 3 3
3 a 1 a 1 2
5
On solving h1 = 3 H
29. P A
+ A Hg = P A
+ gh
a 3 3 3
a 3 2
h2 = 4H/9.
30. For h2 < 4h/9 cylinder does not move up because further buoyant force decreases while the weight of block remains same.
31. There is a no friction between the train and the track because train is not in contact with track.
32. By Lenz’s law there is an electro-magnetic drag force.
33. Electro-magnetic force elevates it.
34. When S1 is closed and S2 is open, the upper loop of the circuit is complete, the capacitor, resistor and the battery are in series so we can use the equation Q = Q (1 – e–t/) for charging of capacitor.
Hence after time interval 2, Q = CV(1 – e–2) = CV (1 – e–2).
35. Initially, the capacitor was uncharged, when the switch S1 was closed, after a long time interval the capacitor will get fully charged and hence the potential difference across the capacitor will become V. So the charge on capacitor will be CV.
q = Q0
cos t i = –
dq
dt = Q0
sin t i
max
= C V = V
36. As Q = Q cos t
dQ
d2Q
dt = –Q0 sin t dt2
= –Q cos t
but =
Q = – LC
d2Q dt 2
LC
d2Q dt2
= – Q cos t = –Q
37. (A) for J K
at const. V , dw = 0 and P T
dQ = du (At constant volume)
Now du is negative , because temperature is decreasing
dQ is negative hence Q < 0
(B) for K L
at const P , V T
volume increases ; Temperature will increased
dW = PdV hence W > 0 , Q > 0
(C) for L M
at constant V, dW = 0
P T , Temperature will increased Now dQ = du
but du is positive
Q > 0
(D) For M J
V is decreasing therefore w < 0 (PV)J < (PV)M
TJ < TM
U < 0
hence Q < 0
38. Fission is the process which involves conversion of some matter into energy and shown by atoms of high atomic number such as U235 .
Fusion also converts some matter into energy but shown by atoms of low atomic number such as H1, H2 .
-decay essentially carried out by weak nuclear forces and also converts matter into energy for example n1 H1 + e0 (–) + + energy
H1 n1 + e0 (+) + + energy
Exothermic nuclear reactions also converts matter into energy and all spontaneous nuclear reaction are exothermic.
39. The electrostatic field developed by dielectric ring depends upon its radius, magnitude of charge and dis- tance. It is independent of time when such a charged ring rotates it makes current and current carrying coil developed the magnetic field and constitutes magnetic moment as
M = A
Same will be true for constant current in the ring
Though the current is sinusoidal i.e. i = i cost apart from the above two it will develope induced electric field
also.
40. Intensity; I R2 (R is aperture of objective lens)
fo
Angular magnification = fe
length of telescope = fo + fe
sharpness of image depends on radius of curvature, dispersion of lens and spherical aberration.
Time : 2.00 Hr Max. Marks : 184
GENERAL INSTRUCTIONS
1. There are 40 questions in this paper.
2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero Mark
if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
3. For each question in Section II, you will be awarded 5 Marks if you give all correct answers and zero Mark
if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
4. For each question in Section III, you will be awarded 6 Marks if you give the correct answer and zero Mark
will be awarded in all other cases.
5. For each question in Section IV, you will be awarded 5 Marks if you give the correct answer and zero Mark
if no answer is given. In all other cases, minus two (–2) Marks will be awarded.
6. For each question in Section V, you will be awarded 6 Marks if you give all correct answers. No negative Mark will be awarded for an incorrectly answered question.
SECTION - I
Single Correct Choice Type
This section contains 12 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A hollow sphere of radius R has moment of inertia about its geometrical axis. If it is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to , then the value of r is equal to :
2
(A) 3
5
4
R (B) 3 R
3
(C) 3 R (D) 2 R
2. System shown in figure is in equilibrium and at rest. The spring and string are massless. Now the string is cut. The acceleration of mass 2m and m just after the string is cut will be:
(A) g/2 upwards , g downwards (B) g upwards, g/ 2 downwards
(C) g upwards , 2g downwards (D) 2g upwards , g downwards
3. A rod BD of mass m is suspended by two identical massless strings AB and CD of equal lengths. A block of mass ‘6m’ is suspended at point P such that BP is equal to ‘x’, if the fundamental frequency of the left wire is thrice the fundamental frequency of right wire, then the value of x is :
(A) l/10 (B) l/30
(C) 4l/10 (D) 8l/9
4. A point object is placed at distance of 30 cm from a thin plano-concave lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at :
(A) 6 cm to the left of the system. (B) 12 cm to the right of the system.
(C) 12 cm to the left of the system. (D) 6 cm to the right of the system.
5. Half life of a radio active substance 'A' is 10 days. The probability that a nucleus will survive for 30 days :
1
(A) 8
3
(B) 8
5
(C) 8
7
(D) 8
6. A graph is shown between object distance u and image distance v for a lens. The focal length of the lens is:
(A) 10 ± 0.1 (B) 10 ± 0.02
(C) 10 ± 0.3 (D) 10 ± 0.4
7. Two bars of radius '3r' and 'r' are kept in contact as shown. An electric current is passed through the bars. Which one of the following is correct?
(A) Heat produced in bar (1) is 3 times the heat produced in bar (2)
(B) Electric field in both halves is equal.
(C) Current density across AB is thrice that of across BC.
(D) Potential difference across BC is 9 times that of across AB.
42𝑙
8. A student performs an experiment for determination of g 2 , l 1m, and he commits an error of l.
For T he takes the time of n oscillations with the stop watch of least count T and he commits a human error of 0.2sec. For which of the following data, the measurement of g will be most accurate ?
(A) L = 1 , T = 0.1, n = 20 (B) L = 1, T = 0.1, n = 60
(C) L = 1 , T = 0.01, n = 20 (D) L = 0.2, T = 0.04, n = 60
9. A tristar system consists of three stars A, B and C having similar mass ‘m’. These stars are equidistant from each other and revolving about a common centre in a circle of radius r. Determine the frequency of their motion?
(A) (B)
(C) (D)
10. Find the time constant for the given RC circuits in correct order :
R = 2 , R = 4 , R = 6 , C = 8 F , C = 4 F
(A) 16, 48, 54 (B) 16, 16, 144
(C) 16, 24, 48 (D) 48, 27/4, 60
11. A biconvex lens of radius of curvature R and refractive index forms a circular image of radius a of the sun. Select the correct option.
R 1
(A) a 1 (B) a R
R
(C) a
(D) a R
12. For one completer rotation a screw gauge moves 0.2 mm on main scale. If the number of circular divisions is
50. Determine the diameter of ball.
(A) 1.76 mm (B) 1.68 mm
(C) 1.72 mm (D) 1.82 mm
SECTION - II
Multiple Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
13. The graph between and stopping potential (V) of three metals having work functions , and in an experiment of photoelectric effect is plotted
1 2 3
as shown in the figure. Which of the following statement(s) is/are correct ? [Here is the wavelength of the incident ray].
(A) Ratio of work functions : : = 1 : 2 : 4
(B) Ratio of work functions
: :
= 4 : 2 : 1
(C) The violet colour light can eject photoelectrons from metals 2 and 3.
(D) Red light is able to eject electrons from metal 3 only.
14. A field curve is shown in the figure. This field can represent
(A) Magnetic field (B) Electrostatic field
(C) Induced electric field (D) Gravitational field of a mass at rest
15. A solid sphere is sent up with velocity V along the inclined surface having inclination .
(A) frictional force acting on sphere is f = mg cos .
(B) work done by friction force is non-zero.
(C) friction will decrease angular velocity and increases its linear velocity during ascent.
(D) If decreases, friction will increases.
16. A dark room with very large thermal capacity is maintained at constant temperature T0, a nearly black body painted with lamp black or platinum black, is kept at a temperature T. Keeping the temperature of the black body constant (at T), sun rays are allowed to fall on the this black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct ?
(A) The quantity of radiation absorbed by the black body in unit time will increase.
(B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in an unit time will increase.
(C) Black body radiates more energy in unit time in the visible spectrum.
(D) The reflected energy in unit time by the black body remains same.
17. For spherical conductor the variation of electric field E with distance from centre is given in diagram and also given that :
qrˆ
E = 0 for r R0 and E = Then which option(s) is/are correct :
4
0r 2
for r R .
(A) Total charge within 2R0 is q. (B) Total electrostatic energy for r R0 is zero.
(C) At r = R0 electric field is discontinuous. (D) There will be no charge anywhere except at r = R0
18. Which of the following statement is correct in the given figure.
(A) net force on the loop is zero
(B) net torque on the loop is zero
(C) loop will rotate clockwise about axis OO’ when seen from O
(D) loop will rotate anticlockwise about OO’ when seen from O
19. Function x = log (Dsin2t + E cos2t ) + Asin2t + B cos2t + C sint cost represents SHM
(A) for any value of A,B ,C , D, and E (except C = 0)
(B) If A = – B,C = 2B, D = E ; amplitude = B
(C) If A = B ; C = 0 ; D = E = 0
(D) If A = B ; C = 2B ; D = E ; amplitude = |B|
20. A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and KA, KB and KC are kinetic energies of the ball at A,B and C respectively, then (assume that
normal reaction throughout the path never be zero) :
(A) hA > hC ; KB > KC (B) hA > hC ; KC > KA
(C) hA = hC ; KB = KC (D) hA < hC ; KB > KC
SECTION - III
Subjective Type
This section contains 4 subjective problems. Circle their correct answers.
21. A plate of mass M of dimensions (a × b) is hinged along one edge. The plate is maintained in horizontal position by colliding a ball of mass m, elastically 100 times per second on shaded region of the plate as shown in figure. Find the required speed of the ball (Given M = 3 kg, m = 0.01 kg, b = 2 m, a = 1 m, g = 10 m/s2)
22. A grove is cut at an angle 37° from the an incline plane inclined at 37° with the ground. A cubical object smaller than the groove size is inserted in the groove as shown in figure. The coefficient of friction between the block and the surface of the groove is 1/5. What will be the acceleration of the object
in m/sec2.
23. In an insulated vessel, 0.1 kg steam at 373 K and 1 kg of ice at 233 K are mixed. What will be the final temperature of the mixture (in kelvin).
Given, Lfusion = 80 cal/g = 336 J/g, Lvaporization = 540 cal/g = 2268 J/g, Sice = 2100 J/kg K = 0.5 cal/gK and Swater = 4200 J/kg K = 1 cal/gK
24. Spectral analysis of Light coming from the stars far off galaxies was observed that the nth line of lyman series is equal to de-broglie wavelength of electron in the first orbit of hydrogen like argon ion (z=18) when 17 of its electrons are stripped off. Find the value of n.
SECTION - IV
Paragraph Type
This section contains 4 Paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for Question Nos. 25 to 27
Two plane harmonic sound waves are expressed by the equations. y (x, t) = A sin (108 t – .54 t)
y (x, t) = A sin (0.5 x – 100 t) (All parameters are in MKS) :
25. How many times does an observer hear maximum intensity in one second ? (A) 4 (B) 10
(C) 6 (D) 8
26. What is the speed of the sound ?
(A) 200 m/s (B) 180 m/s
(C) 192 m/s (D) 96 m/s
27. At x = 0 how many times the amplitude of y1 + y2 is zero in one second at x = 0 ? (A) 96 (B) 100
(C) 104 (D) 108
Paragraph for Question Nos. 28 to 30
A wooden cylinder of diameter 6r, height H and density /4 is kept on a hole of diameter 2r of a tank, filled with liquid of density as shown in the figure.
28. If level of the liquid starts decreasing slowly when the level of liquid is at a height h1 above the cylinder the block starts moving up. At what value of h1, will the
block rise :
17H
(A) 9
13H
(B) 8
21H
(C) 4
(D) Remains same
29. The block in the above question is maintained at the position by external means and the level of liquid is lowered. The height h2 when this external force reduces to zero is
9 H
(A) 32
13 H
(B) 32
5 H
(C) 28
(D) Remains same
30. If height h2 of water level is further decreased, then
(A) cylinder will not move up and remains at its original position
(B) for h2 = H/3, cylinder again starts moving up
(C) for h2 = H/4, cylinder again starts moving up
(D) for h2 = H/5 cylinder again starts moving up
Paragraph for Question Nos. 31 to 33
Modern trains are based on Maglev technology in which trains are magnetically levitated, which runs its EDS Maglev system.
Maglev trains currently in operation are not compatible with conventional track, and therefore require all new infrastructure for their entire route. By contrast conventional high speed trains such as the TGV are able to run at reduced speeds on existing rail infrastructure.
Due to the lack of physical contact between the track and the vehicle, maglev trains experience no rolling friction, leaving only air resistance and electromagnetic drag, potentially improving power efficiency.
A very strong magnetic field is required to levitate massive train. For this reason one way is using superconductors to improve the efficiency of the electromagnets.
Though they are relatively quiet at low speeds, the high speed of some maglev trains cause large air displacement, which corresponds to significant noise pollution.
31. Maglev trains experience no rolling friction because
(A) the tracks used are smooth
(B) there is no physical contact between the track and vehicle
(C) there is pure rolling motion
(D) none of these
32. One way to improve the efficiency of the electromagnets is
(A) use of dielectrics (B) use of conductors
(C) use of superconductors (D) all of these
33. Maglev trains cause significant noise pollution since
(A) at low speeds the train causes large air displacements
(B) at high speeds the train causes large air displacements
(C) sonic booms are produced
(D) none of these
Paragraph for Question Nos. 34 to 36 The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch S1 while keeping switch S2 open. The capacitor can be connected in series with an inductor ‘L’ by closing switch S2
and opening S1.
34. Initially, the inductor was having no current. Now, switch S1 is closed and S2 is kept open. If time constant of this circuit is , then
(A) after time interval , current in the inductor is V/2R
(B) after time interval 2, current in the inductor is V (1 e2 )
R
(C) the work done by the voltage source will be half of the heat dissipated when the inductor is having full current V/R
(D) after time interval 2, charge on the capacitor is CV(1 – e–1)
35. After the inductor gets fully charged, S1 is opened and S2 is closed so that the inductor is connected in series with the capacitor. Then,
(A) at t = 0, energy stored in the circuit is purely in the form of magnetic energy
(B) at any time t > 0, current in the circuit is in the same direction
(C) at t > 0, there is no exchange of energy between the inductor and capacitor
(D) at any time t > 0, maximum charge on the capacitor = V
R
36. If the maximum current in the LC circuit is i , then for t 0
t t
(A) the current in the circuit is i = i cos
0 2
LC
(B) the current in the circuit is i = i cos
0 2
LC
(C) the current in the circuit is i = –LC
d2i dt 2
(D) the current in the circuit is i = –
d2Q dt2
SECTION - V
Matrix - Type
This section contains 4 questions. Each question has four statements (A, B, C and D) given in Column-I and four statements (p,q,r and s) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s and D-q then the answer should be written as : A p,r ; B p, s ; C r, s ; D q.
37. Match the matrix for the given process of ideal gas :
Column I Column II
(A) Process J K (p) w > 0
(B) Process K L (q) w < 0
(C) Process L M (r) Q > 0
(D) Process M J (s) Q < 0
38. Match the matrix for the nuclear reaction given below :-
Column I Column II
(A)
U235 +
n1
X 139 +
Sr94 + 3
n1 + Energy (p) Converts some matter into energy
92 0 54 e 38 0
(B) 4 H1 = He4 + 2+ 2 + Energy (q) Fission
(C) B10 + He4 C13 + H1 + Energy (r) Fusion
(D) n1 H1 + – + + energy (s) Involves weak nuclear forces
39.
40.
A nswers
1. (A) 2. (D) 3. (B) 4. (D) 5. (A)
6. (A) 7. (D) 8. (D) 9. (C) 10. (B)
11. (A) 12. (C) 13. (B), (C), (D) 14. (A), (C) 15. (C)
16. (A), (B), (C), (D) (B) 17. (A), (B), (C), (D) 18. (A), (C) 19. (B), (D) 20. ( A ) ,
21. 15 m/s 22. 2.48 m/s2 23. 273 K 24. 14 25. (A)
26. (A) 27. (D) 28. (C) 29. (A) 30. (A)
31. (B)
(D) 32. (C) 33. (B) 34. (B) 35. ( A ) ,
36. (C)
37. (A) (s), (B) (p) and (r), (C) (r) , (D) (q) and (s).
38. (A) (p) and (q), (B) (p) and (r), (C) (p) and (r), (D) (p) and (s)
39. (A) (r) ; (B) (p) ; (C) (q), (r) and (s) ; (D) (q) and (r)
40. (A) (p) and (q) ; (B) (s) ; (C) (r) ; (D) (r)
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