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2014 AIMPT - Physics
1.
If force (F), velocity (V) and time (T) are take As fundamental units, then the dimensions of mass are
a) `[F V T^(-1)]`
b) `[F V T^(-2)]`
c) `[F V^(-1) T^(-1)]`
d) `[F V^(-1) T]`
2.
A projectile is fired from the surface of the earth with a velocity of `5ms^(-1)` and angle `theta` with the horizontal. Another projectile fired another planet with a velocity of `3 ms^(-1)` at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in `ms^(-2)`) is: (given g = 9.8 `ms^(-2)`)
a) 3.5
b) 5.9
c) 16.3
d) 110.8
3.
A particle is moving such that its position coordinates (x,y)are
(2 m, 3 m) at time t = 0,
(6 m, 7 m) at time t = 2 s and
(13 m, 14 m) at time t = 5s
Average velocity vector (`vecV_(av)`) from t = 0 to t = 5 s is
a) `1/5 (13 hat i + 14 hat i)`
b) `7/3 (hat i + hat i)`
c) `2 (hat i + hat i)`
d) `11/5 (hat i + hat i)`
4.
A system consists of three masses m1, m2 and m3 connected by a strings passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction = u) the pulley if frictionless and of negligible mass. The downward acceleration of mass m1 is (Assue m1 = m2 = m3 = m)
a) `(g(1-gmu))/9`
b) `(2gmu)/3`
c) `(g(1-2mu))/3`
d) `(g(1-2mu))/2`
5.
The force ‘F’ acting on a particle of mass ‘m’ is indicated by the force – time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is
a) 24 Ns
b) 20 Ns
c) 12 Ns
d) 6 Ns
6.
A ballon with mass ‘m’ descending down with an acceleration ‘a’ (where a < g). how much mass should be removed from its so that it starts moving up with an acceleration ‘a’ ?
a) `(2ma)/(g+a)`
b) `(2ma)/(g-a)`
c) `(ma)/(g+a)`
d) `(ma)/(g-a)`
7.
A body of mass (4m) is laying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is
a) `mv^2`
b) `3/2 mv^2`
c) `2mv^2`
d) `4mv^2`
8.
The oscillation of a body on a smooth horizontal surface is represented by the equation, Where, `X = A cos (omega t)` ; X = displacement at time t;`omega`= frequency of oscillation Which one of the following graphs shows correctly the variation ‘a’ with ‘t’?
a) (1)
b) (2)
c) (3)
d) (4)
9.
A solid cylinder of mass 50 g and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions `s^(-2)` is
a) 25 N
b) 50 N
c) 78.5 N
d) 157 N
10.
The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’ rolling down an incline of angle ‘`theta`’ Without slipping and slipping down the incline with rolling is
a) 5 :7
b) 2:3
c) 2:5
d) 7:5
11.
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = `5.98 xx 10^24` kg) have to be compressed to be a black hole ?
a) `10^(-9)` m
b) `10^(-6)` m
c) `10^(-2)` m
d) 100 m
12.
Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by
a) (1)
b) (2)
c) (3)
d) (4)
13.
Copper of fixed volume ‘V’ is drawn into wire of length ‘l’. When the wire is subjected to a constant force ‘F’ the extension produced in the wire is'`Delta l `' . Which of the following graphs is a straight line?
a) `Delta`l versus 1/l
b) `Delta`l versus `l^2`
c) `Delta`l versus 1/`l^2`
d) `Delta`l versus l
14.
A certain number of spherical drops of liquid of radius ‘r’ coalesce to form a single drop of radius ‘R’ and volume ‘V’. if ‘T’ is the surface tension of the liquid, then
a) Energy = 4VT `(1/r - 1/R)` is released.
b) Energy = 3VT `(1/r + 1/R)` is absorbed.
c) Energy = 3VT `(1/r - 1/R)` is released.
d) Energy is neither released nor absorbed.
15.
Steam at `100^o`C is passed into 20 g of water at `10^o`C. when water acquires a temperature of 80oC the mass of water present will be [Take specific heat of water = 1 cal `g^(-1) C^(-1)` and latent heat of steam = 540 cal `g^(-1)`]
a) 24 g
b) 31.5 g
c) 42.5 g
d) 22.5 g
16.
Certain quantity of water cools from `70^o C` to `60^o C` in the first 5 minutes and to `54^oC` in the next 5 minutes. The temperature of the surroundings is
a) `45^o C`
b) `20^o C`
c) `42^o C`
d) `10^o C`
17.
A monoatomic gas at pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 V. the final pressure if the gas is (take `gamma` = 5/3)
a) 64 P
b) 32 Po
c) P/64
d) 16P
18.
A thermodynamic system undergoes cyclic process ABCDA as shown in Fig. the work done by the system in the cycle is
a) `P_oV_o`
b) `2P_oV_o`
c) `(P_oV_o)/2`
d) Zero
19.
The mean free path of molecules of a gas, radius is inversely proportional to
a) `r^3`
b) `r^2`
c) `r`
d) `sqrt(r)`
20.
If n₁,n₂ and n₃ are the fundamental frequencies three segments into which a string is divided, the original fundamental frequency n of the string is given by
a) `1/n = 1/n_1 + 1/n_2 +1/n_3`
b) `1/sqrt(n) = 1/sqrt(n_1) + 1/sqrt(n_2) +1/sqrt(n_3)`
c) `sqrt(n) = sqrt(n_1) + sqrt(n_2) +sqrt(n_3)`
d) `n = n_1 + n_2 +n_3`
21.
The number of possible natural oscillations of column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (velocity of sound = 340 `ms^(-1)`)
a) 4
b) 5
c) 7
d) 6
22.
A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km/hour. He finds the traffic has eased and a car moving ahead of him 18 km/hour is honking at a frequency of 1392 Hz. The speed of sound is 343 m/s, the frequency of the honk as heard by him will be
a) 1332 Hz
b) 1372 Hz
c) 1412 Hz
d) 1454 Hz
23.
Two think dielectric slabs of dielectric constants K1 and K2 (K1
a) (1)
b) (2)
c) (3)
d) (4)
24.
A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are
a) Zero and `Q/(4 pi epsilon_0 R^2)`
b) `Q/(4 pi epsilon_0 R^2)` and Zero
c) `Q/(4 pi epsilon_0 R)` and `Q/(4 pi epsilon_0 R^2)`
d) Both are Zero
25.
In a region the potential is represented by V(x,y,z) = 6x – 8xy – 8y + 6yz, where v is in volts and x, y, z are in meters. The electric force experienced by a change of 2 coulomb situated at point (1,1,1) is
a) `6 sqrt(5)` N
b) 30 N
c) 24 N
d) `4 sqrt(35)` N
26.
Two cities are 150 km apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is 8 volt and the average resistance per km is 0.5 `Omega` . The power loss in the wire is
a) 19.2 w
b) 19.2 kW
c) 19.2 J
d) 12.2 kW
27.
The resistances in the two arms of the meter bridge are 5 `Omega` and R `Omega` respectively, When the resistance. R is shunted with an equal resistance; the new balance point is at `1.6l_1`. the resistance ‘R’ is
a) 10 `Omega`
b) 15 `Omega`
c) 20 `Omega`
d) 25 `Omega`
28.
A potentiometer circuit has been set up for finding the internal resistance of given cell. The main battery, used across the potentiometer wire, has an emf of 2.0 V and a negligible internal resistance. The potentiometer wire itself is 4 m long. When the resistance R connected across the given cell, has values of.
(1) Infinity
(2) 9.5 `Omega`
The ‘balancing lengths’ on the potentiometer wire are found to be 3m and 2.85 m, respectively. The value of internal resistance of the cell is
a) 0.25 `Omega`
b) 0.95 `Omega`
c) 0.5 `Omega`
d) 0.75 `Omega`
29.
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment `vec m`. Which configuration has highest net magnetic dipole moment?
a) (a)
b) (b)
c) (c)
d) (d)
30.
In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be
a) `1/499 G`
b) `499/500 G`
c) `1/500 G`
d) `500/499 G`
31.
Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that ‘O’ is their common point for the two. The wires carry `I_1` and `I_2` currents, respectively. Point ‘P’ is lying at distance‘d’ from ‘O’ along a direction perpendicular to the plane containing the wires. The magnetic field at the point ‘P’ will be
a) `mu_o/(2pid)(l_1/l_2)`
b) `mu_o/(2pid)(l_1+l_2)`
c) `mu_o/(2pid)(l_1^2 - l_2^2)`
d) `mu_o/(2pid)(l_1^2 + l_2^2)^(1/2`
32.
A thin semicircular conducting ring (PQR) of radius ‘r’ is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v, is
a) Zero
b) `(Bv pi r^2)/2` and P is at higher potential
c) `pi rBv` and R is at higher potential
d) `2rBv` and R is at higher potentia
33.
A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6A, the voltage across the secondary coil and the current in the primary coil respectively are
a) 300 V, 15 A
b) 450 V, 15 A
c) 450 V, 13.5 A
d) 600 V, 15 A
34.
Light with an energy flux of `25 xx 10^4 Wm^(-2)` falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm2, the average force exerted on the surface is
a) `1.25 xx 10^(-6)` N
b) `2.50 xx 10^(-6)` N
c) `1.20 xx 10^(-6)` N
d) `3.0 xx 10^(-6)` N
35.
A beam of light of `lambda` = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is
a) 1.2 cm
b) 1.2 mm
c) 2.4 cm
d) 2.4 mm
36.
In the Young’s double – slit experiment, the intensity of light at a point on the screen where the path difference is `lamda` is K, (`lamda` being the wave length of light used). The intensity at point where the path difference is `lamda` /4 will be
a) K
b) K/4
c) K/2
d) Zero
37.
If the focal length of objective lens is increased then magnifying power of
a) Microscope will increase but that of telescope decrease.
b) Microscope and telescope both will increase.
c) Microscope and telescope both will decrease.
d) Microscope will decrease but that of telescope will increase.
38.
The angle of prism is ‘A’ One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index `mu` of the prism is
a) 2 sin A
b) 2 cos A
c) `1/2 cos A`
d) Tan A
39.
When the energy of the incident radiayion is increased by 20% the kinetic energy of the photoelectrons emitted from a metal surface increased from 0.5 eV to 0.8 eV. The work function of the metal is
a) 0.65 eV
b) 1.0 eV
c) 1.3 eV
d) 1.5 eV
40.
If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-broglie wavelength of the particle is
a) 25
b) 75
c) 60
d) 50
41.
Hydrogen atom in ground state is excited by a monochromatic radiation of `lamda` = 975 `A^o`. Number of spectral lines in the resulting spectrum emitted will be
a) 3
b) 2
c) 6
d) 10
42.
The Binding energy per nucleon of
3
7
Li and
2
4
He nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction
3
7
Li +
1
1
H `rarr`
2
4
He +
2
4
He + Q, the value of energy Q released is
a) 19.6 MeV
b) -2.4 MeV
c) 8.4 MeV
d) 17.3 MeV
43.
A radio isotope ‘X’ with a half life 1.4 x `10^9` years decays to ‘Y’ which is stable. A sample of the rock from a cave was found to contain ‘X’ and ‘Y’ in the ratio 1:7. The age of the rock is
a) 1.96 x `10^9` years
b) 3.92 x `10^9` years
c) 4.20 x `10^9` years
d) 8.40 x `10^9` years
44.
The given graph represents V – I charachteristics for semincondutor device. Which of the following statement is correct?
a) It is V – I characteristics for solar cell where point A represents open circuit voltage and point b short circuit current.
b) It is for s solar cell and points A and B represent open circuit voltage and current, respectively.
c) It is for a photodiode and points A and B represent open circuit voltage and current, respectively.
d) It is for LED and points A and B represent open circuit voltage and short circuit current, respectively.
45.
The barrier potential of a p – n junction depends on :
(a) Type of semi conductor material
(b) Amount of doping
(c) Temperature
Which one of the following is correct?
a) (a) and (b) only
b) (b) only
c) (b) and (c) only
d) (a),(b) and (c)
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