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2013 AIMPT - Physics
1.
In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows: `P = (a^2b^2)/(cd)`. % error in P is
a) 14 %
b) 10 %
c) 7%
d) 4%
2.
The velocity of a projectile at the initial point A is `(2 hat i + 3 hat j)` m/s. Its velocity (in m/s) at point B is
a) `- 2 hat i - 3 hat j`
b) `-2 hat i + 3 hat j`
c) `2 hat i - 3 hat j`
d) `2 hat i + 3 hat j`
3.
A stone falls freely under gravity. It covers distances `h_1`, `h_2` and `h_3` in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between `h_1`, `h_2` and `h_3` is
a) `h_1` = `2h_2` = `3h_3`
b) `h_1 = h_2/3 = h_3/5`
c) `h_2 = 3h_1 and h_3 = 3h_2`
d) `h_1 = h_2 = h_3`
4.
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2 m? (g is the acceleration due to gravity)
a) Zero
b) 2 mg
c) 3 mg
d) 6 mg
5.
The upper half of an inclined plane of inclination `theta` is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by
a) `mu = 1/(tan theta)`
b) `mu = 2/(tan theta)`
c) `mu = 2 tan theta`
d) `mu = tan theta`
6.
A uniform force of (`3 hat i + hat j`) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position (`2 hat i + hat j`) metre to position (`4 hat i + 3 hat j - hat k`) metre. The work done by the force on the particle is
a) 9 J
b) 6 J
c) 13 J
d) 15 J
7.
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 `ms^(–1` and the second part of mass 2 kg moves with 8 `ms^(–1` speed. If the third part flies off with 4 `ms^(–1` speed, then its mass is
a) 3 kg
b) 5 kg
c) 7 kg
d) 17 kg
8.
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is
a) `(3g)/(2L)`
b) `g/L`
c) `(2g)/L`
d) `(2g)/(3L)`
9.
A small object of uniform density rolls up a curved surface with an initial velocity ‘v’. It reaches up to a maximum height of `(3v^2)/(4g)` with respect to the initial position. The object is
a) Ring
b) Solid sphere
c) Hollow sphere
d) Disc
10.
A body of mass 'm' taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be
a) Mg2R
b) `2/3`mgR
c) 3mgR
d) `1/3`mgR
11.
Infinite number of bodies, each of mass 2 kg is situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
a) -G
b) `-8/3`G
c) `-4/3`G
d) -4G
12.
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
a) Length = 50 cm, diameter = 0.5 mm
b) Length = 100 cm, diameter = 1 mm
c) Length = 200 cm, diameter = 2 mm
d) Length = 300 cm, diameter = 3 mm
13.
The wettability of a surface by a liquid depends primarily on
a) Viscosity
b) Surface tension
c) Density
d) Angle of contact between the surface and the liquid
14.
The molar specific heats of an ideal gas at constant pressure and volume are denoted by `C_p` and `C_v` respectively. If `gamma = C_p/C_v` and R is the universal gas constant, then `C_v` is equal to
a) `(1+gamma)/(1-gamma)`
b) `R/(1-gamma)`
c) `(1-gamma)/R`
d) `gammaR`
15.
A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using
a) Stefan's Law
b) Wien's displacement Law
c) Kirchoff's Law
d) Newton's Law of cooling
16.
A gas is taken through the cycle `A rarr B rarr C rarr A`, as shown. What is the net work done by the gas?
a) 2000 J
b) 1000 J
c) Zero
d) - 2000 J
17.
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of `C_p/C_v` for the gas is
a) `4/3`
b) 2
c) `5/3`
d) `3/2`
18.
In the given (V – T) diagram, what is the relation between pressures `P_1` and `P_2`?
a) `P_2 = P_1`
b) `P_2 > P_1`
c) `P_2 < P_1`
d) Cannot be predicted
19.
The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from `T_1K` to `T_2K` is
a) `3/8 N_a k_B(T_2 - T_1)`
b) `3/2 N_a k_B(T_2 - T_1)`
c) `3/4 N_a k_B(T_2 - T_1)`
d) `3/4 N_a k_B(T_2/T_1)`
20.
A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength 2`pi`m and frequency of `1/pi` Hz is represented by
a) `Y = sin (x – 2t)`
b) `Y = sin (2 pi x - 2 pi t)`
c) `Y = sin (10 pi x - 20 pi t)`
d) `Y = sin (2 x - 2 t)`
21.
If we study the vibration of a pipe open at both ends, then the following statement is not true
a) Open end will be anti-node
b) Odd harmonics of the fundamental frequency will be generated
c) All harmonics of the fundamental frequency will be generated
d) Pressure change will be maximum at both ends
22.
A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is
a) 254 Hz
b) 246 Hz
c) 240 Hz
d) 260 Hz
23.
Two pith balls carrying equal charges are suspended from a common point by strings of equal length; the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become
a) `(1/sqrt(2))^2`
b) `r/2^(1/3)`
c) `(2r)/sqrt(3)`
d)
`(2r)/3`
24.
A, B and C are three points in a uniform electric field. The electric potential is
a) Maximum at A
b) Maximum at B
c) Maximum at C
d) Same at all the three points A, B and C
25.
A wire of resistance 4 `Omega` is stretched to twice its original length. The resistance of stretched wire would be
a) 2 `Omega`
b) 4 `Omega`
c) 8 `Omega`
d) 16 `Omega`
26.
The internal resistance of a 2.1 V cell which gives a current of 0.2 A through a resistance of 10 `Omega` is
a) 0.2 `Omega`
b) 0.5 `Omega`
c) 0.8 `Omega`
d) 1.0 `Omega`
27.
The resistances of the four arms P, Q, R and S in a Wheatstone's bridge are 10 ohm, 30 ohm, 30 ohm and 90 ohm, respectively. The e.m.f. and internal resistance of the cell are 7 volt and 5 ohm respectively. If the galvanometer resistance is 50 ohm, the current drawn from the cell will be
a) 1.0 A
b) 0.2 A
c) 0.1 A
d) 2.0 A
28.
When a proton is released from rest in a room, it starts with an initial acceleration `a_0` towards west. When it is projected towards north with a speed `v_0` it moves with an initial acceleration `3a_0` toward west. The electric and magnetic fields in the room are
a) 1
b) 2
c) 3
d) 4
29.
A current loop in a magnetic field
a) Experiences a torque whether the field is uniform or non uniform in all orientations
b) Can be in equilibrium in one orientation
c) Can be in equilibrium in two orientations, both the equilibrium states are unstable
d) Can be in equilibrium in two orientations, one stable while the other is unstab
30.
A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be
a) M
b) `3/pi M`
c) `2/pi M`
d) `M/2`
31.
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is
a) Once per revolution
b) Twice per revolution
c) Four times per revolution
d) Six times per revolution
32.
A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when
a) Frequency of the AC source is decreased
b) Number of turns in the coil is reduced
c) A capacitance of reactance `X_C = X_L` is included in the same circuit
d) An iron rod is inserted in the coil
33.
The condition under which a microwave oven heats up a food item containing water molecules most efficiently is
a) The frequency of the microwaves must match the resonant frequency of the water molecules.
b) The frequency of the microwaves has no relation with natural frequency of water molecules.
c) Microwaves are heat waves, so always produce heating.
d) Infra-red waves produce heating in a microwave oven.
34.
Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is
a) `5/27`
b) `3/23`
c) `7/29`
d) `9/31`
35.
The half life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be
a) 40 years
b) 60 years
c) 80 years
d) 100 years
36.
A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)
a) 2.67 MeV
b) 26.7 MeV
c) 6.675 MeV
d) 13.35 MeV
37.
For photoelectric emission from certain metal the cut-off frequency is `nu`. If radiation of frequency `2nu` impinges on the metal plate, the maximum possible velocity of the emitted electron will be (m is the electron mass)
a) `sqrt((hnu)/(2m))`
b) `sqrt((hnu)/(m))`
c) `sqrt((2hnu)/(m))`
d) `2sqrt((hnu)/(m))`
38.
The wavelength `lamda_e` of an electron and `lamda_p` of a photon of same energy E are related by
a) `lamda_p oo lamda_e^2`
b) `lamda_p oo lamda_e`
c) `lamda_p oo sqrt(lamda_e)`
d) `lamda_p oo 1/sqrt(lamda_e)`
39.
A plano-convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices `mu_1` and `mu_2` and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is
a) `R/(2(mu_1+mu_2))`
b) `R/(2(mu_1-mu_2))`
c) `R/(mu_1-mu_2)`
d) `(2R)/(mu_1-mu_2)`
40.
For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea - eye lens can be estimated to be
a) 5 cm
b) 2.5 cm
c) 1.67 cm
d) 1.5 cm
41.
In Young’s double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths `lamda_1` = 12000 `A^o` and `lamda_2` = 10000 `A^o` At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?
a) 8 mm
b) 6 mm
c) 4 mm
d) 3 mm
42.
A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?
a) Diffraction pattern is not observed on the screen in the case of electrons.
b) The angular width of the central maximum of the diffraction pattern will increase.
c) The angular width of the central maximum will decrease.
d) The angular width of the central maximum will be unaffected.
43.
In a n-type semiconductor, which of the following statement is true?
a) Electrons are majority carriers and trivalent atoms are dopants
b) Electron are minority carriers and pentavalent atoms are dopants
c) Holes are minority carriers and pentavalent atoms are dopants
d) Holes are majority carriers and trivalent atoms are dopants
44.
In a common emitter (CE) amplifier having a voltage gain G, the transistor used has transconductance 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance 0.02 mho and current gain 20, the voltage gain will be
a) `2/3 G`
b) `1.5 G`
c) `1/3 G`
d) `5/4 G`
45.
The output (X) of the logic circuit shown in figure will be
a) `X = bar bar A . bar bar B`
b) ` X = bar (AB)`
c) `X = A.B`
d) ` X = bar (A+B)`
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