-
Q.1 to Q.45 carries one mark each, for which only one option is
correct. Any wrong answer
will lead to deduction of 1/3 mark.
1. A whistle whose air column is open at both ends
the speed of sound in air is 340 ms (A) 5/3 (B) 10/3 Ans:
(B)
Solution: f
Vlor
l
Vf
22;
2===
2. One mole of an ideal monoatomic gas is heated Then the change
in the internal energy of the gas is (Given R = 8.32 Jmol(A) 0.83
103 J (B) 4.6 10
Ans : (D)
Solution:
TnCU V 1==
3. The output Y of the logic circuit given below is,
Ans: (B)
Solution:
WBJEE-2014
Physics
Question with Solution
CATEGORY - I
one mark each, for which only one option is correct. Any wrong
answer
will lead to deduction of 1/3 mark.
A whistle whose air column is open at both ends has a
fundamental frequency of 5100 Hz. If is 340 ms1, the length of the
whistle, in cm, is
(C) 5 (D) 20/3
cmm3
10
30
1
51002
340==
One mole of an ideal monoatomic gas is heated at a constant
pressure from 0C to 100C. internal energy of the gas is (Given R =
8.32 Jmol1K
(B) 4.6 103 J (C) 2.08 103 J (D) 1.25 10
JR 310247.1100314.82
31100
2
3==
the logic circuit given below is,
one mark each, for which only one option is correct. Any wrong
answer
has a fundamental frequency of 5100 Hz. If
at a constant pressure from 0C to 100C. 1K1)
(D) 1.25 103 J
J
-
4. In which of the following pairs, the two physical quantities
have different dimensions? (A) Plancks constant and angular
momentum (B) Impulse and linear momentum (C) Moment of inertia and
moment of a force (D) Energy and torque Ans : (C)
Solution: Both moment of inertia and moment of a force are
physical quantities but have different units.
5. A small metal sphere of radius a is falling with a velocity
through a vertical column of a viscous liquid. If the coefficient
of viscosity of the liquid is , then the sphere encounters an
opposing force of
(A) 6a2 (B)
(C) 6a (D)
Ans : (C)
Solution : This is according to Stokes Law.
6. A cricket ball thrown across a field is at heights h1 and h2
from the point of projection at times t1 and t2 respectively after
the throw. The ball is caught by a fielder at the same height as
that of projection. The time of flight of the ball in this journey
is
(A)
(B)
(C)
(D)
Ans: (A)
Solution:
and
Or,
!
!
Or,
11221
221
221
1
1211
11
211
tth - th
t t- tt
t
h
2
t
g
h
t2
t
gt21
h
g2
gsin2u
T +
=
+=
+==
=
-
7. A smooth massless string passes over a smooth fixed pulley.
Two masses m1 and m2 (m1 > m2) are tied at the two ends of the
string. The masses are allowed to move under gravity starting from
rest. The total external force acting on the two masses is
(A) ( )gmm 21 + (B) gmm
mm
21
221 )(
+
(C) ( )gmm 21 (D) g
mm
mm
21
221 )(
+
Ans: (B)
Solution: gmm
mm2
21
21cma
+
= , therefore the total (resultant) force acting on the two
masses = ( )21 mm + gmm
mm
)(
)(a
21
221
cm +
=
8. To determine the coefficient of friction between a rough
surface and a block, the surface is kept
inclined at 45 and the block is released from rest. The block
takes a time t in moving a distance d.The rough surface is then
replaced by a smooth surface and the same experiment is repeated.
The block now takes a time t/2 in moving down the same distance d.
The coefficient of friction is
(A) 3/4 (B) 5/4 C) 1/2 (D) 1/ 2
Ans: (A)
Solution: The coefficient of friction 4
3
2
111
11 tan
22=
=
=n
9. A wooden block is floating on water kept in a beaker. 40% of
the block is above the water surface. Now the beaker is kept inside
a lift that starts going upward with acceleration equal to g/2. The
block will then (A) sink (B) float with 10% above the water surface
(C) float with 40% above the water surface (D) float with 70% above
the water surface
Ans : (C)
10. An electron in a circular orbit of radius 0.05 nm performs
1016 revolutions per second. The magnetic moment due to this
rotation of electron is (in Am2) (A) 2.16 1023 (B) 3.21 1022 (C)
3.21 1024 (D) 1.26 1023 Ans : (D)
Solution: Magnetic moment of the rotating electron M = iA = qfA
= (1.6 1019)(1016)(3.14 (0.05109)2) = 1.26 1023
-
11. A very small circular loop of radius a is initially (at t =
0) coplanar and concentric with a much larger fixed circular loop
of radius b. A constant current I flows in the larger loop. The
smaller loop is rotated with a constant angular speed about the
common diameter. The emf induced in the smaller loop as a function
of time t is
(A) )cos(2
a 02
tb
I
(B) )(sin
2
a 2202
tb
I
(C) )(sin2
a 02
tb
I
(D) )(sin
2
a 202
tb
I
Ans: (C)
Solution: The emf induced in the smaller loop as a function of
time t is given by
tNBA sin= where 20 a,2b
,1
=== AI
BN
Therefore, )(sina2b
.1 20 tI
= = )(sin2
a 02
tb
I
12. A drop of some liquid of volume 0.04 cm3 is placed on the
surface of a glass slide. Then another glass slide is placed on it
in such a way that the liquid forms a thin layer of area 20 cm2
between the surfaces of the two slides. To separate the slides a
force of 16105 dyne has to be applied normal to the surfaces. The
surface tension of the liquid is (in dyne-cm1)
(A) 60 (B) 70 (C) 80 (D) 90 Ans : (C)
Solution : Let thickness of layer is t
1
2
802
2
F liquid theof tension surface Therefore
2
2,,
=====
=====
cmdyneV
TAA
A
V
TA
r
TAP
r
TPAgain
A
Vr
A
Vror
A
VtorAtV
13. A proton of mass m and charge q is moving in a plane with
kinetic energy E. If there exists a uniform magnetic field B,
perpendicular to the plane of the motion, the portion will move in
a circular path of radius
(A) qB
2Em (B)
qB
2Em (C)
2qB
Em (D)
mB
2Eq
Ans: (B)
Solution: qB
2Em
qB
mv==r
-
14. In which of the following phenomena, the heat waves travel
along straight lines with the speed of light ? (A) thermal
conduction (B) forced convection (C) natural convection (D) thermal
radiation
Ans : (D)
15. An artificial satellite moves in a circular orbit around the
earth. Total energy of the satellite is
given by E. The potential energy of (A) 2E (B) 2E
Ans : (B)
Solution: P.E. = 2(T.E.) 16. A particle moves with constant
acceleration along a straight line starting from rest. The
percentage
increase in its displacement during the 4th second comp (A) 33%
(B) 40%
Ans : (B)
Solution:
S
SS Therefore
-a(2n2
1uS
3rd
4th
nth
+=
17. In the circuit shown assume the diode to be ideal. When Vin
the current is (in mA)
(A) zero (B) 20 Ans : (B)
Solution : Iinitial = 0 , Ifinal = 3/150 = 0.02A Therefore
change in I = 0.02A = 20 mA 18. In a transistor output
characteristics commonly used in common emitter configuration, the
base
current IB, the collector current Ifollowing orders of magnitude
in the active
(A) IB and IC both are in A and V(C) IB is in mA, and IC is in A
and VAns : (B)
In which of the following phenomena, the heat waves travel along
straight lines with the speed
(A) thermal conduction (B) forced convection (C) natural
convection (D) thermal radiation
15. An artificial satellite moves in a circular orbit around the
earth. Total energy of the satellite is energy of the satellite is
(C) 2E/3 (D) 2E/3
16. A particle moves with constant acceleration along a straight
line starting from rest. The percentage displacement during the 4th
second compared to that in the 3rd second is
(C) 66% (D) 77%
%40100S
2
7aS and
2
5aS1)-
3rd
4th3rd
=
==
In the circuit shown assume the diode to be ideal. When Vi
increases from 2 V to 6 V, the change
(B) 20 (C) 80/3
= 3/150 = 0.02A change in I = 0.02A = 20 mA
In a transistor output characteristics commonly used in common
emitter configuration, the base collector current IC and the
collector-emitter voltage VCE
following orders of magnitude in the active region both are in A
and VCE in Volts (B) IB is in A, and IC is in mA and V
is in A and VCE in mV (D) IB is in mA, and IC is in mA and V
In which of the following phenomena, the heat waves travel along
straight lines with the speed
(A) thermal conduction (B) forced convection (C) natural
convection (D) thermal radiation
15. An artificial satellite moves in a circular orbit around the
earth. Total energy of the satellite is
16. A particle moves with constant acceleration along a straight
line starting from rest. The percentage ared to that in the 3rd
second is
increases from 2 V to 6 V, the change
(D) 40
In a transistor output characteristics commonly used in common
emitter configuration, the base have values of the
is in mA and VCE in Volts is in mA and VCE in mV
-
19. If n denotes a positive integer, h the Plancks constant, q
the charge and B the magnetic field,
then the quantity
qB2nh
has the dimension of
(A) area (B) length (C) speed (D) acceleration Ans : (A)
Solution: [ ][ ]
[ ] [ ][ ]
[ ] [ ]22
2
r
r
mv
rmv
F
vmvr
qB
mvr
qB2=
===
nh
20. For the radioactive nuclei that undergo either or decay,
which one of the following cannot
occur ? (A) isobar of original nucleus is produced (B) isotope
of the original nucleus is produced (C) nuclei with higher atomic
number than that of the original nucleus is produced (D) nuclei
with lower atomic number than that of the original nucleus is
produced Ans : (B)
Solution: By emission of an particle, atomic number decreases by
two units and mass number decreases by four units that causes the
formation of isodiapher. By emission of a particle, atomic number
increases by one unit without any change of mass number with the
formation of isobar.
21. A car moving with a speed of 72 km-hour1 towards a roadside
source that emits sound at a frequency of 850 Hz. The car driver
listens to the sound while approaching the source and again while
moving away from the source after crossing it. If the velocity of
sound is 340 ms1,the difference of the two frequencies, the driver
hears is (A) 50 Hz (B) 85 Hz (C) 100 Hz (D) 150 Hz Ans : (C)
Solution:
Hz 10040340850
Therefore,
340
20340850 and
340
20340850
beaway movingwhen frequency theand frequency gapproachinLet
21
02
01
21
==
=
+=
+=
+=
=
V
VV
V
VV
-
22. Same quantity of ice is filled in each of the two metal
containers P and Q having the same size, shape and wall thickness
but made of different materials. The containers are kept in
identical surroundings. The ice in P melts completely in time t1
whereas that in Q takes a time t2. The ratio of thermal
conductivities of the materials of P and Q is (A) t2 : t1 (B) t1 :
t2 (C) t1
2 : t22 (D) t2
2 : t12
Ans : (A)
Solution:
1
2
2
1
t
t
K
K or,
t1
K thereforety,conductivi thermalK wheremL tdxdT
KA ==
23. Three capacitors, 3F, 6F and 6F are connected in series to a
source of 120V. The potential difference, in volts, across the 3F
capacitor will be (A) 24 (B) 30 (C) 40 (D) 60 Ans : (D)
Solution:
volts.60
6
1
6
1
3
13
1
120V or,
C
1V e, therefor
C
QV or, CVQ
=
++=
==
24. A galvanometer having internal resistance 10 requires 0.01 A
for a full scale deflection. To convert this galvanometer to a
voltmeter of full-scale deflection at 120V, we need to connect a
resistance of (A) 11990 in series (B) 11990 in parallel (C) 12010
in series (D) 12010 in parallel Ans : (A)
Solution: === 119901001.0
120R
I
VR g
g
25. Consider three vectors
is and of ratio The .C lar toperpendicu is
numbers) are and ( B A form theof XA vector .k4 j3 - i2 C and k
j - i B ,k2 - j iA
r
rrrrrr++=+=+=
(A) 1 : 1 (B) 2 : 1 (C) -1 : 1 (D) 3 : 1 Ans: (A)
Solution: 1 : 1 : Therefore,
09 9 - Or, 0,)24()3( - )2( Or, , 0C).B A(
=
=+=++=+
rrr
26. A parallel plate capacitor is charged and then disconnected
from the charging battery. If the plates
-
are now moved farther apart by pulling at them by means of
insulating handles, then (A) the energy stored in the capacitor
decreases (C) the charge on the capacitor decreases Ans : (D)
Solution: = Q ,C ,d ,d
AC 0
27. When a particle executing SHM oscillates with a frequency ,
then the kinetic energy of the particle (A) changes periodically
with a frequency of (C) changes periodically with a frequency of /2
Ans : (B)
28. The ionization energy of hydrogen is 13.6eV. The energy of
the photon released when an electron jumps from the first excited
state (n=2) to the ground state of a hydrog (A) 3.4 eV (B) 4.53 eV
Ans : (C)
Solution: 132
1
1
16.13
22=
29. One mole of a van der Waals gas obeying the
quasi-static cyclic process which is shown in in this process
is
(A) ( ) ( )2121 VVPP 21
(C) (22
221
1 V
aP
V
aP
2
1
+
Ans: (A)
Solution: For cyclic process, heat absorbed = Work done =Area
=
farther apart by pulling at them by means of insulating handles,
then(A) the energy stored in the capacitor decreases (B) the
capacitance of the capacitor increases
on the capacitor decreases (D) the voltage across the capacitor
increases
V ),(constatnt
27. When a particle executing SHM oscillates with a frequency ,
then the kinetic energy of the
(A) changes periodically with a frequency of (B) changes
periodically with a frequency of 2(C) changes periodically with a
frequency of /2 (D) remains constant
28. The ionization energy of hydrogen is 13.6eV. The energy of
the photon released when an electron excited state (n=2) to the
ground state of a hydrogen atom is
(B) 4.53 eV (C) 10.2 eV (D) 13.6 eV
eV 2.104
36.13 =
29. One mole of a van der Waals gas obeying the the equation (
)bVV
a P
2
+
process which is shown in the P-V diagram. The net heat absorbed
by the gas
(B) ( ) ( )2121 VVPP 21
+
( )21 VV (D) 22
221
1 V
aP
V
aP
2
1
+++
For cyclic process, heat absorbed = Work done =Area = ( 1 PP
21
farther apart by pulling at them by means of insulating handles,
then tance of the capacitor increases
(D) the voltage across the capacitor increases
27. When a particle executing SHM oscillates with a frequency ,
then the kinetic energy of the
(B) changes periodically with a frequency of 2 (D) remains
constant
28. The ionization energy of hydrogen is 13.6eV. The energy of
the photon released when an electron en atom is
) RT= undergoes the
V diagram. The net heat absorbed by the gas
( )21 VV
) ( )212 VVP
-
30. A scientist proposes a new temperature scale in which the
ice point is 25 X (X is the new unit of temperature) and the steam
point is 305 X. The specific heat capacity of water in this new
scale is (in Jkg1 X1) (A) 4.2103 (B) 3.010Ans : (D)
Solution: (30525)X = 100C, Sp. heat capacity of water = 4200
5.12.8X Kg
J 4200=
31. A metal rod is fixed rigidly at two ends so as to prevent
its thermal expansion. If L, and Y respectively denote the length
of the rod, coefficient of linear thermal expansion and Youngs
modulus of its material, then for an increase in stress developed
in the rod is (A) inversely proportional to
(C) directly proportional to Y
Ans : (D)
32. A uniform rod is suspended horizontally from its mid is
suspended at a distance l from the mid side at a distance l1 from
the mid completely immersed in water, W rod back into horizontal
position. The specific gravity of the metal piece is
(A)1W
W (B) 1
WWl
lW
Ans : (C)
33. A particle is moving uniformly in a circular path of radius
r. When it moves through an angular displacement , then the
magnitude of the corresponding
(A) 2
cosr 2
(B) cot r 2
Ans : (D)
30. A scientist proposes a new temperature scale in which the
ice point is 25 X (X is the new unit of steam point is 305 X. The
specific heat capacity of water in this new scale
(B) 3.0103 (C) 1.2103
25)X = 100C, Or, 1C = 2.8X, Sp. heat capacity of water = 4200
JKg-1. 0C-1
1-1-3 XKg J 10
31. A metal rod is fixed rigidly at two ends so as to prevent
its thermal expansion. If L, and Y length of the rod, coefficient
of linear thermal expansion and Youngs then for an increase in
temperature of the rod by T, the longitudinal
(A) inversely proportional to (B) inversely proportional to
Y
Y
T (D) independent of L
32. A uniform rod is suspended horizontally from its mid-point.
A piece of metal whose weight is W from the mid-point. Another
weight W1 is suspended on the other
from the mid-point to bring the rod to a horizontal position.
When completely immersed in water, W1 needs to be kept at a
distance l2 from the midrod back into horizontal position. The
specific gravity of the metal piece is
21
1
lW (C)
21
1
ll
l
(D)
2
1
l
l
33. A particle is moving uniformly in a circular path of radius
r. When it moves through an angular magnitude of the corresponding
linear displacement will be
2
cot
(C) 2
r tan 2
(D) 2
sin r 2
30. A scientist proposes a new temperature scale in which the
ice point is 25 X (X is the new unit of steam point is 305 X. The
specific heat capacity of water in this new scale
(D) 1.5103
31. A metal rod is fixed rigidly at two ends so as to prevent
its thermal expansion. If L, and Y length of the rod, coefficient
of linear thermal expansion and Youngs
temperature of the rod by T, the longitudinal
(B) inversely proportional to Y
(D) independent of L
point. A piece of metal whose weight is W is suspended on the
other
bring the rod to a horizontal position. When W is from the
mid-point to get the
33. A particle is moving uniformly in a circular path of radius
r. When it moves through an angular linear displacement will be
2
-
34. A luminous object is separated from a screen by distance d.
A convex lens is placed between the object and the screen such that
it forms a distinct image on the screen. The maximum possible focal
length of this convex lens is Ans : (D)
35. The intensity of magnetization of a bar magnet is 5.0 104
Am1. The magnetic length and the area of cross section of the
magnet are 12 cm and 1 cm2 respectively. The magnitude of magnetic
moment of this bar magnet is (in SI unit) (A) 0.6 (B) 1.3 (C) 1.24
(D) 2.4 Ans : (A)
Solution: 6.01060101210 5.0VIM Or, ,V
MI 264 =====
36. An infinite sheet carrying a uniform surface charge density
lies on the xy-plane. The work
done to carry a charge q from the point )k6 j2 - i( a Bpoint the
to)k3 j2 i( aA +=++=rr
is space) free ofy permitivit theis andlength ofdimension ith
theconstant w a is a (where 0
aq 3 (D)
2
aq 5 (C)
aq 2 (B)
2
aq 3 A)(
0000
Ans: (A)
Solution:
2
aq 3 )k3 j4 (- a .k
2 q done Work Therefore,
)k3 j4 (- aAB
00
=+
=
+=
37. A uniform solid spherical ball is rolling down a smooth
inclined plane from a height h. The velocity attained by the ball
when it reaches the bottom of the inclined plane is v. If the ball
is now thrown vertically upwards with the same velocity v, the
maximum height to which the ball will rise is (A) 5h/8 (B) 3h/5 (C)
5h/7 (D) 7h/9
Ans : (C)
Solution: mgh=
+
2
22
R
k1mv
2
1
Or, v = 7
h 10g
7
h5h Thus
h g2u v,projection alFor vertic
/
/22
=
=
-
38. Two coherent monochromatic beams of intensities I and 4I
respectively are superposed. The maximum and minimum intensities in
the resulting pattern are (A) 5I and 3I (B) 9I and 3I (C) 4I and I
(D) 9I and I Ans : (D)
Solution: 1
9
I
I3
I4I
I4I
I
I22
Min
Max =
=
+=
39. If the bandgap between valence band and conduction band in a
material is 5.0 eV, then the material is (A) semiconductor (B) good
conductor (C) superconductor (D) insulator
Ans : (D)
Solution : The band gap of 5 eV corresponds to that of an
insulator. 40. Consider a blackbody radiation in a cubical box at
absolute temperature T. If the length of each side of the box is
doubled and the temperature of the walls of the box and that of the
radiation is halved, then the total energy (A) halves (B) doubles
(C) quadruples (D) remains the same
Ans : (D)
Solution : Let us consider that the temperature of the body and
cubical box is same initially i.e. T Which finally becomes T/2.
Because temperature of body and surrounding remains same. Hence no
net loss of radiation occur through the body. Thus total energy
remains constant. 41. Four cells, each of emf E and internal
resistance r, are connected in series across an external resistance
R. By mistake one of the cells is connected in reverse. Then the
current in the external circuit is
(A) R4r
2E
+ (B)
R4r
3E
+ (C)
R3r
3E
+ (D)
R3r
2E
+
Ans: (A)
Solution: =+
=R4r
E-3E i
R4r
2E
+
42. The energy of gamma () ray photon is E and that of an X-ray
photon is Ex. If the visible light photon has an energy of Ev ,
then we can say that (A) Ex > E > Ev (B) E > Ev > Ex
(C) E > Ex > Ev (D) Ex > Ev > E Ans : (C )
-
43. The intermediate image formed by the (A) real, inverted and
magnified (C) virtual, erect and magnified
44. The displacement of a particle in a periodic motion is given
by
This displacement may be considered as the result of
superposition of n independent harmonic oscillations, Here n is (A)
1 (B) 2 Ans : (C)
Solution:
1) (1000sin t)(1000sin 2
t)(1000 sin 2t
cos4y 2
++=
=
=
45. Consider two concentric spherical metal shells of radii r
charge q and the inner one is grounded, the charge on the inner
shell is
(A) qr
r
1
2 (B)
Ans : (C)
Solution: ; 0 r
qk
r
qk
21
/
=+
Q.46 to Q.55 carry two marks each, for which only one option is
correct. Any wrong answer
will lead to deduction of 2/3 mark
46. A circuit consists of three batteries of emf E1 = 1 V, E2 =
2 V and E3 = 3 V and internal resistances 1 , 2 and 1 respectively
which are connected in parallel as shown in the figure. The
potential difference between points P
Ans: (B)
43. The intermediate image formed by the objective of a compound
microscope is(A) real, inverted and magnified (B) real, erect and
magnified(C) virtual, erect and magnified (D) virtual, inverted and
magnified
The displacement of a particle in a periodic motion is given by
2
t cos4y 2
=
considered as the result of superposition of n independent
harmonic
(C) 3 (D) 4
t)(1001sin t)(1000sin 2 t 1) (1000sin t 1)
t.cos 2 t)(1000sin 2 t)(1000sin t)cos1( 2
+=+
+=+=
spherical metal shells of radii r1 and r2 (r2 > r1). If the
outer shell has a one is grounded, the charge on the inner shell
is
(B) Zero (C) qr
r
2
1 (D)
qr
r q Or,
2
1/ =
CATEGORY - II
Q.46 to Q.55 carry two marks each, for which only one option is
correct. Any wrong answer
deduction of 2/3 mark.
46. A circuit consists of three batteries of emf E1 = 1 V, E2 =
2 V and E3 = 3 V and internal 1 respectively which are connected in
parallel as shown in the figure.
The potential difference between points P and Q is
objective of a compound microscope is (B) real, erect and
magnified (D) virtual, inverted and magnified
t).(1000 sin 2
t
considered as the result of superposition of n independent
harmonic
t)(999sin t)
t)(1000sin t.
+
). If the outer shell has a
q
Q.46 to Q.55 carry two marks each, for which only one option is
correct. Any wrong answer
46. A circuit consists of three batteries of emf E1 = 1 V, E2 =
2 V and E3 = 3 V and internal 1 respectively which are connected in
parallel as shown in the figure.
-
47. A solid uniform sphere resting on a rough horizontal plane
is given a horizontal impulse directed through its center so that
it starts sliding with an initial velocity without slipping the
speed of its
(A) 0V72
(C) 0V75
Ans: (C)
Solution: Along the point of conta
20 RV
mR5
2mVRRmV
+=
48. A long conducting wire carrying a current I is bent at
120(see figure). The magnetic field B at a point P on the right
bisector of bending angle at a distance d from the bend is (
permeability of free space)
(A) d 2
I3 0
d 3
I (C) 0
Ans: (D)
49. An object is placed 30 cm away from a convex lens of focal
length 10 cm and a sharp image is formed on a screen. Now a concave
lens is placed in contact with the convex lens. The screen now has
to be moved by 45 cm to get a concave lens is (in cm) (A) 72 (B) 60
Ans : (D)
Solution:
length ocalff( ,u
1
v
1
f
1
30
1
v
1
10
1 ,
u
1
v
1
f
1
/==
+==
47. A solid uniform sphere resting on a rough horizontal plane
is given a horizontal impulse directed that it starts sliding with
an initial velocity V0. When it finally starts rolling
without slipping the speed of its center is
(B) 0V73
(D) 0V76
Along the point of contact angular momentum will remain
conserved
0V7
5V ,, =Or
48. A long conducting wire carrying a current I is bent at
120(see figure). The magnetic field B at a bisector of bending
angle at a distance d from the bend is (
(B) d 2
I 0
d 2
I 3 (D) 0
49. An object is placed 30 cm away from a convex lens of focal
length 10 cm and a sharp image is Now a concave lens is placed in
contact with the convex lens. The screen
now has to be moved by 45 cm to get a sharp image again. The
magnitude of focal length of the
(C) 36 (D) 20
cm 20for 30
1
60
1
f
1 n),combinatio oflength
( vplaced is lens concave When cm. 15 v,30
1 /
=+=
==
47. A solid uniform sphere resting on a rough horizontal plane
is given a horizontal impulse directed . When it finally starts
rolling
erved.
48. A long conducting wire carrying a current I is bent at
120(see figure). The magnetic field B at a bisector of bending
angle at a distance d from the bend is (0 is the
49. An object is placed 30 cm away from a convex lens of focal
length 10 cm and a sharp image is Now a concave lens is placed in
contact with the convex lens. The screen
sharp image again. The magnitude of focal length of the
cm
cm 60)1545( =+
-
50. A 10 watt electric heater is used to heat a container filled
with 0.5 kg of water. It is found that the temperature of water and
the container rises by 3 K in 15 minutes. The container is then
emptied, dried and filled with 2 kg of oil. The same system by 2K
in 20 minutes. Assuming that there is no heat loss heat of water as
4200 Jkg1K
(A) 1.50103 (B) 2.5510Ans : (B)
Solution:
0
cc
cc
,12000)2900(C4
of caseIn .900)C(m
C(m342002
1
=+
+
Cc = Sp. heat capacity of container 51. A glass slab consists of
thin uniform layers of progressively decreasing refractive indices
RI (see figure) such that the RI of any layer is difference in RI
between any two consecutive denotes the numbers of the successive
layers. A ray of light from layer at an angle of incidence of 30.
After undergoing the m parallel to the interface. If = 1.5 and =
0.015, the value of m is
(A) 20 (B) 30 Ans : (D)
Solution: By Snells law, sin i = constant,
50 m
m5.1(43
,
=
=Or
50. A 10 watt electric heater is used to heat a container filled
with 0.5 kg of water. It is found that the and the container rises
by 3 K in 15 minutes. The container is then emptied,
kg of oil. The same heater now raises the temperature of
containerby 2K in 20 minutes. Assuming that there is no heat loss
in the process and the specific
1, the specific heat of oil in the same unit is equal(B) 2.55103
(C) 3.00103 (D) 5.1010
1-1-30
cc0
c
KKg J1055.2C ,
)6020(10 2)C(m)2C(2 oil, of
. 6015103)
=
=+
=
Or
Cc = Sp. heat capacity of container and C0 = Sp. heat capcity of
oil.
51. A glass slab consists of thin uniform layers of
progressively decreasing refractive indices RI (see RI of any layer
is -m. Here and denote the RI of 0
difference in RI between any two consecutive layers,
respectively. The integer m = 0, 1, 2, 3..... denotes the numbers
of the successive layers. A ray of light from the 0th layer enters
the 1layer at an angle of incidence of 30. After undergoing the mth
refraction, the ray emerges
interface. If = 1.5 and = 0.015, the value of m is
(C) 40 (D) 50
By Snells law, sin i = constant, 1.5 sin 30 = ( m) sin 90,
10.15) m
50. A 10 watt electric heater is used to heat a container filled
with 0.5 kg of water. It is found that the and the container rises
by 3 K in 15 minutes. The container is then emptied,
heater now raises the temperature of container-oil in the
process and the specific
, the specific heat of oil in the same unit is equal to (D)
5.10103
)
51. A glass slab consists of thin uniform layers of
progressively decreasing refractive indices RI (see m. Here and
denote the RI of 0th layer and the
, respectively. The integer m = 0, 1, 2, 3..... layer enters the
1st
refraction, the ray emerges
m) sin 90,
-
52. The de-Broglie wavelength of an electron is the same as that
of a 50 keV X of the energy of the photon to the kinetic energy of
the electron is (the energy equivalent of electron mass is 0.5 MeV)
(A) 1 : 50 (B) 1 : 20 Ans : (C)
53. Three identical square plates rotate about the axes shown in
the figure in such a way that their kinetic energies are equal.
Each of the rotation axes passes through the centre of the square.
Then the ratio of angular speeds
(A) 1 : 1 : 1 (B) 2 : 2 :1 Ans : (B)
Solution:
::,
Therefore, ,2
1
321
2
=
=
Or
IK
54. To determine the composition of a bimetallic alloy, a sample
is first weighed in air and then in water. These weights are found
to be w constituent metals are 1 and (where w is the density of
water)
[ w2112w
1 w)(w)(
(A)
[ w2112w
1 w)(w)(
(C) +
Ans: (A)
55. Sound waves are passing through two routes semicircular path
of radius r and are again combined into one pipe and superposed as
shown in the figure. If the velocity of sound waves in the pipe
maximum amplitude will be integral multiples of
Broglie wavelength of an electron is the same as that of a 50
keV X-ray photon. The ratio photon to the kinetic energy of the
electron is (the energy equivalent of
(C) 20 : 1 (D) 50 : 1
Three identical square plates rotate about the axes shown in the
figure in such a way that equal. Each of the rotation axes passes
through the centre of the angular speeds 1 : 2 : 3 is
2 : 2 :1 (C) 1 : 2 : 1 (D) 1: 2 : 2
1:2:22
1:1:1
1 Therefore,
==
I
54. To determine the composition of a bimetallic alloy, a sample
is first weighed in air and then in found to be w1 and w2
respectively. If the densities of the two and 2 respectively, then
the weight of the first metal in the sample is
is the density of water)
]22w [ w2112w
1 (w)(
(B)
+
]12w [ w1112w
1 (w)(
(D)
55. Sound waves are passing through two routes-one in straight
path and the other along a and are again combined into one pipe and
superposed as shown in
the figure. If the velocity of sound waves in the pipe is v,
then frequencies of resultant waves of maximum amplitude will be
integral multiples of
ray photon. The ratio photon to the kinetic energy of the
electron is (the energy equivalent of
Three identical square plates rotate about the axes shown in the
figure in such a way that equal. Each of the rotation axes passes
through the centre of the
54. To determine the composition of a bimetallic alloy, a sample
is first weighed in air and then in respectively. If the densities
of the two
weight of the first metal in the sample is
]22w w) +
]12w w)
one in straight path and the other along a and are again
combined into one pipe and superposed as shown in
is v, then frequencies of resultant waves of
-
2)-(r
V (A)
1)-(r V
(B) 1)-(r
2V (C)
1)(r V
(D)+
Ans: (A)
Solution: Path difference = (r 2r) = r( 2) = n Again velocity V
= where is the frequency.
2)-(r
V Or,
V Therefore, == n
CATEGORY - III
Q.56 to Q.60 carry two marks each, for which one or more than
one options may be correct.
Marking of correct options will lead to a maximum mark of two on
pro rata basis. There will
be no negative marking for these questions. However, any marking
of wrong option will lead to
award of zero mark against the respective question irrespective
of the number of correct
options marked.
56. Find the correct statement(s) about photoelectric effect (A)
There is no significant time delay between the absorption of a
suitable radiation and the emission of electrons (B) Einstein
analysis gives a threshold frequency above which no electron can be
emitted (C) The maximum kinetic energy of the emitted
photoelectrons is proportional to the frequency of incident
radiation (D) The maximum kinetic energy of electrons does not
depend on the intensity of radiation Ans : (A & D)
57. A thin rod AB is held horizontally so that it can freely
rotate in a vertical plane about the end A as shown in the figure.
The potential energy of the rod when it hangs vertically is taken
to be zero. The end B of the rod is released from rest from a
horizontal position. At the instant the rod makes an angle with the
horizontal.
-
(A) the speed of end B is proportional to sin (B) the potential
energy is proportional to (1 cos ) (C) the angular acceleration is
proportional to cos (D) the torque about A remains the same as its
initial value Ans : (A,C)
58. A stream of electrons and protons are directed towards a
narrow slit in a screen (see figure). The intervening region has a
uniform electric field E (vertically downwards) and a uniform
magnetic field B (out of the plane of the figure) as shown.
Then
speed their of veirrespecti upwards deflected be always
willelectrons (D)
speed their of veirrespectislit he through tgo willprotonsnor
electronsneither (C)
not willspeed same theof electrons slit, he through tpass will
B
E speed with protons (B)
slit he through tpass will B
E speed with protons and electrons (A)
r
r
r
r
Ans: (C, D)
59. A heating element of resistance r is fitted inside an
adiabatic cylinder which carries a frictionless piston of mass m
and cross-section A as shown in diagram. The cylinder contains one
mole of an ideal diatomic gas. The current flows through the
element such that the temperature rises with
Then, .P ispiston theabove pressure catmospheri
The constant. remains pressure while,constants) are and ( t2
1 t T as t time
0
2 +=
speedconstant with upwards movespiston the(D)
onacceleraticonstant with upwards movespiston the(C)
t) ( Rr 2
5 iselement theflowingcurrent the(B)
t) ( R2
5 isenergy internalin increase of rate The (A)
+
+
Ans : (A & C)
-
60. Half of the space between the plates of a parallel-plate
capacitor is filled with a dielectric material of dielectric
constant K. The remaining half contains air as shown in the figure.
The capacitor is now given a charge Q. Then
removed. dielectricwith capacitor
same theof ecapacitanc theis C where2
CK)(1 is aboveshown capacitor theof ecapacitanc (D)
1KQ
ispart filled-air theabove plate top theof half on the charge
(C)
unequal are densities charge theplate bottom theof halves twoon
the (B)
region filled-air in then that higher tha isregion
filled-dielectric in the field electric (A)
00+
+
Ans: (B, C, D)
