JEE Mains 12 April 2019 Question Paper Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
12/04/2019
Evening
Page 2


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
12/04/2019
Evening
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. A uniform cylindrical rod of length L and radius
r, is made from a material whose Young’s
modulus of Elasticity equals Y. When this rod is
heated by temperature T and simultaneously
subjected to a net longitudinal compressional
force F, its length remains unchanged. The
coefficient of volume expansion, of the material
of the rod, is (nearly) equal to:
(1) 9F / ( ?r
2
YT)
(2) 3F / ( ?r
2
YT)
(3) F / (3 ?r
2
YT)
(4) 6F / ( ?r
2
YT)
Answer (2)
Sol.
FL FL
YL LT
A| L| AY
? ??? ? ?
?
F
AYT
??
2
3F
3
rYT
?? ? ?
?
2. A block of mass 5 kg is (i) pushed in case (A)
and (ii) pulled in case (B), by a force F = 20 N,
making an angle of 30° with the horizontal, as
shown in the figures. The coefficient of friction
between the block and floor is ? = 0.2. The
difference between the accelerations of the
block, in case (B) and case (A) will be :
(g = 10 ms
–2
)
30°
F = 20 N
(A)
30°
F = 20 N
(B)
(1) 0.4 ms
–2
(2) 3.2 ms
–2
(3) 0 ms
–2
(4) 0.8 ms
–2
Answer (4)
Sol. N = 60 N
F = 0.2 × 60 = 12 N
2
A
20 3
12
2
5.3
a1.06m/s
55
??
?
??
??
??
???
N
60°
30°
?N ? a
A
20 N
mg = 50 N
For B N = 40 N
B
20 3
F8N 8 5a
2
? ? ??
2
B
17.3 8 9.3
a1.86m/s
55
?
?? ?
a
B
 – a
A
 = 0.8 m/s
2
wavelengths, ?
1
/ ?
2
, of the photons emitted in
this process is
(1) 7/5
(2) 27/5
(3) 9/7
(4) 20/7
Answer (4)
Sol.
1
111 7
RR
916 144
??
?? ?
??
?
??
...(i)
2
111 5
RR
49 36
??
?? ?
??
?
??
...(ii)
?
11
22
5144 20
36 7 7
?? ?
?? ?
?? ?
4. A moving coil galvanometer, having a
resistance G, produces full scale deflection
when a current I
g
 flows through it. This
galvanometer can be converted into (i) an
ammeter of range 0 to I
0
(I
0
 > I
g
) by connecting
a shunt resistance R
A
 to it and (ii) into a
voltmeter of range 0 to V(V = GI
0
) by
connecting a series resistance R
V
 to it. Then,
3. The electron in a hydrogen atom first jumps
from the third excited state to the second
excited state and subsequently to the first
excited state. The ratio of the respective
Page 3


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
12/04/2019
Evening
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. A uniform cylindrical rod of length L and radius
r, is made from a material whose Young’s
modulus of Elasticity equals Y. When this rod is
heated by temperature T and simultaneously
subjected to a net longitudinal compressional
force F, its length remains unchanged. The
coefficient of volume expansion, of the material
of the rod, is (nearly) equal to:
(1) 9F / ( ?r
2
YT)
(2) 3F / ( ?r
2
YT)
(3) F / (3 ?r
2
YT)
(4) 6F / ( ?r
2
YT)
Answer (2)
Sol.
FL FL
YL LT
A| L| AY
? ??? ? ?
?
F
AYT
??
2
3F
3
rYT
?? ? ?
?
2. A block of mass 5 kg is (i) pushed in case (A)
and (ii) pulled in case (B), by a force F = 20 N,
making an angle of 30° with the horizontal, as
shown in the figures. The coefficient of friction
between the block and floor is ? = 0.2. The
difference between the accelerations of the
block, in case (B) and case (A) will be :
(g = 10 ms
–2
)
30°
F = 20 N
(A)
30°
F = 20 N
(B)
(1) 0.4 ms
–2
(2) 3.2 ms
–2
(3) 0 ms
–2
(4) 0.8 ms
–2
Answer (4)
Sol. N = 60 N
F = 0.2 × 60 = 12 N
2
A
20 3
12
2
5.3
a1.06m/s
55
??
?
??
??
??
???
N
60°
30°
?N ? a
A
20 N
mg = 50 N
For B N = 40 N
B
20 3
F8N 8 5a
2
? ? ??
2
B
17.3 8 9.3
a1.86m/s
55
?
?? ?
a
B
 – a
A
 = 0.8 m/s
2
wavelengths, ?
1
/ ?
2
, of the photons emitted in
this process is
(1) 7/5
(2) 27/5
(3) 9/7
(4) 20/7
Answer (4)
Sol.
1
111 7
RR
916 144
??
?? ?
??
?
??
...(i)
2
111 5
RR
49 36
??
?? ?
??
?
??
...(ii)
?
11
22
5144 20
36 7 7
?? ?
?? ?
?? ?
4. A moving coil galvanometer, having a
resistance G, produces full scale deflection
when a current I
g
 flows through it. This
galvanometer can be converted into (i) an
ammeter of range 0 to I
0
(I
0
 > I
g
) by connecting
a shunt resistance R
A
 to it and (ii) into a
voltmeter of range 0 to V(V = GI
0
) by
connecting a series resistance R
V
 to it. Then,
3. The electron in a hydrogen atom first jumps
from the third excited state to the second
excited state and subsequently to the first
excited state. The ratio of the respective
(1)
2
g 2 A
AV
V0g
I
R
RR Gand
RII
??
????
??
?
??
(2)
2
g0g 2 A
AV
0g V g
III
R
RR G and
II R I
?? ?? ?
?? ?? ??
?? ??
?
?? ??
(3)
g 2 A
AV
V0 g
I
R
RR G and
R(I I)
??
?
(4)
2
0g g 2 A
AV
gV0g
(I I ) I
R
RR G and
IR (II )
?? ?? ?
?? ?? ??
?? ??
?
?? ??
Answer (1)
Sol. V = I
g
(R
v
 + G) = GI
0
...(1)
(I
0 
– I
g
)R
A
 = I
g
G ...(2)
From (1), 
0g
v
g
G(II )
R
I
?
?
From (2), 
g
A
0g
IG
R
II
?
?
? R
A
R
V
 = G
2
??
???
??
?
??
2
g
A
V0g
I
R
RII
5. A spring whose unstretched length is l has a
force constant k. The spring is cut into two
pieces of unstretched lengths l
1
 and l
2
 where,
l
1
 = nl
2
 and n is an integer. The ratio k
1
/k
2
 of
the corresponding force constants, k
1
 and k
2
will be
(1) n
2
(2)
2
1
n
(3) n (4)
1
n
Answer (4)
Sol. l
1
 = nl
2
1
k
l
? ?
1 2
21
k l 1
kl n
?? ?
6. One kg of water, at 20°C, is heated in an
electric kettle whose heating element has a
mean (temperature averaged) resistance of 20 ?.
The rms voltage in the mains is 200 V. Ignoring
heat loss from the kettle, time taken for water to
evaporate fully, is close to
[Specific heat of water = 4200 J/(kg °C),
Latent heat of water = 2260 kJ/kg]
(1) 16 minutes (2) 3 minutes
(3) 22 minutes (4) 10 minutes
Answer (3)
Sol. ?Q = 1 × 4200 × 80 + 2260 × 10
3
 J
= (336 + 2260) × 10
3
 J = 2596 × 10
3
 J
?Q = I
rms
 V
rms
200
t 200 t 2000t
20
?? ?
?
2596
t s 21.6minutes 22minutes
2
?? ?
7. An electron, moving along the x-axis with an
initial energy of 100 eV, enters a region of
magnetic field 
?
??

3
ˆ
B(1.5 10 T) k at S (See
figure). The field extends between x = 0 and
x = 2 cm. The electron is detected at the point
Q on a screen placed 8 cm away from the point
S. The distance d between P and Q (on the
screen) is
(electron’s charge = 1.6 × 10
–19
 C, mass of
electron = 9.1 × 10
–31
 kg)
2 cm
8 cm
d
Q
P S
(1) 11.65 cm (2) 12.87 cm
(3) 2.25 cm (4) 1.22 cm
Answer (2)
Sol. Radius of path, ??
2mKE mv
R
eB eB
??
?
??
?? ? ? ?
??
??
?? ?
31 29
3
19 3
2 9.1 10 100e 2 9.1 10
m
e1.5 10
1.6 10 1.5 10
2 cm
Q
A
C
P
R
?
?
?
?
?
?? ?
?
5
3
3.37 10
100 cm 2.25 cm
1.5 10
?? ?
28
sin
2.25 9
Page 4


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
12/04/2019
Evening
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. A uniform cylindrical rod of length L and radius
r, is made from a material whose Young’s
modulus of Elasticity equals Y. When this rod is
heated by temperature T and simultaneously
subjected to a net longitudinal compressional
force F, its length remains unchanged. The
coefficient of volume expansion, of the material
of the rod, is (nearly) equal to:
(1) 9F / ( ?r
2
YT)
(2) 3F / ( ?r
2
YT)
(3) F / (3 ?r
2
YT)
(4) 6F / ( ?r
2
YT)
Answer (2)
Sol.
FL FL
YL LT
A| L| AY
? ??? ? ?
?
F
AYT
??
2
3F
3
rYT
?? ? ?
?
2. A block of mass 5 kg is (i) pushed in case (A)
and (ii) pulled in case (B), by a force F = 20 N,
making an angle of 30° with the horizontal, as
shown in the figures. The coefficient of friction
between the block and floor is ? = 0.2. The
difference between the accelerations of the
block, in case (B) and case (A) will be :
(g = 10 ms
–2
)
30°
F = 20 N
(A)
30°
F = 20 N
(B)
(1) 0.4 ms
–2
(2) 3.2 ms
–2
(3) 0 ms
–2
(4) 0.8 ms
–2
Answer (4)
Sol. N = 60 N
F = 0.2 × 60 = 12 N
2
A
20 3
12
2
5.3
a1.06m/s
55
??
?
??
??
??
???
N
60°
30°
?N ? a
A
20 N
mg = 50 N
For B N = 40 N
B
20 3
F8N 8 5a
2
? ? ??
2
B
17.3 8 9.3
a1.86m/s
55
?
?? ?
a
B
 – a
A
 = 0.8 m/s
2
wavelengths, ?
1
/ ?
2
, of the photons emitted in
this process is
(1) 7/5
(2) 27/5
(3) 9/7
(4) 20/7
Answer (4)
Sol.
1
111 7
RR
916 144
??
?? ?
??
?
??
...(i)
2
111 5
RR
49 36
??
?? ?
??
?
??
...(ii)
?
11
22
5144 20
36 7 7
?? ?
?? ?
?? ?
4. A moving coil galvanometer, having a
resistance G, produces full scale deflection
when a current I
g
 flows through it. This
galvanometer can be converted into (i) an
ammeter of range 0 to I
0
(I
0
 > I
g
) by connecting
a shunt resistance R
A
 to it and (ii) into a
voltmeter of range 0 to V(V = GI
0
) by
connecting a series resistance R
V
 to it. Then,
3. The electron in a hydrogen atom first jumps
from the third excited state to the second
excited state and subsequently to the first
excited state. The ratio of the respective
(1)
2
g 2 A
AV
V0g
I
R
RR Gand
RII
??
????
??
?
??
(2)
2
g0g 2 A
AV
0g V g
III
R
RR G and
II R I
?? ?? ?
?? ?? ??
?? ??
?
?? ??
(3)
g 2 A
AV
V0 g
I
R
RR G and
R(I I)
??
?
(4)
2
0g g 2 A
AV
gV0g
(I I ) I
R
RR G and
IR (II )
?? ?? ?
?? ?? ??
?? ??
?
?? ??
Answer (1)
Sol. V = I
g
(R
v
 + G) = GI
0
...(1)
(I
0 
– I
g
)R
A
 = I
g
G ...(2)
From (1), 
0g
v
g
G(II )
R
I
?
?
From (2), 
g
A
0g
IG
R
II
?
?
? R
A
R
V
 = G
2
??
???
??
?
??
2
g
A
V0g
I
R
RII
5. A spring whose unstretched length is l has a
force constant k. The spring is cut into two
pieces of unstretched lengths l
1
 and l
2
 where,
l
1
 = nl
2
 and n is an integer. The ratio k
1
/k
2
 of
the corresponding force constants, k
1
 and k
2
will be
(1) n
2
(2)
2
1
n
(3) n (4)
1
n
Answer (4)
Sol. l
1
 = nl
2
1
k
l
? ?
1 2
21
k l 1
kl n
?? ?
6. One kg of water, at 20°C, is heated in an
electric kettle whose heating element has a
mean (temperature averaged) resistance of 20 ?.
The rms voltage in the mains is 200 V. Ignoring
heat loss from the kettle, time taken for water to
evaporate fully, is close to
[Specific heat of water = 4200 J/(kg °C),
Latent heat of water = 2260 kJ/kg]
(1) 16 minutes (2) 3 minutes
(3) 22 minutes (4) 10 minutes
Answer (3)
Sol. ?Q = 1 × 4200 × 80 + 2260 × 10
3
 J
= (336 + 2260) × 10
3
 J = 2596 × 10
3
 J
?Q = I
rms
 V
rms
200
t 200 t 2000t
20
?? ?
?
2596
t s 21.6minutes 22minutes
2
?? ?
7. An electron, moving along the x-axis with an
initial energy of 100 eV, enters a region of
magnetic field 
?
??

3
ˆ
B(1.5 10 T) k at S (See
figure). The field extends between x = 0 and
x = 2 cm. The electron is detected at the point
Q on a screen placed 8 cm away from the point
S. The distance d between P and Q (on the
screen) is
(electron’s charge = 1.6 × 10
–19
 C, mass of
electron = 9.1 × 10
–31
 kg)
2 cm
8 cm
d
Q
P S
(1) 11.65 cm (2) 12.87 cm
(3) 2.25 cm (4) 1.22 cm
Answer (2)
Sol. Radius of path, ??
2mKE mv
R
eB eB
??
?
??
?? ? ? ?
??
??
?? ?
31 29
3
19 3
2 9.1 10 100e 2 9.1 10
m
e1.5 10
1.6 10 1.5 10
2 cm
Q
A
C
P
R
?
?
?
?
?
?? ?
?
5
3
3.37 10
100 cm 2.25 cm
1.5 10
?? ?
28
sin
2.25 9
PQ = PA + AQ
= 2.25 [1 – cos ?] + 11.64
= 1.22 + 11.64 = 12.86 cm
8. A Carnot engine has an efficiency of 
1
.
6
 When
the temperature of the sink is reduced by 62°C,
its efficiency is doubled. The temperatures of
the source and the sink are, respectively,
(1) 99°C, 37°C (2) 37°C, 99°C
(3) 124°C, 62°C (4) 62°C, 124°C
Answer (1)
Sol. ??
C
H
T 1
1
6T
? ?
C
H
T 5
T6
...(i)
?
??
C
H
(T62) 1
1
3T
?
?
?
C
H
T62 2
T3
...(ii)
? ?
??
?
C
C
T62 26 4
T355
? T
C
 = 310 K = 37°C
T
H
 = 372 K = 99°C
9. A small speaker delivers 2 W of audio output.
At what distance from the speaker will one
detect 120 dB intensity sound?
[Given reference intensity of sound as
10
–12
 W/m
2
]
(1) 30 cm (2) 40 cm
(3) 10 cm (4) 20 cm
Answer (2)
Sol.
?
?
10
12
I
120 10log
10
?
?
?
12
12
I
10
10
? I = 1 W/m
2
?
?
2
2
1
4r
? ??
?
2
r m 0.399 m
4
   = 40 cm
10. A system of three polarizers P
1
, P
2
, P
3
 is set up
such that the pass axis of P
3
 is crossed with
respect to that of P
1
. The pass axis of
P
2
 is inclined at 60°C to the pass axis of P
3
.
When a beam of unpolarized light of intensity I
0
is incident on P
1
, the intensity of light
transmitted by the three polarizers is I. The
ratio (I
0
/I) equals (nearly) :
(1) 1.80 (2) 5.33
(3) 10.67 (4) 16.00
Answer (3)
Sol. Angle between pass axes of P
1
 and P
2
 is 30°.
I
0
P
1
P
2
P
3
0
I
2
??
?
??
??
2 0
I
cos 30
2
??
?? ?
??
??
22 0
I
cos 30 cos 60
2
?? ?? ?? ? ? ?
22 000
II3I 31
I cos 30 cos 60
224432
? ??
0
I 32
10.67
I3
11. A solid sphere, of radius R acquires a terminal
velocity v
1
 when falling (due to gravity) through
a viscous fluid having a coefficient of viscosity
?. The sphere is broken into 27 identical solid
spheres. If each of these spheres acquires a
terminal velocity, v
2
, when falling through the
same fluid, the ratio 
??
??
??
1
2
v
v
 equals :
(1)
1
27
(2) 9
(3)
1
9
(4) 27
Answer (2)
Sol. R
3
 = 27r
3
? R = 3r
??
??
??
??
2
1
2
V R
9
Vr
12. Figure shows a DC voltage regulator circuit,
with a Zener diode of breakdown voltage
= 6 V. If the unregulated input voltage varies
between 10 V to 16 V, then what is the
maximum Zener current?
R = 4 k
L
?
I
L
I
Z
R = 2 k
S
?
I
S
(1) 7.5 mA (2) 1.5 mA
(3) 2.5 mA (4) 3.5 mA
Answer (4)
Page 5


Time : 3 hrs. M.M. : 360
Answers & Solutions
for for for for for
JEE (MAIN)-2019 (Online) Phase-2
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
4. Each question is allotted 4 (four) marks for each correct response. ¼ (one-fourth) marks will be deducted
for indicating incorrect response of each question. No deduction from the total score will be made if no
response is indicated for an item in the answer sheet.
5. There is only one correct response for each question.
(Physics, Chemistry and Mathematics)
12/04/2019
Evening
JEE (MAIN)-2019 (Online) Phase-2
PART–A : PHYSICS
1. A uniform cylindrical rod of length L and radius
r, is made from a material whose Young’s
modulus of Elasticity equals Y. When this rod is
heated by temperature T and simultaneously
subjected to a net longitudinal compressional
force F, its length remains unchanged. The
coefficient of volume expansion, of the material
of the rod, is (nearly) equal to:
(1) 9F / ( ?r
2
YT)
(2) 3F / ( ?r
2
YT)
(3) F / (3 ?r
2
YT)
(4) 6F / ( ?r
2
YT)
Answer (2)
Sol.
FL FL
YL LT
A| L| AY
? ??? ? ?
?
F
AYT
??
2
3F
3
rYT
?? ? ?
?
2. A block of mass 5 kg is (i) pushed in case (A)
and (ii) pulled in case (B), by a force F = 20 N,
making an angle of 30° with the horizontal, as
shown in the figures. The coefficient of friction
between the block and floor is ? = 0.2. The
difference between the accelerations of the
block, in case (B) and case (A) will be :
(g = 10 ms
–2
)
30°
F = 20 N
(A)
30°
F = 20 N
(B)
(1) 0.4 ms
–2
(2) 3.2 ms
–2
(3) 0 ms
–2
(4) 0.8 ms
–2
Answer (4)
Sol. N = 60 N
F = 0.2 × 60 = 12 N
2
A
20 3
12
2
5.3
a1.06m/s
55
??
?
??
??
??
???
N
60°
30°
?N ? a
A
20 N
mg = 50 N
For B N = 40 N
B
20 3
F8N 8 5a
2
? ? ??
2
B
17.3 8 9.3
a1.86m/s
55
?
?? ?
a
B
 – a
A
 = 0.8 m/s
2
wavelengths, ?
1
/ ?
2
, of the photons emitted in
this process is
(1) 7/5
(2) 27/5
(3) 9/7
(4) 20/7
Answer (4)
Sol.
1
111 7
RR
916 144
??
?? ?
??
?
??
...(i)
2
111 5
RR
49 36
??
?? ?
??
?
??
...(ii)
?
11
22
5144 20
36 7 7
?? ?
?? ?
?? ?
4. A moving coil galvanometer, having a
resistance G, produces full scale deflection
when a current I
g
 flows through it. This
galvanometer can be converted into (i) an
ammeter of range 0 to I
0
(I
0
 > I
g
) by connecting
a shunt resistance R
A
 to it and (ii) into a
voltmeter of range 0 to V(V = GI
0
) by
connecting a series resistance R
V
 to it. Then,
3. The electron in a hydrogen atom first jumps
from the third excited state to the second
excited state and subsequently to the first
excited state. The ratio of the respective
(1)
2
g 2 A
AV
V0g
I
R
RR Gand
RII
??
????
??
?
??
(2)
2
g0g 2 A
AV
0g V g
III
R
RR G and
II R I
?? ?? ?
?? ?? ??
?? ??
?
?? ??
(3)
g 2 A
AV
V0 g
I
R
RR G and
R(I I)
??
?
(4)
2
0g g 2 A
AV
gV0g
(I I ) I
R
RR G and
IR (II )
?? ?? ?
?? ?? ??
?? ??
?
?? ??
Answer (1)
Sol. V = I
g
(R
v
 + G) = GI
0
...(1)
(I
0 
– I
g
)R
A
 = I
g
G ...(2)
From (1), 
0g
v
g
G(II )
R
I
?
?
From (2), 
g
A
0g
IG
R
II
?
?
? R
A
R
V
 = G
2
??
???
??
?
??
2
g
A
V0g
I
R
RII
5. A spring whose unstretched length is l has a
force constant k. The spring is cut into two
pieces of unstretched lengths l
1
 and l
2
 where,
l
1
 = nl
2
 and n is an integer. The ratio k
1
/k
2
 of
the corresponding force constants, k
1
 and k
2
will be
(1) n
2
(2)
2
1
n
(3) n (4)
1
n
Answer (4)
Sol. l
1
 = nl
2
1
k
l
? ?
1 2
21
k l 1
kl n
?? ?
6. One kg of water, at 20°C, is heated in an
electric kettle whose heating element has a
mean (temperature averaged) resistance of 20 ?.
The rms voltage in the mains is 200 V. Ignoring
heat loss from the kettle, time taken for water to
evaporate fully, is close to
[Specific heat of water = 4200 J/(kg °C),
Latent heat of water = 2260 kJ/kg]
(1) 16 minutes (2) 3 minutes
(3) 22 minutes (4) 10 minutes
Answer (3)
Sol. ?Q = 1 × 4200 × 80 + 2260 × 10
3
 J
= (336 + 2260) × 10
3
 J = 2596 × 10
3
 J
?Q = I
rms
 V
rms
200
t 200 t 2000t
20
?? ?
?
2596
t s 21.6minutes 22minutes
2
?? ?
7. An electron, moving along the x-axis with an
initial energy of 100 eV, enters a region of
magnetic field 
?
??

3
ˆ
B(1.5 10 T) k at S (See
figure). The field extends between x = 0 and
x = 2 cm. The electron is detected at the point
Q on a screen placed 8 cm away from the point
S. The distance d between P and Q (on the
screen) is
(electron’s charge = 1.6 × 10
–19
 C, mass of
electron = 9.1 × 10
–31
 kg)
2 cm
8 cm
d
Q
P S
(1) 11.65 cm (2) 12.87 cm
(3) 2.25 cm (4) 1.22 cm
Answer (2)
Sol. Radius of path, ??
2mKE mv
R
eB eB
??
?
??
?? ? ? ?
??
??
?? ?
31 29
3
19 3
2 9.1 10 100e 2 9.1 10
m
e1.5 10
1.6 10 1.5 10
2 cm
Q
A
C
P
R
?
?
?
?
?
?? ?
?
5
3
3.37 10
100 cm 2.25 cm
1.5 10
?? ?
28
sin
2.25 9
PQ = PA + AQ
= 2.25 [1 – cos ?] + 11.64
= 1.22 + 11.64 = 12.86 cm
8. A Carnot engine has an efficiency of 
1
.
6
 When
the temperature of the sink is reduced by 62°C,
its efficiency is doubled. The temperatures of
the source and the sink are, respectively,
(1) 99°C, 37°C (2) 37°C, 99°C
(3) 124°C, 62°C (4) 62°C, 124°C
Answer (1)
Sol. ??
C
H
T 1
1
6T
? ?
C
H
T 5
T6
...(i)
?
??
C
H
(T62) 1
1
3T
?
?
?
C
H
T62 2
T3
...(ii)
? ?
??
?
C
C
T62 26 4
T355
? T
C
 = 310 K = 37°C
T
H
 = 372 K = 99°C
9. A small speaker delivers 2 W of audio output.
At what distance from the speaker will one
detect 120 dB intensity sound?
[Given reference intensity of sound as
10
–12
 W/m
2
]
(1) 30 cm (2) 40 cm
(3) 10 cm (4) 20 cm
Answer (2)
Sol.
?
?
10
12
I
120 10log
10
?
?
?
12
12
I
10
10
? I = 1 W/m
2
?
?
2
2
1
4r
? ??
?
2
r m 0.399 m
4
   = 40 cm
10. A system of three polarizers P
1
, P
2
, P
3
 is set up
such that the pass axis of P
3
 is crossed with
respect to that of P
1
. The pass axis of
P
2
 is inclined at 60°C to the pass axis of P
3
.
When a beam of unpolarized light of intensity I
0
is incident on P
1
, the intensity of light
transmitted by the three polarizers is I. The
ratio (I
0
/I) equals (nearly) :
(1) 1.80 (2) 5.33
(3) 10.67 (4) 16.00
Answer (3)
Sol. Angle between pass axes of P
1
 and P
2
 is 30°.
I
0
P
1
P
2
P
3
0
I
2
??
?
??
??
2 0
I
cos 30
2
??
?? ?
??
??
22 0
I
cos 30 cos 60
2
?? ?? ?? ? ? ?
22 000
II3I 31
I cos 30 cos 60
224432
? ??
0
I 32
10.67
I3
11. A solid sphere, of radius R acquires a terminal
velocity v
1
 when falling (due to gravity) through
a viscous fluid having a coefficient of viscosity
?. The sphere is broken into 27 identical solid
spheres. If each of these spheres acquires a
terminal velocity, v
2
, when falling through the
same fluid, the ratio 
??
??
??
1
2
v
v
 equals :
(1)
1
27
(2) 9
(3)
1
9
(4) 27
Answer (2)
Sol. R
3
 = 27r
3
? R = 3r
??
??
??
??
2
1
2
V R
9
Vr
12. Figure shows a DC voltage regulator circuit,
with a Zener diode of breakdown voltage
= 6 V. If the unregulated input voltage varies
between 10 V to 16 V, then what is the
maximum Zener current?
R = 4 k
L
?
I
L
I
Z
R = 2 k
S
?
I
S
(1) 7.5 mA (2) 1.5 mA
(3) 2.5 mA (4) 3.5 mA
Answer (4)
Sol. I
Z
 is maximum when input voltage is 16 V.
??
?
S
3
10
I5 mA
210
??
?
L
3
6
I1.5 mA
410
I
Z(max)
 = I
S
 – I
L
 = 3.5 mA
13. A smooth wire of length 2 ?r is bent into a
circle and kept in a vertical plane. A bead can
slide smoothly on the wire. When the circle is
rotating with angular speed ? about the
vertical diameter AB, as shown in figure, the
bead is at rest with respect to the circular ring
at position P as shown. Then the value of ?
2
 is
equal to:
O
A
r
r/2
B
?
P
(1)
??
g3
r
(2)
2g
r
(3)
??
2g
r3
(4)
3g
2r
Answer (3)
Sol.
P
?
N
?
mg
1
1
sin 30
2
?
?? ? ?
Ncos ? = mg ?(i)
2
mr
Nsin
2
?
?? ?(ii)
2
r
tan
2g
?
??
?
2
2gtan 2g
r
r3
?
?? ?
14. A transparent cube of side d, made of a
material of refractive index ?
2
, is immersed in
a liquid of refractive index ?
1
( ?
1
 < ?
2
). A ray is
incident on the face AB at an angle ?(shown in
the figure). Total internal reflection takes place
at point E on the face BC.
BE C
?
D A
?
1
 ?
2
Then ??must satisfy:
(1)
1 1
2
sin
?
?
??
?
(2)
1 1
2
sin
?
?
??
?
(3)
?
?
?? ?
?
2
1 2
2
1
sin 1 (4)
?
?
?? ?
?
2
1 2
2
1
sin 1
Answer (4)
Sol. ?
2
sinr
1
 > ?
1     
r
1
?
2
r
2
?
1
?
1
1
2
sinr
?
?
?
1 1
1
2
rsin
?
?? ?
?
??
?
??
?
1
sin ? = ?
2
sinr
2
 = ?
2
sin (90° – r
1
)
22
11
11
sin sin (90 r ) cosr
??
?? ? ? ?
??
?
22
21 1 2
12
sin
?
??
??? ?
?? ??
?? ??
??
?
2
1 2
2
1
sin 1
?
??
?
?? ? ??
?
??
??
15. A particle is moving with speed vbx ? along
positive x-axis. Calculate the speed of the
particle at time t = ? (assume that the particle
is at origin at t = 0).
(1) b
2
? (2)
2
b
4
?
(3)
2
b
2
?
(4)
2
b
2
?
Answer (3)