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 Page 1


 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
IIT-JAM - 2021 
SECTION – A 
cos x
e
Multiple Choice Questions (MCQ) 
Q1 – Q10 Carry One Mark Each 
Q1. The function  is Taylor expanded about 0 x = . The coefficient of 
2
x is  
(a) 
1
2
-  (b) 
2
e
-  (c) 
2
e
  (d) Zero  
Ans. : (b)  
Solution: ( )
cos x
fx e = 
Taylor expansion about 
0
xx = is 
( ) ( ) ( ) ( )
( )
( )
2
0
0 0 0 0
...
2!
xx
fx fx x x f x f x
-
' '' = + - + +8 
? Taylor expansion about 0 x = 
( ) ( ) ( )
( )
2
0
00
2!
f
f x f xf x
''
' = + + + - -8 
Coefficient of 
2
x is 
( ) 0
2!
f ''
 
( )
cos x
fx e = ( )
cos
sin
x
f x xe ' ? =- 
( ) ( ) ( )
cos cos 2 cos
cos sin sin cos sin
xx x
f x xe x xe x x e
??
'' =- + - =- +
??
 
( ) ( )
1
0 10 f e e '' ? = -+ =- 
? coefficients of 
( )
2
0
2! 2
f
e
x
''
-
= =  
Q2. Let M be a 22 × matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues 
are  
(a) 2 and 4  (b) 3 and 3  (c) 2 and 6  (d) 2 - and 3 -  
Ans. : (a)  
Solution: M is a 22 × matrix  
We know trace = sum of eigenvalues  
and determinant = product of eigenvalues  
Let eigenvalues  are
1
? and 
2
? . 
12
6 ?? ?+ =  and  
12
8 ?? = 
1
2 ? = , 
2
4 ? =  
Page 2


 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
IIT-JAM - 2021 
SECTION – A 
cos x
e
Multiple Choice Questions (MCQ) 
Q1 – Q10 Carry One Mark Each 
Q1. The function  is Taylor expanded about 0 x = . The coefficient of 
2
x is  
(a) 
1
2
-  (b) 
2
e
-  (c) 
2
e
  (d) Zero  
Ans. : (b)  
Solution: ( )
cos x
fx e = 
Taylor expansion about 
0
xx = is 
( ) ( ) ( ) ( )
( )
( )
2
0
0 0 0 0
...
2!
xx
fx fx x x f x f x
-
' '' = + - + +8 
? Taylor expansion about 0 x = 
( ) ( ) ( )
( )
2
0
00
2!
f
f x f xf x
''
' = + + + - -8 
Coefficient of 
2
x is 
( ) 0
2!
f ''
 
( )
cos x
fx e = ( )
cos
sin
x
f x xe ' ? =- 
( ) ( ) ( )
cos cos 2 cos
cos sin sin cos sin
xx x
f x xe x xe x x e
??
'' =- + - =- +
??
 
( ) ( )
1
0 10 f e e '' ? = -+ =- 
? coefficients of 
( )
2
0
2! 2
f
e
x
''
-
= =  
Q2. Let M be a 22 × matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues 
are  
(a) 2 and 4  (b) 3 and 3  (c) 2 and 6  (d) 2 - and 3 -  
Ans. : (a)  
Solution: M is a 22 × matrix  
We know trace = sum of eigenvalues  
and determinant = product of eigenvalues  
Let eigenvalues  are
1
? and 
2
? . 
12
6 ?? ?+ =  and  
12
8 ?? = 
1
2 ? = , 
2
4 ? =  
 
 
  
 
 
 
 
 
  
 
   
 
 
Q3. A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 
300 times smaller than its farthest distance from the star. If the corresponding speeds are 
c
v and 
f
v , then 
c
f
v
v
 is 
(a) 
1
300
  (b) 
1
300
  (c) 300  (d) 300  
Ans. : (d)    
Solution: Using conservation of angular momentum  
300
300
f
cc
c c f f
f c c
r
vr
mv r mv r
vr r
= ?= = = 
Q4. An object of density ? is floating in a liquid with 75% of its volume submerged. The 
density of the liquid is   
(a) 
4
3
?  (b) 
3
2
?  (c) 
8
5
?  (d) 2 ?  
Ans. : (a)    
Solution:  Weight of object equal to buoyancy force  
 
34
43
V g Vdg d ?? = ?= 
Q5. An experiment with a Michelson interferometer is performed in vacuum using a laser of 
wavelength 610nm . One of the beams of the interferometer passes through a small glass 
cavity 1.3cm long. After the cavity is completely filled with a medium of refractive 
index ,472 n dark fringes are counted to move past a reference line. Given that the speed 
of light is 
8
3 10 / ms × , the value of n is  
(a) 1.01  (b) 1.04  (c) 1.06  (d) 1.10  
Ans. : (a)  
Solution: Change in optical path xm ? ?= ( ) 2 1 n tm ? ? -= 
9
2
472 610 10
1
2 2 1 3 10
n
n
t
?
-
-
××
? -= =
× · ×
 
1 0 011 n ? -= · 1 011 n ?= · 
Page 3


 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
IIT-JAM - 2021 
SECTION – A 
cos x
e
Multiple Choice Questions (MCQ) 
Q1 – Q10 Carry One Mark Each 
Q1. The function  is Taylor expanded about 0 x = . The coefficient of 
2
x is  
(a) 
1
2
-  (b) 
2
e
-  (c) 
2
e
  (d) Zero  
Ans. : (b)  
Solution: ( )
cos x
fx e = 
Taylor expansion about 
0
xx = is 
( ) ( ) ( ) ( )
( )
( )
2
0
0 0 0 0
...
2!
xx
fx fx x x f x f x
-
' '' = + - + +8 
? Taylor expansion about 0 x = 
( ) ( ) ( )
( )
2
0
00
2!
f
f x f xf x
''
' = + + + - -8 
Coefficient of 
2
x is 
( ) 0
2!
f ''
 
( )
cos x
fx e = ( )
cos
sin
x
f x xe ' ? =- 
( ) ( ) ( )
cos cos 2 cos
cos sin sin cos sin
xx x
f x xe x xe x x e
??
'' =- + - =- +
??
 
( ) ( )
1
0 10 f e e '' ? = -+ =- 
? coefficients of 
( )
2
0
2! 2
f
e
x
''
-
= =  
Q2. Let M be a 22 × matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues 
are  
(a) 2 and 4  (b) 3 and 3  (c) 2 and 6  (d) 2 - and 3 -  
Ans. : (a)  
Solution: M is a 22 × matrix  
We know trace = sum of eigenvalues  
and determinant = product of eigenvalues  
Let eigenvalues  are
1
? and 
2
? . 
12
6 ?? ?+ =  and  
12
8 ?? = 
1
2 ? = , 
2
4 ? =  
 
 
  
 
 
 
 
 
  
 
   
 
 
Q3. A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 
300 times smaller than its farthest distance from the star. If the corresponding speeds are 
c
v and 
f
v , then 
c
f
v
v
 is 
(a) 
1
300
  (b) 
1
300
  (c) 300  (d) 300  
Ans. : (d)    
Solution: Using conservation of angular momentum  
300
300
f
cc
c c f f
f c c
r
vr
mv r mv r
vr r
= ?= = = 
Q4. An object of density ? is floating in a liquid with 75% of its volume submerged. The 
density of the liquid is   
(a) 
4
3
?  (b) 
3
2
?  (c) 
8
5
?  (d) 2 ?  
Ans. : (a)    
Solution:  Weight of object equal to buoyancy force  
 
34
43
V g Vdg d ?? = ?= 
Q5. An experiment with a Michelson interferometer is performed in vacuum using a laser of 
wavelength 610nm . One of the beams of the interferometer passes through a small glass 
cavity 1.3cm long. After the cavity is completely filled with a medium of refractive 
index ,472 n dark fringes are counted to move past a reference line. Given that the speed 
of light is 
8
3 10 / ms × , the value of n is  
(a) 1.01  (b) 1.04  (c) 1.06  (d) 1.10  
Ans. : (a)  
Solution: Change in optical path xm ? ?= ( ) 2 1 n tm ? ? -= 
9
2
472 610 10
1
2 2 1 3 10
n
n
t
?
-
-
××
? -= =
× · ×
 
1 0 011 n ? -= · 1 011 n ?= · 
 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
Q6. For a semiconductor material, the conventional flat band energy diagram is shown in the 
figure. The variables , YX respectively, are 
(a) Energy, Momentum  
(b) Energy, Distance 
(c) Distance, Energy  
(d) Momentum, Energy  
Ans. : (b)  
Solution: Along the y-axis energy varies while along x-axis distance is variable.  
Q7. For the given circuit, 
D
V is the threshold voltage of the diode. The graph that best 
deposits variation of 
0
V with 
i
V is 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
 
0
i
V
0
V
0
i
V
0
V
0
i
V
0
V
D
V 0
i
V
0
V
i
V
1k ?
1k ?
0
V
+
-
X
valence band
conduction band
Y
Page 4


 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
IIT-JAM - 2021 
SECTION – A 
cos x
e
Multiple Choice Questions (MCQ) 
Q1 – Q10 Carry One Mark Each 
Q1. The function  is Taylor expanded about 0 x = . The coefficient of 
2
x is  
(a) 
1
2
-  (b) 
2
e
-  (c) 
2
e
  (d) Zero  
Ans. : (b)  
Solution: ( )
cos x
fx e = 
Taylor expansion about 
0
xx = is 
( ) ( ) ( ) ( )
( )
( )
2
0
0 0 0 0
...
2!
xx
fx fx x x f x f x
-
' '' = + - + +8 
? Taylor expansion about 0 x = 
( ) ( ) ( )
( )
2
0
00
2!
f
f x f xf x
''
' = + + + - -8 
Coefficient of 
2
x is 
( ) 0
2!
f ''
 
( )
cos x
fx e = ( )
cos
sin
x
f x xe ' ? =- 
( ) ( ) ( )
cos cos 2 cos
cos sin sin cos sin
xx x
f x xe x xe x x e
??
'' =- + - =- +
??
 
( ) ( )
1
0 10 f e e '' ? = -+ =- 
? coefficients of 
( )
2
0
2! 2
f
e
x
''
-
= =  
Q2. Let M be a 22 × matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues 
are  
(a) 2 and 4  (b) 3 and 3  (c) 2 and 6  (d) 2 - and 3 -  
Ans. : (a)  
Solution: M is a 22 × matrix  
We know trace = sum of eigenvalues  
and determinant = product of eigenvalues  
Let eigenvalues  are
1
? and 
2
? . 
12
6 ?? ?+ =  and  
12
8 ?? = 
1
2 ? = , 
2
4 ? =  
 
 
  
 
 
 
 
 
  
 
   
 
 
Q3. A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 
300 times smaller than its farthest distance from the star. If the corresponding speeds are 
c
v and 
f
v , then 
c
f
v
v
 is 
(a) 
1
300
  (b) 
1
300
  (c) 300  (d) 300  
Ans. : (d)    
Solution: Using conservation of angular momentum  
300
300
f
cc
c c f f
f c c
r
vr
mv r mv r
vr r
= ?= = = 
Q4. An object of density ? is floating in a liquid with 75% of its volume submerged. The 
density of the liquid is   
(a) 
4
3
?  (b) 
3
2
?  (c) 
8
5
?  (d) 2 ?  
Ans. : (a)    
Solution:  Weight of object equal to buoyancy force  
 
34
43
V g Vdg d ?? = ?= 
Q5. An experiment with a Michelson interferometer is performed in vacuum using a laser of 
wavelength 610nm . One of the beams of the interferometer passes through a small glass 
cavity 1.3cm long. After the cavity is completely filled with a medium of refractive 
index ,472 n dark fringes are counted to move past a reference line. Given that the speed 
of light is 
8
3 10 / ms × , the value of n is  
(a) 1.01  (b) 1.04  (c) 1.06  (d) 1.10  
Ans. : (a)  
Solution: Change in optical path xm ? ?= ( ) 2 1 n tm ? ? -= 
9
2
472 610 10
1
2 2 1 3 10
n
n
t
?
-
-
××
? -= =
× · ×
 
1 0 011 n ? -= · 1 011 n ?= · 
 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
Q6. For a semiconductor material, the conventional flat band energy diagram is shown in the 
figure. The variables , YX respectively, are 
(a) Energy, Momentum  
(b) Energy, Distance 
(c) Distance, Energy  
(d) Momentum, Energy  
Ans. : (b)  
Solution: Along the y-axis energy varies while along x-axis distance is variable.  
Q7. For the given circuit, 
D
V is the threshold voltage of the diode. The graph that best 
deposits variation of 
0
V with 
i
V is 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
 
0
i
V
0
V
0
i
V
0
V
0
i
V
0
V
D
V 0
i
V
0
V
i
V
1k ?
1k ?
0
V
+
-
X
valence band
conduction band
Y
 
 
  
 
 
 
 
 
  
 
   
 
 
Ans. : (a)  
Solution: 
Q8.  Arrange the following telescopes, where D is the telescope diameter and ? is the 
wavelength, in order of decreasing resolving power:  
I. 100 , 21 D m cm ? = =                                II. 2 , 500 D m nm ? = = 
III. 1 , 100 D m nm ? = =                               IV. 2 , 10 D m mm ? = = 
(a) III, II, IV, I     (b) II, III, I, IV  
(c) IV, III, II, I     (d) III, II, I, IV  
Ans. : (d)  
Solution: 1.22 d
D
?
? = 
3
2.56 10
I
d ?
-
= × ;                         
7
3.05 10
II
d?
-
= × 
7
1.22 10
III
d ?
-
= × ;                       
3
6.1 10
IV
d ?
-
= × 
Resolving power 
1
d ?
= 
 
III II I IV
RP RP RP RP > >> 
Q9. Metallic lithium has bcc crystal structure. Each unit cell is a cube of side a . The number 
of atoms per unit volume is  
(a) 
3
1
a
   (b) 
3
2
2a
  (c) 
3
2
a
   (d) 
3
4
a
  
• •
• •
+
-
.. oc
.. sc i
V
1k ?
1k ?
0
V
+
-
Negative half Cycle
Postive half Cycle
.. oc
.. sc
i
V
1k ?
1k ?
0
V
+
-
+
-
• •
• • 0 =
0
1
1
ii
k
V VV
k
=-=
Page 5


 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
IIT-JAM - 2021 
SECTION – A 
cos x
e
Multiple Choice Questions (MCQ) 
Q1 – Q10 Carry One Mark Each 
Q1. The function  is Taylor expanded about 0 x = . The coefficient of 
2
x is  
(a) 
1
2
-  (b) 
2
e
-  (c) 
2
e
  (d) Zero  
Ans. : (b)  
Solution: ( )
cos x
fx e = 
Taylor expansion about 
0
xx = is 
( ) ( ) ( ) ( )
( )
( )
2
0
0 0 0 0
...
2!
xx
fx fx x x f x f x
-
' '' = + - + +8 
? Taylor expansion about 0 x = 
( ) ( ) ( )
( )
2
0
00
2!
f
f x f xf x
''
' = + + + - -8 
Coefficient of 
2
x is 
( ) 0
2!
f ''
 
( )
cos x
fx e = ( )
cos
sin
x
f x xe ' ? =- 
( ) ( ) ( )
cos cos 2 cos
cos sin sin cos sin
xx x
f x xe x xe x x e
??
'' =- + - =- +
??
 
( ) ( )
1
0 10 f e e '' ? = -+ =- 
? coefficients of 
( )
2
0
2! 2
f
e
x
''
-
= =  
Q2. Let M be a 22 × matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues 
are  
(a) 2 and 4  (b) 3 and 3  (c) 2 and 6  (d) 2 - and 3 -  
Ans. : (a)  
Solution: M is a 22 × matrix  
We know trace = sum of eigenvalues  
and determinant = product of eigenvalues  
Let eigenvalues  are
1
? and 
2
? . 
12
6 ?? ?+ =  and  
12
8 ?? = 
1
2 ? = , 
2
4 ? =  
 
 
  
 
 
 
 
 
  
 
   
 
 
Q3. A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 
300 times smaller than its farthest distance from the star. If the corresponding speeds are 
c
v and 
f
v , then 
c
f
v
v
 is 
(a) 
1
300
  (b) 
1
300
  (c) 300  (d) 300  
Ans. : (d)    
Solution: Using conservation of angular momentum  
300
300
f
cc
c c f f
f c c
r
vr
mv r mv r
vr r
= ?= = = 
Q4. An object of density ? is floating in a liquid with 75% of its volume submerged. The 
density of the liquid is   
(a) 
4
3
?  (b) 
3
2
?  (c) 
8
5
?  (d) 2 ?  
Ans. : (a)    
Solution:  Weight of object equal to buoyancy force  
 
34
43
V g Vdg d ?? = ?= 
Q5. An experiment with a Michelson interferometer is performed in vacuum using a laser of 
wavelength 610nm . One of the beams of the interferometer passes through a small glass 
cavity 1.3cm long. After the cavity is completely filled with a medium of refractive 
index ,472 n dark fringes are counted to move past a reference line. Given that the speed 
of light is 
8
3 10 / ms × , the value of n is  
(a) 1.01  (b) 1.04  (c) 1.06  (d) 1.10  
Ans. : (a)  
Solution: Change in optical path xm ? ?= ( ) 2 1 n tm ? ? -= 
9
2
472 610 10
1
2 2 1 3 10
n
n
t
?
-
-
××
? -= =
× · ×
 
1 0 011 n ? -= · 1 011 n ?= · 
 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
Q6. For a semiconductor material, the conventional flat band energy diagram is shown in the 
figure. The variables , YX respectively, are 
(a) Energy, Momentum  
(b) Energy, Distance 
(c) Distance, Energy  
(d) Momentum, Energy  
Ans. : (b)  
Solution: Along the y-axis energy varies while along x-axis distance is variable.  
Q7. For the given circuit, 
D
V is the threshold voltage of the diode. The graph that best 
deposits variation of 
0
V with 
i
V is 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
 
0
i
V
0
V
0
i
V
0
V
0
i
V
0
V
D
V 0
i
V
0
V
i
V
1k ?
1k ?
0
V
+
-
X
valence band
conduction band
Y
 
 
  
 
 
 
 
 
  
 
   
 
 
Ans. : (a)  
Solution: 
Q8.  Arrange the following telescopes, where D is the telescope diameter and ? is the 
wavelength, in order of decreasing resolving power:  
I. 100 , 21 D m cm ? = =                                II. 2 , 500 D m nm ? = = 
III. 1 , 100 D m nm ? = =                               IV. 2 , 10 D m mm ? = = 
(a) III, II, IV, I     (b) II, III, I, IV  
(c) IV, III, II, I     (d) III, II, I, IV  
Ans. : (d)  
Solution: 1.22 d
D
?
? = 
3
2.56 10
I
d ?
-
= × ;                         
7
3.05 10
II
d?
-
= × 
7
1.22 10
III
d ?
-
= × ;                       
3
6.1 10
IV
d ?
-
= × 
Resolving power 
1
d ?
= 
 
III II I IV
RP RP RP RP > >> 
Q9. Metallic lithium has bcc crystal structure. Each unit cell is a cube of side a . The number 
of atoms per unit volume is  
(a) 
3
1
a
   (b) 
3
2
2a
  (c) 
3
2
a
   (d) 
3
4
a
  
• •
• •
+
-
.. oc
.. sc i
V
1k ?
1k ?
0
V
+
-
Negative half Cycle
Postive half Cycle
.. oc
.. sc
i
V
1k ?
1k ?
0
V
+
-
+
-
• •
• • 0 =
0
1
1
ii
k
V VV
k
=-=
 
 
  
 
 
 
 
 
 
 
 
   
 
 
 
Ans. : (c)  
Solution: The effective number of atoms in BCC is  
1
81 2
8
eff
n = × += 
 The volume of the bcc unit cell of side a is 
3
a . 
 Thus, the number of atoms per unit volume is 
3
2
a
= .  
Therefore, the correct option is (c). 
Q10. The moment of inertia of a solid sphere (radius R and mass M ) about the axis which is 
at a distance of 
2
R
 from the centre is  
(a) 
2
3
20
MR  (b) 
2
1
2
MR  (c) 
2
13
20
MR  (d) 
2
9
10
MR 
Ans. : (c)  
Solution:  
Using parallel axis theorem  
 
2
0. C M
I I Md = + ; 
2
R
d = ,
2
.
2
5
C M
I MR = 
 
2
2
2 2 22
0
2 2 8 5 13
5 2 5 4 20 20
R MR
I MR M MR MR MR
+ ?? ? ?
= + = += =
?? ? ?
?? ? ?
 
Q11 – Q30. carry two marks each 
Q11. Let ( ) , xy denote the coordinates in a rectangular Cartesian coordinate system C . Let 
( ) , xy '' denote the coordinates in another coordinate system C ' defined by 
     23 x xy ' = + 
     34 y xy '=-+ 
The area element in C ' , is 
(a) 
1
17
dx dy ''  (b) 12dx dy ''  (c) dx dy ''  (d) x dx dy '' '  
Ans. : (a)  
Solution: ( ) ( ) ,, C xy C x y ' '' ? 
dxdy Jdx dy '' = 
where 
( )
( )
,
,
xy
J xy
xx
J
xy
Jx y
yy
??
'' ??
= =
?? ''
'' ??
 
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FAQs on Physics - 2021 Past Year Paper - IIT JAM Past Year Papers and Model Test Paper (All Branches)

1. How does Newton's first law of motion apply to the article's content?
Ans. Newton's first law of motion states that an object at rest will stay at rest, and an object in motion will stay in motion with the same speed and direction unless acted upon by an external force. In the context of the article, this law can be applied to explain the motion of objects mentioned, such as the movement of electrons in a conductor or the motion of a pendulum.
2. What is the relationship between voltage and current mentioned in the article?
Ans. The relationship between voltage and current is defined by Ohm's law, which states that the current flowing through a conductor is directly proportional to the voltage across the conductor, provided the temperature and other physical conditions remain constant. This relationship is crucial for understanding the behavior of electrical circuits and is relevant to the article's content.
3. Can you explain the concept of electromagnetic induction mentioned in the article?
Ans. Electromagnetic induction is the process by which a changing magnetic field induces an electric current in a conductor. This phenomenon is described by Faraday's law of electromagnetic induction. In the context of the article, electromagnetic induction is relevant for understanding the generation of electricity through the movement of magnetic fields, such as in generators or transformers.
4. How does the article relate to the conservation of energy?
Ans. The article relates to the conservation of energy by discussing various phenomena, such as the conversion of electrical energy into other forms, such as light or heat. The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. Understanding this principle is essential for analyzing the energy transformations described in the article.
5. Can you explain the concept of wave-particle duality mentioned in the article?
Ans. Wave-particle duality is a fundamental concept in quantum mechanics that suggests that particles, such as electrons or photons, can exhibit both wave-like and particle-like properties. This concept is relevant to the article's content as it discusses the behavior of electrons and photons, which can be described as both particles and waves. The wave-particle duality helps explain certain phenomena, such as the interference and diffraction of light or the wave nature of electrons in quantum mechanics.
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