1.
Two concentric spherical shells A and B are kept as shown with the switch open. The potentials at A and B are 5 V and 3 V respectively. If the switch is closed, then potential of sphere A will become (A) 5 V (B) 3 V (C) 2 V (D) 7 V
B A S
2.
The radius of nucleus with mass number 7 is 2 fm. The radius of nucleus with mass 189 is : (A) 2 fm (B) 8 fm (C) 4 fm (D) 6 fm
3.
A satellite is orbiting around the earth in an orbit of radius of R, its velocity is V. Now its 3 velocity is made times. Its path is now : (A) Circular (B) hyperbolic (C) Parabolic (D) Elliptical
4.
Two radioactive samples have activity ratio 5 : 1. If the temperature of samples is made 2 times, then the activity ratio is (A) 1 : 5 (B) 5 : 1 (C) 1 : 2.5 (D) 2.5 : 1
5.
For maximum power from battery the internal resistance of battery r is R
R
R
R R R
R
R R
r
(A) 10 R (C) R/8
4R 9
(B) (D) 10R/9
6.
A
A disc having radius r = 2m is placed on smooth horizontal surface. Velocity of point A and B is given as shown in figure. Distance between point O and axis of rotation at that particular instant of time. (A) 1 m (B) 0.5m (C) 0.25 m (D) 2 m
2 .5 m /s e c
O
1 .5 m /s e c
B
2R
L
R
K
7.
8.
9.
2R
E
Time constant of L-R circuit will be L 2L R R (A) (B) L 2R (C) (D) None of above As shown in circuit diagram an ideal voltmeter and an ideal ammeter reading are zero. Sum of potential drop across box and 5 resistances will be (given 12Volt that there are no fault in voltmeter and ammeter) (A) 7 volt (B) 5 volt (C) 12 volt (D) Data insufficient
Box
A
As shown in figure, value of inductive reactance XL will be if source voltage is 100 volt R 1 = 20
X
L 1
= 30
R 2 = 10 X
C
= 40
I = 2A X
L
V
(A) 40
(B) 30
(C) 50
(D) Can have any value
V
10.
(A) 2 metres
2 2
(B)
17 2
5 (C)
11.
12.
2m
Two vertical walls are separated by a distance of 2 metres. Wall ‘A’ is smooth while wall B is rough with a coefficient of friction = 0.5. A uniform rod is propped between them. The length of the longest rod that can be probed between the walls is equal to :
metres
(D)
metres
P Q Wall A
Wall B
metres
Radius of curvature of a concave spherical surface separating air-glass medium is R. A point object is placed on the principal axis in the glass (g = 1.5). For the image to be real, seen by observer in air, distance of the object from P should be : (A) 2R < u < 3R
(B) u < 2R
(C) u = R
(D) u > 3R
a ir
g la s s
o b je c t
P
Loop ABCD and long straight wire are in the same plane. Side CD = 2AB. Distance between long straight wire and AB is equal to distance BD. Net force on the loop is : C
B
I
I A
D
(A) Towards the long straight wire (C) Parallel to the long straight wire 13.
(B) Away from the long straight wire (D) Net force on the loop will be zero
A hollow circular tube of radius R and negligible internal diameter is fixed on horizontal surface. Ball A of mass m is given velocity V0 in the shown direction. It collides with ball B of mass 2m. Collision is perfectly elastic. If centre of loop is origin of co-ordinate system, then co-ordinate of next collision.
y axis m B = 2m
x axis
(0,0) O
V0 mA = m
3 R R, 2 2
(A)
(C) 14.
(B)
R 3 , R 2 2
(D)
3 R R, 2 2
R R , 2 2
An ideal mono-atomic gas is taken through the cyclic process shown in figure. Linear expansion from A to B followed by adiabatic compression back to original state. P
A (4 ,1 6 )
B (3 2 ,1 ) V
(A) (B) (C) (D) 15.
Efficiency of cyclic process is zero During process A to B heat is released only During process A to B heat is absorbed only During linear process heat enters and leaves the process
10 2 Mirror is moving towards the particle with speed 2 cm/sec. Speed of A and B are and 5 cm/sec respectively in the direction shown in figure. Magnitude of velocity of image of the particle B with respect to image of A.
V0 = 2 cm/sec
B 45°
A
325 cm / sec
(A)
15cm / sec
(B) 269 cm / sec
13cm / sec
(C)
(D)
MORE THAN ONE OPTION
16.
Backlash error may occur in which of the following instruments ? (A) Slide calipers and screw gauge (B) Spherometer and screw gauge (C) Slide cappliers and spherometer (D) Slide calipers, screw gauge and spherometer
17.
In a resonance-column experiment to measure the velocity of sound, the first resonance is obtained at a length l1 and the second resonance at a length l2. Then which of the following is incorrect l2 3l1 (A) l2 3l1 (B) l2 3l1 (C) (D) May be any of the above, depending on the frequency of the tuning fork used
18.
In experiments using the metre bridge, post-office box, and potentiometer, a galvanometer is used. Which property of the galvanometer makes it suitable for these experiments ? (A) It has a relatively high coil resistance (B) It measures the magnitude of the current
(C) It can indicate currents flowing through it in either direction (D) It is very sensitive to small currents 19.
A hollow closed conductor of irregular shape is given some charge. Which of the following statements are incorrect? (A) The entire charge will appear on its outer surface (B) All points on the conductor will have same potential (C) All points on its surface will have the same charge density (D) All points near its surface (just inside) and outside it will have the same electric field intensity
20.
A thin-walled, spherical conducting shell S of radius R is given charge Q. The same amount of charge is also placed at its centre C. Which of the following statements are correct ? Q 2R 2 (A) On the outer surface of S, the charge density is (B) The electric field is zero at all points inside S (C) At a point just outside S, the electric field is double the field at a point just inside S. (D) At any point inside S, the electric field is inversely proportional to the square of its distance from C
21.
A man can swim with a velocity v relative to water. He has to cross a river of width d flowing with a velocity u (u > v). The distance through which he is carried downstream by the river is x. Which of the following statements are correct? (A) If he crosses the river in minimum time, x = du/v (B) x cannot be less than du/v (C) For x to be minimum, he has to swim in a direction making an angle of /2 + sin1 (v/u) with the direction of the flow of water. (D) x will be maximum if he swims in a direction making an angle of /2 sin1(v/u) with the direction of the flow of water 22.
The X-ray beam coming from an X-ray tube will not be (A) Monochromatic (B) Having all wave lengths larger than a certain minimum wavelength (C) Having all wavelength smaller than certain maximum wavelengths (D) Having all wavelengths lying between a minimum and maximum wavelength
23.
Which of the following functions represent a stationary wave ? Here a, b and c are constants (A) y = a cos (bx) sin (ct) (B) y = a sin (bx) cos (ct) (C) y = a sin (bx + ct) (D) y = a sin (bx + ct) + a sin (bx ct)
24.
25.
A semi-circular wire of radius r, carrying a current i, is placed in a uniform magnetic field of magnitude B. The force acting on it (A) Can be zero (B) Can have the maximum magnitude 2 Bir (C) Can have the maximum magnitude Bir (D) Can have the maximum magnitude Bir L1
Two thin convex lenses are separated as shown. The focal length of lens L1 is 15 cm and that of lens L2 is 30 cm. An object is placed at distance 30 cm from lens L 1. The location of image formed finally will be at : (A) infinity (B) 15 cm behind the lens L1 (C) optical centre of lens L2 (D) 60 cm away from object
L2
O 30cm
30cm
PASSAGE TYPE
Rolling is the combination of translation and rotation. The point of contact plays a crucial role as it decides the direction of friction. A uniform disc of mass M and radius R is given a linear velocity v 0 and angular speed 0 as shown in the diagram on a rough horizontal surface. 26.
v t = 0 R R ough
The graph of angular speed of disc about its centre is best represented by :
t0
t
(A)
t
(B)
t
(C)
t
(D)
t0
t
2v = 0 R
27.
The disc is now replaced by a uniform solid sphere of mass M and radius R. Again sphere is given same velocity and angular speed under same situation. Then graph of angular speed about centre vs time ‘t’ is given by
t
(A)
t
(B)
t
(C) 28.
t
(D)
The velocity of centre of mass of sphere in previous question when pure rolling starts will be equal to 2V0 5V0 5 6 (A) (B) V0 7 (C) (D) zero
The property of a surface of liquid to shrink whenever it gets a chance to do so is because of surface tension. The energy that a surface layer has is called as surface energy and is given by product of surface tension and surface area. Consider a solid cube of edge ‘a’ made of ice. The cube is kept in a gravity free cabin. Now the whole cube is melted. Surface tension of water = T. Viscosity of air = . 29.
The cube will : (A) remain in cubical shape and fly up (C) become flat and water will stay on
a
(B) remain in cubical shape and move down (D) become spherical
30.
The surface energy of liquid thus formed will be equal to : (A) (6) (a2) (T) (B) (5) (a3/2) (T) (C) (32/3) (T.a2) (4)1/3 (D) (12) (a2) (T)
31.
Now if this melted liquid is dropped in air, in gravity field and viscosity of liquid is , then :
(A) liquid will move down with a constant speed (B) liquid will remain at rest
(C) liquid will move up with speed (D) None of above
2 a 2 ( )g 3 9 4
2/3
.
2 72 a g 9
The inductor stores the magnetic energy which is proportional to square of current through it. Consider a circuit in which an ideal inductor is connected with some resistances as shown. The key is closed at time t = 0 2R R
L
R
2R
32.
t = 0
The current drawn from the battery after a long time is : 2 3R 2R (A) (B) 2 R (C) (D) zero
33.
The time at which power generation in the inductor is at its maximum rate is equal to : ln (2) (L) ln (2) R R (A) (B) L 3 (3L) ln (2) ln R 2 2R (C) (D)
34.
The maximum rate of power generation in inductor is equal to :
(A)
2 3R 2R
(B)
2
(C)
(D)
2 24R 2 12R
An insulated cylinder contains nitrogen gas which is sealed on the top by a heavy metal piston of mass m. Piston is free to move with negligible friction. Initial height of the piston is 0.3 m at temperature 27°C when it is given some heat with the help of an electrical circuit, piston slowly rises to height 0.5 m above the bottom of the cylinder. 35.
Expansion of gas in the cylinder is : (A) Isothermal process
(B) Adiabatic process
(C) Isobaric process
(D) Isochoric process
36.
Final temperature of the nitrogen gas inside the cylinder is : (A) 400 K (B) 300 K (C) 200 K (D) 500 K
37.
During expansion of the gas, net heat absorbed by the nitrogen gas is : (A) Equal to work done by nitrogen gas on the piston (B) Greater than work done by nitrogen gas on the piston (C) Less than work done by nitrogen gas on the piston (D) Will be always twice of the work done by the gas on the piston
m h = .3 m
K E
MATCH THE FOLLOWING
38.
In the experiment of photoelectric effect match the following : Column I Column II A. If frequency of incident light is decreased (p) Stopping potential must decrease B. Intensity of incident light is decreased while (q) Photo-electric effect may stop. frequency is constant and greater than threshold frequency C. Metal is replaced by another metal of higher (r) Saturation current must increase. work function, incident radiation is same with same photon efficiency. D. Intensity of incident light is increased while (s) Saturation current must decrease. frequency is constant and greater than threshold frequency.
INTEGER TYPE ANS IS IN BETWEEN 0 TO 20
39.
A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3 ampere. A thin coil having 10 turns of wire and of radius 0.01 m carries a current of 0.4 ampere. Calculate the torque (in S.I. unit in the order of 10 6) required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid. [Take : 2 = 10]
40.
In a Coolidge tube the atomic number of target material is 41. A potential difference of 20 kV is applied across the tube. Let K be K line produced by tube and min be cut off wavelength. Calculate K min in the order of 108 m.
41.
When a box ‘A’ is connected across an a.c. source of 200 V, 0.4 A of current flows in circuit. When a capacitor of reactance 400 is connected in series with box and connected across a.c. source, the power factor of circuit becomes 1. What is power factor of box ‘A’. (Express your answer in the order of 101)
42.
A ring of mass M is attached with spring of spring constant 10Mg K R . The other end of the spring is attached to fixed horizontal rod. Ring is free to slide on fixed horizontal rod. Ring is released from the condition shown in figure. Natural length of the spring is R. Find ratio of maximum and minimum normal reaction on ring. Initially ring is at rest
R
37°
43.
44
In the figure, a sphere of radius 2 metre rolls on a plank. The accelerations of the sphere and the plank are indicated. The value of in rad/s2 is
2m a 2= 4 m /s
2
a 1= 2 m /s 2
A bullet splinter of mass of 10 gm moving with a speed of 400 m/s hits an ice block of mass 990 gm kept on a frictionless floor and gets stuck in it. How much ice will melt if 50% of the lost Kinetic energy goes to ice? (Temperature of ice block = 0oC) give ans in gm
45 For a gas, y = 1.286. What is the number of degrees of freedom of the gas
46. In the above circuit, find the potential difference across AB.
8f
8f P
A
1 10 V
3
8f
2 Q
4
8f
B
E (2 iˆ 3jˆ 4kˆ) 47. Electric field in a region is given by points (0, 0, 0) and (1,2,3) will be
V/m. The potential difference between
48. In the circuit shown in figure each cell has emf 5V and has an internal
resistance of 0.2 ohm. What is the reading of ideal voltmeter V.
+ V
49.
The network shown in figure is part of a complete circuit. If at a certain instant the current (I) is 5A, and is decreasing at a rate of 10 3 A/s then VB – VA = I
A
1
15 V
5mH
B
50 . A particle of mass 1 kg is moving along x-axis and a force F is also acting along x-axis in such a way such that its displacement is varying as: x = 3t 2. Find work done by force F when it will move 2m.
Fig.13
51
A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, the amplitude of the motion is(give ans in cm)
52. In the arrangement shown in the figure below at a particular instant the block D is coming down with a speed of 12 m/s and C is moving up with 4 m/s. At the same instant it is also known that w.r.t. Pulley P, the block A is moving down with speed 3 m/s. Determine the magnitude of velocity of block B w.r.t. ground.
53. To generate a power of 3.2 MW, the number of fissions of U 235 per minute is
(Energy released per fission = 200 MeV, 1 eV = 1.6 10–19 J)
