(d) 1 2
q
e f
0 −
4. A thin metal disc of radius 0.25 m and mass 2 kg starts from rest and rolls down an inclined plane. If its rotational kinetic energy is 4 J at the foot of the inclined plane, then its linear velocity at the same point is (a) 1.2 m s–1 (b) 2 2 m s−1 (c) 20 m s–1 (d) 2 m s – 1
5. Two radioactive elements X and Y have half lives of 50 minutes and 100 minutes respectively. Initially
both of them have same numbers of atoms. After 200 minutes what is the value of following fraction ? Number of atoms of X unchanged/Number of atoms of Y unchanged.
(a) 4 (b) 2 (c) 1
2 (d) 1
6. For the circuit shown in figure, the current through 4 the inductor is 0.9 A. While the current through the capacitor is 0.4 A. The current drawn from the generator is
(a) I = 1.13 A
L C
(b) I = 0.9 A (c) I = 0.5 A (d) I = 0.6 A
7. A boy of mass 50 kg is standing on a weighing machine placed on the floor of a lift. The machine reads his weight in N. What is the reading of the machine if the lift is moving upwards with a uniform speed of 10 m s–1? (Take g = 10 m s–2)
(a) 510 N (b) 480 N (c) 490 N (d) 500 N 8. Two cells A and B are connected in the secondary
circuit of a potentiometer one at a time and the balancing length are respectively 400 cm and 440 cm. The emf of the cell A is 1.08 V. The emf of the second cell B is
(a) 1.08 V (b) 1.188 V (c) 11.88 V (d) 12.8 V
9. A simple pendulum is executing SHM with a period of 6 s between two extreme positions B and C about a point O. If the length of the arc BC is 10 cm, how long will the pendulum take the move from position C to a position D towards O exactly midway between C and O.
(a) 0.5 s (b) 1 s (c) 1.5 s (d) 3 s
10. The critical angle of a transparent crystal is 45°.
Then its polarising angle is Examon
5th June
PRACTICE PAPER 2016
(a) q =tan ( )−1 2 (b) q =sin ( )−1 2 (c) q =
cos−1 1
2 (d) q =cot ( )−1 2
11. Two particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is
(a) GmR (b) Gm4R
(c) Gm R
3 (d) Gm2R
12. A man standing on a road has to hold his umbrella at 30° with the vertical to keep the rain away.
He throws the umbrella and starts running at 10 km h–1. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is (a) 20 km h–1 (b) 10 3 km h−1 (c) 20 3 km h−1 (d) 10 km h–1 13. The combination of gates shown below yields
X B
A
(a) NOT gate (b) XOR gate (c) NAND gate (d) OR gate
14. A mass of 10 kg is suspended from a spring balance.
It is pulled a side by a horizontal string so that it makes an angle of 60° with the vertical. The new reading of the balance is
(a) 20 kg wt (b) 10 kg wt (c) 10 3 kg wt (d) 20 3 kg wt
15. A garden hose having an internal diameter 2.0 cm is connected to a lawn sprinkler that consists of an enclosure with 24 holes, each 0.125 cm in diameter.
If water in the hose has a speed of 90.0 cm s–1, find the speed of the water having the sprinkler hole.
(a) 860 cm s–1 (b) 960 cm s–1 (c) 760 cm s–1 (d) 660 cm s–1
16. The radius of a thin wire is 0.16 mm. The area of cross-section of wire in mm2 with correct number of significant figures is
(a) 0.081 (b) 0.080 (c) 0.0804 (d) 0.080457
17. A transistor is operated in common emitter configuration at VC = 2 V such that a change in the base current from 100 mA to 300 mA produces a change in the collector current from 10 mA to 20 mA. The current gain is
(a) 75 (b) 100 (c) 25 (d) 50
18. 1% of 1012 Hz of a satellite link was used from telephony. Find the number of channels (or subscribers) if band width of each channel is 8 kHz.
(a) 2.5 × 107 (b) 1.25 × 107 (c) 2.5 × 108 (d) 1.25 × 106
19. A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed.
If the stone makes 25 revolutions in 14 s, what is the magnitude of acceleration of the stone?
(a) 60 m s–2 (b) 100 m s–2 (c) 110 m s–2 (d) 120 m s–2
20. At 27 °C, a gas is suddenly compressed such that its pressure becomes 1
8
th
of original pressure.
Temperature of the gas will be g =
5 3
(a) 420 K (b) 327°C (c) 300 K (d) –142°C 21. A solenoid of 0.4 m length with 500 turns carries a
current of 3 A. A coil of 10 turns and of radius 0.01 m carries a current of 0.4 A. The torque required to hold the coil with its axis at right angles to that of solenoid in the middle part of it, is
(a) 6p2 × 10–7 N m (b) 3p2 × 10–7 N m (c) 9p2 × 10–7 N m (d) 12p2 × 10–7 N m 22. A solid cylinder of mass 3 kg is rolling on a
horizontal surface with velocity 4 m s–1. It collides with a horizontal spring of force constant 200 N m–1. The maximum compression produced in the spring will be
(a) 0.5 m (b) 0.6 m (c) 0.7 m (d) 0.2 m 23. Two objects of mass 20 g and 30 g are connected by
a light rod of length 1 m and move in a horizontal circle as shown in the figure. The speed of each is 2 m s–1. What is the total angular momentum of the objects about the centre?
(a) 0.05 kg m2 s–1
1 m 20 g
(b) 0.01 kg m2 s–1 30 g
(c) 0.15 kg m2 s–1 (d) 0.25 kg m2 s–1
24. Electric field on the axis of a small electric dipole at a distance r is
E1 and
E2 at a distance of 2r on a line of perpendicular bisector. Then
(a)
E E
2 1
= − 8 (b)
E E
2 1
= −16 (c)
E E
2 1
= − 4 (d)
E E
2 1
= 8
25. The fundamental frequency of a sonometer wire of length l is u0. A bridge is now introduced at a distance Dl(<< l) from the centre of the wire. The number of beats heard if both sides of the bridges are set into vibration in their fundamental modes are
(a) 4u Dl0
l (b) 2u Dl0
l (c) 8u Dl0
l (d) u0 Dl
l
26. P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be
(a) 4R (b) 2.5R (c) 3R (d) 4 3
R 27. The equivalent resistance between points A and B is
A
B
2
2 2
2 2
(a) 2 W (b) 4 W (c) 1 W (d) 6 W 28. A magnetising field of 2 × 103 A m–1 produces a
magnetic flux density of 8p T in an iron rod. The relative permeability of the rod will be
(a) 102 (b) 100 (c) 104 (d) 101
29. The period of oscillation of a mass 1.6 kg suspended from a spring is 2 s. If along with it another mass m kg is also suspended, the period of oscillation increases by one second. The mass m will be (a) 1 kg (b) 2 kg (c) 1.6 kg (d) 2.6 kg 30. Two bodies of masses m and 4m are placed at a
distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
(a) − 4Gm
r (b) − 6Gmr
(c) − 9Gm
r (d) zero
31. The radii and Young’s moduli of two uniform wires A and B are in the ratio 2 : 1 and 1 : 2 respectively.
Both wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is
(a) 1.0 (b) 1.5 (c) 2.0 (d) 3.0 32. Starting with a sample of pure 66Cu, 7
8 of it decays into Zn in 15 minutes. The corresponding half life is (a) 7 1
2 minutes (b) 5 minutes (c) 15 minutes (d) 10 minutes 33. Two masses M and M/2 are joined
M/2 M
together by means of light inextensible string passed over a frictionless pulley as shown in figure. When the bigger mass is released, the small one will ascend with an acceleration of
(a) g
3 (b) 3
2g (c) g (d) g 2
34. A circuit has a resistance of 11 W, an inductive reactance of 25 W and a capacitance reactance of 18 W. It is connected to an ac source of 260 V and 50 Hz. The current through the circuit is
(a) 11 A (b) 15 A (c) 18 A (d) 20 A 35. Which of the following characteristics is not
associated with a ferromagnetic material?
(a) It is strongly attracted by a magnet.
(b) It tends to move from a region of strong magnetic field to a region of weak magnetic field.
(c) Its origin is the spin of electrons.
(d) Above the Curie temperature, it exhibits paramagnetic properties.
36. Light of certain colour has 2000 waves to the millimetre in air. What will be the wavelength of this light in medium of refractive index 1.25?
(a) 1000 Å (b) 2000 Å (c) 3000 Å (d) 4000 Å
37. A coil of resistance 10 W and inductance 5 H is connected to a 100 V battery. Then the energy stored in the coil is
(a) 250 J (b) 250 erg (c) 125 J (d) 125 erg
38. A step-down transformer is used on a 1000 V line to deliver 20 A at 120 V at the secondary coil. If the efficiency of the transformer is 80%, the current drawn from the line is
(a) 3 A (b) 30 A (c) 0.3 A (d) 2.4 A 39. A radioactive nucleus of mass M emits a photon
of frequency u and the nucleus recoils. The recoil energy will be
(a) Mc2 – hu (b) hMc
2 2
2 u2
(c) zero (d) hu
40. The decreasing order of wavelength of infrared, microwaves, ultraviolet and gamma rays is
(a) microwaves, infrared, ultraviolet, gamma rays (b) gamma rays, ultraviolet, infrared, microwaves (c) microwaves, gamma rays, infrared, ultraviolet (d) infrared, microwaves, ultraviolet, gamma rays 41. In the Davisson and Germer experiment, the
velocity of electrons emitted from the electron gun can be increased by
(a) increasing the potential difference between the anode and filament
(b) increasing the filament current (c) decreasing the filament current
(d) decreasing the potential difference between the anode and filament
42. In a hydrogen atom, the magnetic field at the centre of the atom produced by an electron in the nth orbit is proportional to
(a) 12
n (b) 1n3 (c) 14
n (d) 1n5
43. A force F acting on a body depends on its displacement S as F ∝ S–1/3. The power delivered by F will depend on displacement as
(a) S2/3 (b) S1/3 (c) S0 (d) S–5/3 44. A ball of mass m is moving towards a batsman with
a speed v. The batsman strikes the ball and deflects it by an angle q without changing its speed. The impulse imparted to the ball is
(a) mvsinq (b) mvcosq (c) 2
mv sin q 2 (d) 2
mv cos q2
45. When a plastic thin film of refractive index 1.45 is placed in the path of one of the interfering waves then the central fringe is displaced through width
of five fringes. The thickness of the film, if the wavelength of light is 5890 Å, will be
(a) 6.54 × 10–4 cm (b) 6.54 × 10–3 cm (c) 6.54 × 10–5 cm (d) 6.54 × 10–2 cm
46. An infinite number of charges each equal to 0.2 mC are arranged in a line at distances 1, 2, 4, 8 .... metre from a fixed point. The potential at the fixed point is (a) 1800 V (b) 2000 V
(c) 3600 V (d) 2250 V
47. When a lens of refractive index m1 is placed in a liquid of refractive index m2, the lens looks to be disappeared only if
(a) m m
1 2
= 2 (b) m1 3m2
=2 (c) m1 = m2 (d) m1 5m2
=2 48. Dimensions [ML–1T–1] are related to
(a) torque (b) work
(c) energy (d) coefficient of viscosity 49. A Carnot engine whose efficiency is 40%, receives
heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is (a) 900 K (b) 600 K (c) 700 K (d) 800 K 50. A doubly ionized lithium atom is hydrogen like
with atomic number 3. Find the wavelength of the radiation required to excite the electron in Li2+ from the first to the third Bohr orbit. The ionization energy of the hydrogen atom is 13.6 eV.
(Take hc = 1240 eV nm)
(a) 11.4 nm (b) 10.7 nm (c) 12.7 nm (d) 13.4 nm
51. A rectangular vessel when full of water, takes 10 min to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?
(a) 9 min (b) 7 min (c) 5 min (d) 3 min 52. The work done by a force acting on a body is as
shown in the graph. The total work done in covering an initial distance of 20 m is
F (in N) 5 10 15 20
5 10 15 20 25 30 S (in m) 0
(a) 225 J (b) 200 J (c) 400 J (d) 175 J
53. In a double slit experiment, with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5 × 10–2 m towards the slits, the change in fringe width is 10–3 m. Then the wavelength of light used is (Given that distance between the slits is 0.03 mm) (a) 4000 Å (b) 4500 Å
(c) 5000 Å (d) 6000 Å
54. A mixture consists of n1 moles of a monoatomic gas and n2 moles of diatomic gas, then the g of the mixture is