SET
A : PHYSICS |
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Directions:
Questions number 1 - 3 are based on the following paragraph.
An initially parallel cylindrical beam travels in a medium
of refractive index  (I)
= 
+ 2I,
where
and 2
are positive constants and I is the intensity of the light
beam. The intensity of the beam is decreasing with increasing
radius. |
| 1. |
The
initial shape of the wavefront of the beam is |
| (1) |
planar |
| (2) |
convex |
| (3) |
concave |
| (4) |
convex near the
axis and concave near the periphery |
| Soln: |
Initially parallel cylindrical beam travels. So, Initial shape of the wavefront of the beam is Planar.
Hence, the answer is option (1). |
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| 2. |
The speed of light
in the medium is |
| (1) |
maximum on the
axis of the beam |
| (2) |
minimum on the
axis of the beam |
| (3) |
the same everywhere
in the beam |
| (4) |
directly proportional
to the intensity |
| Soln: |
Speed of light is increasing with increment in radius. So the velocity of light is minimum on the axis.
Hence, the answer is
option (2). |
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| 3. |
As the beam enters
the medium, it will |
| (1) |
travel as a cylindrical
beam |
| (2) |
diverge |
| (3) |
convorge |
| (4) |
diverge near the
axis and converge near the periphery |
| Soln: |
The RI of the
medium is (I)
= 0
+ I
is decreasing with increase in radius. Therefore RI is
decreasing with radius. Hence, the velocity of light will
increase, hence the beam will diverge.
Hence, the answer is
option (2). |
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Directions:
Questions number 4—5 are based on the following
paragraph.
A nucleus of mass M +  m
is at rest and decays into two daughter nuclei of equal
mass 
each. Speed of light is c. |
| 4. |
The speed of daughter
nuclei is |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Initial velocity
of nucleus is = 0
therefore kinetic energy of daughter nuclei = Energy
radiated
Hence, the answer is option (3).
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| 5. |
The binding energy
per nucleon for the parent nucleus is E and that for the
daughter nuclei is E Then |
| (1) |
E1 =
2E2 |
| (2) |
E2 =
2E1 |
| (3) |
E1 >
E2 |
| (4) |
E2 >
E1 |
| Soln: |
No of daughter nucleons in daughter nuclei is less than that of parent nucleus.
Hence E2 >
E1.
Hence, the answer is option (4). |
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Directions
: Question number. 6—7 contain Statement-1 and
Statement-2. Of the four choices given after the statements,
choose the one. that best describes the two statements. |
| 6. |
Statement
- 1: When ultraviolet light is incident on a
photocell, its stopping potential is v0 and
the maximum kinetic energy of the photoelectrons is Kmax.
When the ultraviolet light is replaced by X-rays, both
v0 and Kmax increase.
Statement
- 2: Photoelectrons are emitted with speeds ranging
from zero to a maximum value because of the range of frequencies
prelent in the incident light. |
| (1) |
Statement-1 is
true, Statement-2 is false. |
| (2) |
Statement-1 is
true, Statement-2 is true; Statement-2 is the correct
explanation of Statement-1. |
| (3) |
Statement-1 is
true, Statement-2 is true; Statement-2 is not
the correct explanation of Statement-1. |
| (4) |
Statement-1. is
false, Statement-2 is true. |
| Soln: |
According to photoelectric equation,  . if v increases Kmax will increase and v0 increases. We know  . So statement 1 is correct. If v < v0 then no electron will be emitted.
Hence, the answer is option (1). |
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| 7. |
Statement-1:
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement-2: Principle of conservation
momentum holds true for all kinds collisions. |
| (1) |
Statement-1 is
true, Statement-2 is false. |
| (2) |
Statement-1 is
true, Statement-2 is true; Statement-2 is the correct
explanation of Statement-1. |
| (3) |
Statement-1 is
true, Statement-2 is true; Statement-2 is not the correct
explanation of Statement-1. |
| (4) |
Statement-1 is
false, Statement-2 is true. |
| Soln: |
In compeletly inelastic collision particles loses all the kinetic energy will be transferred into another form of the energy. Principle of conservation of momentum holds true for all kinds of collision.
Hence, the answer is option (2). |
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| 8. |
The figure shows
the position — time (x — t) graph of one-dimensional
motion of a body of mass O kg. The magnitude of each impulse
is
|
| (1) |
0.2 Ns |
| (2) |
0.4 Ns |
| (3) |
0.8 Ns |
| (4) |
1.6 Ns |
| Soln: |
Impulse = force
x time = F x a x t
Here, t = 2 sec, m = 0.4 kg, from second kinematical
equation,
Therefore Impulse = 0.4 x 1 x 2 = 0.8 Ns.
Hence, the answer is option (3).
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| 9. |
Two long parallel
wires are at a distance 2d apart. They carry steady equal
currents flowing out of the plane of the paper as shown.
The variation of the magnetic field B along the line XX'
is given by |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
At the mid point of the two wires, magnetic field will be zero.
Hence, the answer is
option (2). |
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| 10. |
A ball is made
of a material of density 
where oil
< <
water
with oil
and water
representing the densities of oil and water, respectively.
The oil and water are immiscible. If the above ball is
in equilibrium in a mixture of this oil and water, which
of the following pictures represents its equilibrium position? |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
We have oil
< <
water
So, the ball will float on water and sink into oil. Water
is heavier than the oil will float on water and ball remain
between the water and oil.
Hence, the answer is option (3). |
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| 11. |
A thin semi-circular
ring of radius r has a positive charge q distributed uniformly
over it. The net field E at the centre O is
|
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Hence, the answer is option (4). |
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| 12. |
A diatomic ideal
gas is used in a Carnot as the working substance. If during
the adiabatic expansion part of the cycle the volume of
the gas increases from V to 32 V, the efficiency of the
engine is |
| (1) |
025 |
| (2) |
0.5 |
| (3) |
0.75 |
| (4) |
0.99 |
| Soln: |
Hence, the answer is option (3). |
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| 13. |
The respective
number of significant figures for the numbers 23.023,
0.0003 and
2.1 x10-3 are
|
| (1) |
4, 4, 2 |
| (2) |
5, 1, 2 |
| (3) |
5, 1, 5 |
| (4) |
5, 5, 2 |
| Soln: |
Significant figure for 23.023 = 5
Significant figure for 0.0003 = 1
Significant figure for 2.1 x 10-3 = 2
Hence, the answer is option (2). |
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| 14. |
The combination
of gates shown below yields
|
| (1) |
NAND gate |
| (2) |
OR gate |
| (3) |
NOT gate |
| (4) |
XOR gate |
| Soln: |
Hence, the answer is option (2). |
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| 15. |
If a source of
power 4 kW produces 1020 photons/second, the
radiation belongs to a part of the spectrum called |
| (1) |
y-rays |
| (2) |
X-rays |
| (3) |
ultraviolet rays |
| (4) |
microwaves |
| Soln: |
Power of the source = 4kW = 4 x 103.
Energy in 1 second =
Number of photons in 1 second = 1020 = n.
Therefore the energy of each photons = hv = E/n =
Hence, the answer is option (2). |
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| 16. |
A radioactive
nucleus (initial mass number A and atomic number Z) emits
3 
- particles and 2 positrons. The ratio of number of neutrons
to that of protons in the final nucleus will be |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Hence, the answer is option (3). |
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| 17. |
Let there be a
spherically symmetric charge distribution with charge
density varying as
upto r = R, and for P(r)=0 for r > R, where r is the
origin.
The electric field at a distance r(r < R) from the origin the distance
from field at a. distance is given by |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Hence, the answer is option (3). |
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| 18. |
In a series LCR
circuit B = 200 
and the voltage and the frequency of the main
supply is 220 V and 50 Hz respectively. On taking out
the capacitance from the circuit the current lags behind
the voltage by 300. On taking out the inductor
from the circuit the current leads the voltage by 300.
The power dissipated in the LCR circuit is |
| (1) |
242 W |
| (2) |
305 W |
| (3) |
210 W |
| (4) |
Zero W |
| Soln: |
In a series resonant circuit, XC = XL
Hence, the answer is option (1). |
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| 19. |
In the circuit
shown below, the key K is closed at t = 0. The current
through the battery is
|
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Growth of current in an inductor is 
Therefore at t = 0 I = 0. Therefore no current passes through inductor and through R1.
Therefore t =  , is maximum .
The
Hence, the answer is option (3). |
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| 20. |
A particle is
moving with velocity
 ,
where K is a constant.
The general equation for its path is |
| (1) |
y2 =
x2 + constant |
| (2) |
y = x2
constant |
| (3) |
y2 =
x + constant |
| (4) |
xy = constant |
| Soln: |
Hence, the answer is option (1). |
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| 21. |
Let C be the capacitance
of a capacitor discharging through a resistor B. Suppose
t1 is the time taken for the energy stored
in the capacitor to reduce to half its initial value and
t2 is the time taken for the charge to reduce
to one-fourth its initial value,
Then the ration t1/t2 |
| (1) |
2 |
| (2) |
1 |
| (3) |
1/2 |
| (4) |
1/4 |
| Soln: |
Energy stored  Energy is half of initial value. We have  We have
Therefore In time t2 charge reduces to half of its original value.
Therefore 
Hence, the answer is option (4). |
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| 22. |
A rectangular
loop has a sliding connector PQ of length 1 and resistance
R
and it is moving with a speed v as shown. The set-up is
placed in a uniform magnetic field going into the plane
of the paper. The three currents I1, I2
and I are
|
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Hence, the answer is option (3). |
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| 23. |
The equation of
a wave on a string of linear mass density 0.04 kg m-1
is given by
The tension in the string is |
| (1) |
6.25 N |
| (2) |
4.0 N |
| (3) |
12.5 N |
| (4) |
0.5 N |
| Soln: |
We have, 
m
= 0.04 kg/m.
From equation  Therefore
Therefore velocity of the wave 
Therefore T = 6.25N.
Hence, the answer is option (1). |
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| 24. |
Two fixed frictionless
inclined planes making an angle 30° and. 60° with
the. vertical are shown in the figure. Two blocks A and
B are placed on the two planes. What is the relative vertical
acceleration of A with respect B?
|
| (1) |
4.9 ms-2
in vertical direction |
| (2) |
4.9 ms-2
in horizontal direction |
| (3) |
9.8 ms-2
in vertical direction |
| (4) |
Zero |
| Soln: |
vertical acceleration
of A and B is g. Hence relative vertical acceleration
of B with respect to A is zero.
Hence, the answer is option (4). |
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| 25. |
For a particle
in uniform circular motion, the acceleration 
at point P (R,  )
on the circle of radius R is (Here
is measured from the x-axis) |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
towards the centre .
therefore the horizontal acceleration
= 
and
vertical = 
Hence, the answer is option (4). |
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| 26. |
A small particle
of mass m is projected at an angle ? with the k-axis with
an initial velocity v0 in the x-y plane as
shown in the figure. At a time 
the angular momentum of the particle is
|
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
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Where 
are unit vectors along x, y and z - axis respectively. |
| Soln: |
Hence, the answer is option (4). |
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| 27. |
Two identical
charged spheres are suspended by strings of equal lengths.
The strings make an angle of 30° with each other.
When suspended in a liquid of density 0.8 g cm-3
the angle remains the same. If density of the material
of the sphere is 1.6 g cm-3 the dielectric
constant of the liquid is |
| (1) |
1 |
| (2) |
4 |
| (3) |
3 |
| (4) |
2 |
| Soln: |
. Therefore tan15
= F/W. When sphere are suspended in liquid of density
and dielectric constant k then 
Hence, the answer is option (4). |
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| 28. |
A point P moves
in. counter-clockwise direction on a circular path as
shown in the figure. The movement of P’ is such
that it sweeps out a length s = t3 + 5, where
s is in meters and t is in seconds. The radius of the
path is 20 m. The acceleration of ‘P’ when
t=2s is nearly
|
| (1) |
14 m/s2 |
| (2) |
13 m/s2 |
| (3) |
12 m/s2 |
| (4) |
7.2 m/s2 |
| Soln: |
Hence, the answer is option (1). |
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| 29. |
The potential
energy function for the force between two atoms in a diatomic
molecule is approximately given by U(x) = 
where a and b are constants and x is the dissociation
energy of the molecule is D = [U (x = )
- Uat equilibrium], D is |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
At equilibrium
Therefore D = 0 – U at equilibrium 
Hence, the answer is option (4). |
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| 30. |
Two conductors
have the same resistance at 00C but their temperature
coefficients of resistance are 1
and 2.
The respective temperature coefficients of their series
and parallel combinations are nearly |
| (1) |
 |
| (2) |
 |
| (3) |
 |
| (4) |
 |
| Soln: |
Resistances
in 
Hence, the answer is option (1). |
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Disclaimer:
The information on this page is relevant to educational
and instructive learning along with the understanding
of the statistics and facts of the various Engineering, Medical, Management & Law
entrance exams being conducted across the country.
‘To err is human to forgive divine’.
The data reproduced here is true, valid and to
the best of our students’ knowledge but
our students too are human.
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