Test series - Notes - JEE

 Page 1


FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
FIITJEE 
 
ALL INDIA TEST SERIES 
 
FULL TEST – II 
 
JEE (Main)-2020 
 
TEST DATE: 22-12-2019 
 
Time Allotted: 3 Hours Maximum Marks: 300 
 
General Instructions: 
 
?  The test consists of total 75 questions.  
?  Each subject (PCM) has 25 questions.  
?  This question paper contains Three Parts. 
?  Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 
?  Each part has only three sections: Section-A, Section-B and Section-C.     
   Section-A (01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one 
 correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong 
 answer. 
 
  Section-B (21 – 22, 46 – 47, 71 – 72) contains 6 Numerical based questions with answer as 
 numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no 
 negative marking.  
 
 Section-C (23 – 25, 48 – 50, 73 – 75) contains 9 Numerical answer type questions with answer 
XXXXX.XX and each question carries +4 marks for correct answer. There is no negative marking.  
Page 2


FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
FIITJEE 
 
ALL INDIA TEST SERIES 
 
FULL TEST – II 
 
JEE (Main)-2020 
 
TEST DATE: 22-12-2019 
 
Time Allotted: 3 Hours Maximum Marks: 300 
 
General Instructions: 
 
?  The test consists of total 75 questions.  
?  Each subject (PCM) has 25 questions.  
?  This question paper contains Three Parts. 
?  Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 
?  Each part has only three sections: Section-A, Section-B and Section-C.     
   Section-A (01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one 
 correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong 
 answer. 
 
  Section-B (21 – 22, 46 – 47, 71 – 72) contains 6 Numerical based questions with answer as 
 numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no 
 negative marking.  
 
 Section-C (23 – 25, 48 – 50, 73 – 75) contains 9 Numerical answer type questions with answer 
XXXXX.XX and each question carries +4 marks for correct answer. There is no negative marking.  
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
2 
P Ph hy ys si ic cs s PART – I 
  
  
SECTION – A  
(One Options Correct Type) 
 
 
This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and 
(D), out of which ONLY ONE option is correct.  
 
1. During a rainy day, rain is falling vertically down with a velocity 2 m/s. A boy at rest starts his 
motion with a constant acceleration of 2 m/s
2
 along a straight road. Find the rate at which the 
angle of the axis of the umbrella with vertical should be changed so that the rain always appears 
to fall parallel to the axis of the umbrella.  
 (A)  
2
1
1 t ?
  
 (B)  
2
2
1 t ?
 
 (C)  
2
1
2 t ?
  
 (D)  
2
1
1 2t ?
 
 
2. Power versus time graph for a given force is shown in the 
figure. Then work done by the force upto time t( ? t
0
).  
 (A)  First increases then decreases.  
 (B)  First decreases then increases.  
 (C)  Always increases.  
 (D)  Always decreases.  
 
 
t
 
 
t
0 
 
P
 
 
 
 
3. A cobalt (atomic no. = 27) target is bombarded with electrons and the wave lengths of its 
characteristic X-rays spectrum are measured. A second weak characteristic spectrum is also 
found due to an impurity in the target. The wavelength of the K
?
 lines are 225.0 pm (cobalt) and 
100.0 pm (impurity). Atomic number of the impurity is  
 (A)  39  
 (B)  40  
 (C)  59  
 (D)  60  
 
4. A circular conducting loop of radius r
0
 and having resistance ? per unit 
length as shown in the figure is placed in a magnetic field B which is 
constant. The ends of the loop are crossed and pulled in opposite 
directions with a velocity v such that the loop always remains circular 
and the radius of the loop goes on decreasing, then  
 (A)  current induced in the loop is 
Bv
2 ? ?
. 
 (B)  current induced in the loop is 
Bv
? ?
. 
 ? 
?   ?   ?   ? 
?   ?   ?   ?  ?    
?   ?   ?  ?   ?    
?   ?  ?   ?  
? 
 
B
 
 
v
 
 
v
 
 
 
 (C)  current induced in the loop is 
2Bv
? ?
. 
Page 3


FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
FIITJEE 
 
ALL INDIA TEST SERIES 
 
FULL TEST – II 
 
JEE (Main)-2020 
 
TEST DATE: 22-12-2019 
 
Time Allotted: 3 Hours Maximum Marks: 300 
 
General Instructions: 
 
?  The test consists of total 75 questions.  
?  Each subject (PCM) has 25 questions.  
?  This question paper contains Three Parts. 
?  Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 
?  Each part has only three sections: Section-A, Section-B and Section-C.     
   Section-A (01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one 
 correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong 
 answer. 
 
  Section-B (21 – 22, 46 – 47, 71 – 72) contains 6 Numerical based questions with answer as 
 numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no 
 negative marking.  
 
 Section-C (23 – 25, 48 – 50, 73 – 75) contains 9 Numerical answer type questions with answer 
XXXXX.XX and each question carries +4 marks for correct answer. There is no negative marking.  
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
2 
P Ph hy ys si ic cs s PART – I 
  
  
SECTION – A  
(One Options Correct Type) 
 
 
This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and 
(D), out of which ONLY ONE option is correct.  
 
1. During a rainy day, rain is falling vertically down with a velocity 2 m/s. A boy at rest starts his 
motion with a constant acceleration of 2 m/s
2
 along a straight road. Find the rate at which the 
angle of the axis of the umbrella with vertical should be changed so that the rain always appears 
to fall parallel to the axis of the umbrella.  
 (A)  
2
1
1 t ?
  
 (B)  
2
2
1 t ?
 
 (C)  
2
1
2 t ?
  
 (D)  
2
1
1 2t ?
 
 
2. Power versus time graph for a given force is shown in the 
figure. Then work done by the force upto time t( ? t
0
).  
 (A)  First increases then decreases.  
 (B)  First decreases then increases.  
 (C)  Always increases.  
 (D)  Always decreases.  
 
 
t
 
 
t
0 
 
P
 
 
 
 
3. A cobalt (atomic no. = 27) target is bombarded with electrons and the wave lengths of its 
characteristic X-rays spectrum are measured. A second weak characteristic spectrum is also 
found due to an impurity in the target. The wavelength of the K
?
 lines are 225.0 pm (cobalt) and 
100.0 pm (impurity). Atomic number of the impurity is  
 (A)  39  
 (B)  40  
 (C)  59  
 (D)  60  
 
4. A circular conducting loop of radius r
0
 and having resistance ? per unit 
length as shown in the figure is placed in a magnetic field B which is 
constant. The ends of the loop are crossed and pulled in opposite 
directions with a velocity v such that the loop always remains circular 
and the radius of the loop goes on decreasing, then  
 (A)  current induced in the loop is 
Bv
2 ? ?
. 
 (B)  current induced in the loop is 
Bv
? ?
. 
 ? 
?   ?   ?   ? 
?   ?   ?   ?  ?    
?   ?   ?  ?   ?    
?   ?  ?   ?  
? 
 
B
 
 
v
 
 
v
 
 
 
 (C)  current induced in the loop is 
2Bv
? ?
. 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
3 
 (D)  current induced in the loop is 
Bv
2 ?
. 
 
5. When a particle of mass m is suspended vertically by a spring of unstretched length ‘a’, the spring 
is stretched to a total length ‘ ?’. The particle is pulled down by a small distance ‘b’ from 
equilibrium position and then released. The angular frequency of the simple harmonic motion 
executed by the particle is    
 (A)  
2
g
( a) ?
?
?
  
 (B)  
2
ga
( a) ? ?
 
 (C)  
g
( a) ? ?
  
 (D)  
2
gb
( a) ? ?
 
 
6.  In YDSE, let A and B be two slits as shown. Thin films of 
thickness t
A
 and t
B
 and refractive indices ?
A
 and ?
B
 are 
placed in front of A and B respectively. If ?
A
t
A
 = ?
B
t
B
, then 
the central maxima will  
 (A)  not shift  
 (B)  shift towards A, if t
B
 > t
A
  
 (C)  shift towards B, if t
B
 > t
A
   
 (D)  shift towards A, if t
A
 > t
B
 
 
A
 
 
B
 
 
?
A
, t
A 
 
?
B
, t
B 
 
 
  
7. A sound source S and observer O
1
 and O
2
 are placed as 
shown in figure. S is always at rest and O
1
 and O
2
 start 
moving along positive y-axis and positive x-axis 
respectively with the same constant speed v
0
 at t = 0 away 
from S. At t = 5 sec, f
1
 and f
2
 represent apparent 
frequencies of sound received by O
1
 and O
2
 respectively. 
Then the ratio 
1
2
f
f
? ?
? ?
? ?
is  
 y
 
 
O
1 
 
S
 
 
(0, a)
 
 
( ?a, 0)
 
 
(a, 0)
 
 
x
 
 
O
2 
 
 
 (A)  zero   
 (B)  between zero and one  
 (C)  one   
 (D)  more than one   
 
8. A cubical block of side ‘a’ and density ‘ ?’ slides down a fixed inclined 
plane of inclination ? = 37 ? with a constant velocity v as shown. There is 
a thin film of viscous liquid of thickness ‘t’ between the inclined plane and 
the block. Then the coefficient of viscosity of the liquid will be  
 (A)  
3 agt
5v
?
  
 (B)  
4 agt
5v
?
 
 (C)  
agt
v
?
  
 
? = 37 ?
 
 
v
 
 
 
Page 4


FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
FIITJEE 
 
ALL INDIA TEST SERIES 
 
FULL TEST – II 
 
JEE (Main)-2020 
 
TEST DATE: 22-12-2019 
 
Time Allotted: 3 Hours Maximum Marks: 300 
 
General Instructions: 
 
?  The test consists of total 75 questions.  
?  Each subject (PCM) has 25 questions.  
?  This question paper contains Three Parts. 
?  Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 
?  Each part has only three sections: Section-A, Section-B and Section-C.     
   Section-A (01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one 
 correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong 
 answer. 
 
  Section-B (21 – 22, 46 – 47, 71 – 72) contains 6 Numerical based questions with answer as 
 numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no 
 negative marking.  
 
 Section-C (23 – 25, 48 – 50, 73 – 75) contains 9 Numerical answer type questions with answer 
XXXXX.XX and each question carries +4 marks for correct answer. There is no negative marking.  
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
2 
P Ph hy ys si ic cs s PART – I 
  
  
SECTION – A  
(One Options Correct Type) 
 
 
This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and 
(D), out of which ONLY ONE option is correct.  
 
1. During a rainy day, rain is falling vertically down with a velocity 2 m/s. A boy at rest starts his 
motion with a constant acceleration of 2 m/s
2
 along a straight road. Find the rate at which the 
angle of the axis of the umbrella with vertical should be changed so that the rain always appears 
to fall parallel to the axis of the umbrella.  
 (A)  
2
1
1 t ?
  
 (B)  
2
2
1 t ?
 
 (C)  
2
1
2 t ?
  
 (D)  
2
1
1 2t ?
 
 
2. Power versus time graph for a given force is shown in the 
figure. Then work done by the force upto time t( ? t
0
).  
 (A)  First increases then decreases.  
 (B)  First decreases then increases.  
 (C)  Always increases.  
 (D)  Always decreases.  
 
 
t
 
 
t
0 
 
P
 
 
 
 
3. A cobalt (atomic no. = 27) target is bombarded with electrons and the wave lengths of its 
characteristic X-rays spectrum are measured. A second weak characteristic spectrum is also 
found due to an impurity in the target. The wavelength of the K
?
 lines are 225.0 pm (cobalt) and 
100.0 pm (impurity). Atomic number of the impurity is  
 (A)  39  
 (B)  40  
 (C)  59  
 (D)  60  
 
4. A circular conducting loop of radius r
0
 and having resistance ? per unit 
length as shown in the figure is placed in a magnetic field B which is 
constant. The ends of the loop are crossed and pulled in opposite 
directions with a velocity v such that the loop always remains circular 
and the radius of the loop goes on decreasing, then  
 (A)  current induced in the loop is 
Bv
2 ? ?
. 
 (B)  current induced in the loop is 
Bv
? ?
. 
 ? 
?   ?   ?   ? 
?   ?   ?   ?  ?    
?   ?   ?  ?   ?    
?   ?  ?   ?  
? 
 
B
 
 
v
 
 
v
 
 
 
 (C)  current induced in the loop is 
2Bv
? ?
. 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
3 
 (D)  current induced in the loop is 
Bv
2 ?
. 
 
5. When a particle of mass m is suspended vertically by a spring of unstretched length ‘a’, the spring 
is stretched to a total length ‘ ?’. The particle is pulled down by a small distance ‘b’ from 
equilibrium position and then released. The angular frequency of the simple harmonic motion 
executed by the particle is    
 (A)  
2
g
( a) ?
?
?
  
 (B)  
2
ga
( a) ? ?
 
 (C)  
g
( a) ? ?
  
 (D)  
2
gb
( a) ? ?
 
 
6.  In YDSE, let A and B be two slits as shown. Thin films of 
thickness t
A
 and t
B
 and refractive indices ?
A
 and ?
B
 are 
placed in front of A and B respectively. If ?
A
t
A
 = ?
B
t
B
, then 
the central maxima will  
 (A)  not shift  
 (B)  shift towards A, if t
B
 > t
A
  
 (C)  shift towards B, if t
B
 > t
A
   
 (D)  shift towards A, if t
A
 > t
B
 
 
A
 
 
B
 
 
?
A
, t
A 
 
?
B
, t
B 
 
 
  
7. A sound source S and observer O
1
 and O
2
 are placed as 
shown in figure. S is always at rest and O
1
 and O
2
 start 
moving along positive y-axis and positive x-axis 
respectively with the same constant speed v
0
 at t = 0 away 
from S. At t = 5 sec, f
1
 and f
2
 represent apparent 
frequencies of sound received by O
1
 and O
2
 respectively. 
Then the ratio 
1
2
f
f
? ?
? ?
? ?
is  
 y
 
 
O
1 
 
S
 
 
(0, a)
 
 
( ?a, 0)
 
 
(a, 0)
 
 
x
 
 
O
2 
 
 
 (A)  zero   
 (B)  between zero and one  
 (C)  one   
 (D)  more than one   
 
8. A cubical block of side ‘a’ and density ‘ ?’ slides down a fixed inclined 
plane of inclination ? = 37 ? with a constant velocity v as shown. There is 
a thin film of viscous liquid of thickness ‘t’ between the inclined plane and 
the block. Then the coefficient of viscosity of the liquid will be  
 (A)  
3 agt
5v
?
  
 (B)  
4 agt
5v
?
 
 (C)  
agt
v
?
  
 
? = 37 ?
 
 
v
 
 
 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
4 
 (D)  
5 agt
3v
?
 
 
9. A diverging lens of focal length f
1
 is placed infront of and coaxially with a concave mirror of focal 
length f
2
. The separation between the lens and the mirror is d. A parallel beam of light incident on 
the lens returns as a parallel beam from the arrangement.  
 (A)  The beam diameter of the incident and reflected beams will not be same.  
 (B)  d = 2|f
2
| ? |f
1
| 
 (C)  If the entire arrangement is immersed in water, the conditions will remains unaltered.  
 (D)  none of the above  
 
10. A parallel plate capacitor with initial plate distance d
0
 is charged upto voltage V
0
 and then 
detached from the charger. Now the distance between the plates is varied periodically according 
to the law d = d
0
 + d
1
 sin ?t. The value of d
1
 if the potential difference across the capacitor 
changes according to the law  
 
0
1
V V 1 sin t
2
? ?
? ? ?
? ?
? ?
is  
 (A)  d
0
   
 (B)  
0
d
2
 
 (C)  
0
3d
2
  
 (D)  2d
0
  
 
11. The area of each plate of a capacitor is S and it is completely filled 
with a dielectric as shown in figure. The dielectric constant and 
resistivity of the material of the slab inserted in the capacitor are K  
and ? respectively. The emf of the ideal cell is V. The current 
flowing through dielectric slab immediately after the key is 
switched on is  
 (A)  
V
S
d ?
  
 (B)  
2V
S
d ?
 
 (C)  
V
S
2 d ?
  
 (D)  zero 
 
k
 
 
V
 
 
d
 
 
 
  
12. A thin insulating rod of length ? carries a charge q distributed uniformly on it. The rod is pivoted at 
its mid point and is rotated at a frequency f about a fixed axis perpendicular to the rod and 
passing through the pivot. The magnetic moment of the rod system is  
 (A)  
2
1
qf
12
? ?  
 (B)  
2
qf ? ? 
 (C)  
2
1
qf
6
? ?  
 (D)  
2
1
qf
3
? ? 
 
Page 5


FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
FIITJEE 
 
ALL INDIA TEST SERIES 
 
FULL TEST – II 
 
JEE (Main)-2020 
 
TEST DATE: 22-12-2019 
 
Time Allotted: 3 Hours Maximum Marks: 300 
 
General Instructions: 
 
?  The test consists of total 75 questions.  
?  Each subject (PCM) has 25 questions.  
?  This question paper contains Three Parts. 
?  Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 
?  Each part has only three sections: Section-A, Section-B and Section-C.     
   Section-A (01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one 
 correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong 
 answer. 
 
  Section-B (21 – 22, 46 – 47, 71 – 72) contains 6 Numerical based questions with answer as 
 numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no 
 negative marking.  
 
 Section-C (23 – 25, 48 – 50, 73 – 75) contains 9 Numerical answer type questions with answer 
XXXXX.XX and each question carries +4 marks for correct answer. There is no negative marking.  
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
2 
P Ph hy ys si ic cs s PART – I 
  
  
SECTION – A  
(One Options Correct Type) 
 
 
This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and 
(D), out of which ONLY ONE option is correct.  
 
1. During a rainy day, rain is falling vertically down with a velocity 2 m/s. A boy at rest starts his 
motion with a constant acceleration of 2 m/s
2
 along a straight road. Find the rate at which the 
angle of the axis of the umbrella with vertical should be changed so that the rain always appears 
to fall parallel to the axis of the umbrella.  
 (A)  
2
1
1 t ?
  
 (B)  
2
2
1 t ?
 
 (C)  
2
1
2 t ?
  
 (D)  
2
1
1 2t ?
 
 
2. Power versus time graph for a given force is shown in the 
figure. Then work done by the force upto time t( ? t
0
).  
 (A)  First increases then decreases.  
 (B)  First decreases then increases.  
 (C)  Always increases.  
 (D)  Always decreases.  
 
 
t
 
 
t
0 
 
P
 
 
 
 
3. A cobalt (atomic no. = 27) target is bombarded with electrons and the wave lengths of its 
characteristic X-rays spectrum are measured. A second weak characteristic spectrum is also 
found due to an impurity in the target. The wavelength of the K
?
 lines are 225.0 pm (cobalt) and 
100.0 pm (impurity). Atomic number of the impurity is  
 (A)  39  
 (B)  40  
 (C)  59  
 (D)  60  
 
4. A circular conducting loop of radius r
0
 and having resistance ? per unit 
length as shown in the figure is placed in a magnetic field B which is 
constant. The ends of the loop are crossed and pulled in opposite 
directions with a velocity v such that the loop always remains circular 
and the radius of the loop goes on decreasing, then  
 (A)  current induced in the loop is 
Bv
2 ? ?
. 
 (B)  current induced in the loop is 
Bv
? ?
. 
 ? 
?   ?   ?   ? 
?   ?   ?   ?  ?    
?   ?   ?  ?   ?    
?   ?  ?   ?  
? 
 
B
 
 
v
 
 
v
 
 
 
 (C)  current induced in the loop is 
2Bv
? ?
. 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
3 
 (D)  current induced in the loop is 
Bv
2 ?
. 
 
5. When a particle of mass m is suspended vertically by a spring of unstretched length ‘a’, the spring 
is stretched to a total length ‘ ?’. The particle is pulled down by a small distance ‘b’ from 
equilibrium position and then released. The angular frequency of the simple harmonic motion 
executed by the particle is    
 (A)  
2
g
( a) ?
?
?
  
 (B)  
2
ga
( a) ? ?
 
 (C)  
g
( a) ? ?
  
 (D)  
2
gb
( a) ? ?
 
 
6.  In YDSE, let A and B be two slits as shown. Thin films of 
thickness t
A
 and t
B
 and refractive indices ?
A
 and ?
B
 are 
placed in front of A and B respectively. If ?
A
t
A
 = ?
B
t
B
, then 
the central maxima will  
 (A)  not shift  
 (B)  shift towards A, if t
B
 > t
A
  
 (C)  shift towards B, if t
B
 > t
A
   
 (D)  shift towards A, if t
A
 > t
B
 
 
A
 
 
B
 
 
?
A
, t
A 
 
?
B
, t
B 
 
 
  
7. A sound source S and observer O
1
 and O
2
 are placed as 
shown in figure. S is always at rest and O
1
 and O
2
 start 
moving along positive y-axis and positive x-axis 
respectively with the same constant speed v
0
 at t = 0 away 
from S. At t = 5 sec, f
1
 and f
2
 represent apparent 
frequencies of sound received by O
1
 and O
2
 respectively. 
Then the ratio 
1
2
f
f
? ?
? ?
? ?
is  
 y
 
 
O
1 
 
S
 
 
(0, a)
 
 
( ?a, 0)
 
 
(a, 0)
 
 
x
 
 
O
2 
 
 
 (A)  zero   
 (B)  between zero and one  
 (C)  one   
 (D)  more than one   
 
8. A cubical block of side ‘a’ and density ‘ ?’ slides down a fixed inclined 
plane of inclination ? = 37 ? with a constant velocity v as shown. There is 
a thin film of viscous liquid of thickness ‘t’ between the inclined plane and 
the block. Then the coefficient of viscosity of the liquid will be  
 (A)  
3 agt
5v
?
  
 (B)  
4 agt
5v
?
 
 (C)  
agt
v
?
  
 
? = 37 ?
 
 
v
 
 
 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
4 
 (D)  
5 agt
3v
?
 
 
9. A diverging lens of focal length f
1
 is placed infront of and coaxially with a concave mirror of focal 
length f
2
. The separation between the lens and the mirror is d. A parallel beam of light incident on 
the lens returns as a parallel beam from the arrangement.  
 (A)  The beam diameter of the incident and reflected beams will not be same.  
 (B)  d = 2|f
2
| ? |f
1
| 
 (C)  If the entire arrangement is immersed in water, the conditions will remains unaltered.  
 (D)  none of the above  
 
10. A parallel plate capacitor with initial plate distance d
0
 is charged upto voltage V
0
 and then 
detached from the charger. Now the distance between the plates is varied periodically according 
to the law d = d
0
 + d
1
 sin ?t. The value of d
1
 if the potential difference across the capacitor 
changes according to the law  
 
0
1
V V 1 sin t
2
? ?
? ? ?
? ?
? ?
is  
 (A)  d
0
   
 (B)  
0
d
2
 
 (C)  
0
3d
2
  
 (D)  2d
0
  
 
11. The area of each plate of a capacitor is S and it is completely filled 
with a dielectric as shown in figure. The dielectric constant and 
resistivity of the material of the slab inserted in the capacitor are K  
and ? respectively. The emf of the ideal cell is V. The current 
flowing through dielectric slab immediately after the key is 
switched on is  
 (A)  
V
S
d ?
  
 (B)  
2V
S
d ?
 
 (C)  
V
S
2 d ?
  
 (D)  zero 
 
k
 
 
V
 
 
d
 
 
 
  
12. A thin insulating rod of length ? carries a charge q distributed uniformly on it. The rod is pivoted at 
its mid point and is rotated at a frequency f about a fixed axis perpendicular to the rod and 
passing through the pivot. The magnetic moment of the rod system is  
 (A)  
2
1
qf
12
? ?  
 (B)  
2
qf ? ? 
 (C)  
2
1
qf
6
? ?  
 (D)  
2
1
qf
3
? ? 
 
 AITS-FT-II-PCM-JEE(Main)/20 
FIITJEE Ltd., FIITJEE House, 29-A, Kalu  Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 
website: www.fiitjee.com 
5 
13. A particle of charge q and mass m starts moving from the origin under the action of an electric 
field 
0
ˆ
E E i ?
?
and 
0
ˆ
B B i ?
?
 with a velocity 
0
ˆ
v v j ?
?
. The speed of the particle will become 2v
0
 after a 
time  
 (A)  
0
0
2mv
t
qE
?  
 (B)  
0
0
2B q
t
mv
? 
 (C)  
0
0
3B q
t
mv
?  
 (D)  
0
0
3mv
t
qE
? 
 
14. A cell of internal resistance 1 ? is connected across a resistor R. A voltmeter having variable 
resistance G is used to measure potential difference across the resistor. The plot of voltmeter 
reading V against G is shown. What is the value of external resistor R? 
 
20 V
 
 
10 V
 
 
5 V
 
 
V
 
 
G( ?) ?
 
 
 
 
24V
 
 
V
 
 
R
 
 
1 ?
 
 
 
  (A)  5 ?  
 (B)  4 ? 
  (C)  3 ?  
 (D)  1 ? 
 
15. Consider the equation 
d
F ds A F P
dt
? ?
? ?
? ? ?
? ? ? ?
? ?
?
? ? ?
?
. Then dimensions of A will be (where F
?
= force, 
ds
?
= small displacement, t = time and P
?
= linear momentum) 
 (A)  [M
0
L
0
T
0
]  
 (B)  [M
1
L
0
T
0
] 
 (C)  [M
?1
L
0
T
0
]  
 (D)  [M
0
L
0
T
?1
] 
 
16. In the figure shown the cart of mass 6 m is initially at rest on a smooth 
horizontal surface. A particle of mass m is attached to the end of the light 
rigid rod which can rotate freely about end A in a vertical plane. If the rod 
is released from rest from the horizontal position as shown, find the 
velocity (v
rel
) of the particle with respect to the cart when the rod is vertical.  
 
( ?, m) 
6m 
A 
 
 (A)  
7
g
3
?  
 (B)  
7
g
6
? 
 (C)  
14
g
3
?