IIT-JEE 2012 Paper-1 (solved) Class 12 Notes | EduRev

Class 12 : IIT-JEE 2012 Paper-1 (solved) Class 12 Notes | EduRev

 Page 1


        Solutions to IIT-JEE-2012 
CODE 
PAPER 1 
Time: 3 Hours      Maximum Marks: 210 
 
INSTRUCTIONS 
A.  General: 
1. This booklet is your Question paper. Do not break the seats of his booklet before being instructed to do so by the
invigilators. 
2. The question paper CODE is printed on the right hand top corner of this page and on the back page of this booklet.
3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
for rough work.
4 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are 
NOT allowed inside the examination hall.
5. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided
separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
impression is created on the bottom sheet.
7. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
8. On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
choices are legible. Read carefully the instructions printed at the beginning of each section.
B. Filling the Right Part of the ORS: 
9. The ORS also has a CODES printed on its left and right parts.
10. Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
same.
11. Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble
UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
darken the paper CODE given on the right side of ORS(R
4
).
C. Question paper format and Marking scheme: 
The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections. 
12. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. 
13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
ONE or MORE are correct. 
14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both
inclusive).  
D. Marking Scheme 
15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (-- - - 1) mark will be awarded in 
this section.  
16. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for 
incorrect answer in this section.  
17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
answer ONLY.  In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect 
answer in this section.  
8 
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 
Write your Name, Registration Number and sign in the space provided on the back page of this booklet. 
Page 2


        Solutions to IIT-JEE-2012 
CODE 
PAPER 1 
Time: 3 Hours      Maximum Marks: 210 
 
INSTRUCTIONS 
A.  General: 
1. This booklet is your Question paper. Do not break the seats of his booklet before being instructed to do so by the
invigilators. 
2. The question paper CODE is printed on the right hand top corner of this page and on the back page of this booklet.
3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
for rough work.
4 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are 
NOT allowed inside the examination hall.
5. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided
separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
impression is created on the bottom sheet.
7. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
8. On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
choices are legible. Read carefully the instructions printed at the beginning of each section.
B. Filling the Right Part of the ORS: 
9. The ORS also has a CODES printed on its left and right parts.
10. Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
same.
11. Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble
UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
darken the paper CODE given on the right side of ORS(R
4
).
C. Question paper format and Marking scheme: 
The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections. 
12. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. 
13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
ONE or MORE are correct. 
14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both
inclusive).  
D. Marking Scheme 
15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (-- - - 1) mark will be awarded in 
this section.  
16. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for 
incorrect answer in this section.  
17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
answer ONLY.  In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect 
answer in this section.  
8 
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 
Write your Name, Registration Number and sign in the space provided on the back page of this booklet. 
IITJEE-2011-Paper 1-CPM-2 
PAPER-1 [Code – 8] 
   
IITJEE 2012 
 
SECTION I : Single Correct Answer Type 
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of 
which ONLY ONE is correct. 
1. In the determination of Young’s modulus
2
4MLg
Y
d
? ?
=
? ?
p
? ?
l
 by using Searle’s method, a wire of length L = 2m 
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire 
is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They 
have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to 
the maximum probable error of the Y measurement  
(A)  due to the errors in the measurements of d and l are the same.  
(B)  due to the error in the measurement of d is twice that due to the error in the measurement of l. 
(C)  due to the error in the measurement of l is twice that due to the error in the measurement of d. 
(D)  due to the error in the measurement of d is four times that due to the error in the measurement of l. 
Sol. (A) 
0.5
L.C. 0.005
100
= = mm 
Y 2 (d)
Y d
? ? ?
= +
l
l
3
3
0.005 10 1
50 0.25 10
- - ? ×
= =
×
l
l
3
3
(d) 2 0.005 10 1
2
d 50 0.5 10
- - ? × ×
= =
×
2. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ?. If the
angular momentum of the system, calculated about O and P are denoted by 
O
L
r
 and 
P
L
r
 respectively, then
z
 
P
 
O
 
m
 
?
 
(A) 
O
L
r
 and 
P
L
r
 do not vary with time. 
(B) 
O
L
r
 varies with time while 
P
L
r
 remains constant. 
(C) 
O
L
r
 remains constant while 
P
L
r
 varies with time. 
(D) 
O
L
r
 and 
P
L
r
 both vary with time. 
Sol. (C) 
PART - I: PHYSICS  
Page 3


        Solutions to IIT-JEE-2012 
CODE 
PAPER 1 
Time: 3 Hours      Maximum Marks: 210 
 
INSTRUCTIONS 
A.  General: 
1. This booklet is your Question paper. Do not break the seats of his booklet before being instructed to do so by the
invigilators. 
2. The question paper CODE is printed on the right hand top corner of this page and on the back page of this booklet.
3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
for rough work.
4 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are 
NOT allowed inside the examination hall.
5. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided
separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
impression is created on the bottom sheet.
7. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
8. On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
choices are legible. Read carefully the instructions printed at the beginning of each section.
B. Filling the Right Part of the ORS: 
9. The ORS also has a CODES printed on its left and right parts.
10. Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
same.
11. Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble
UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
darken the paper CODE given on the right side of ORS(R
4
).
C. Question paper format and Marking scheme: 
The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections. 
12. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. 
13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
ONE or MORE are correct. 
14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both
inclusive).  
D. Marking Scheme 
15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (-- - - 1) mark will be awarded in 
this section.  
16. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for 
incorrect answer in this section.  
17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
answer ONLY.  In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect 
answer in this section.  
8 
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 
Write your Name, Registration Number and sign in the space provided on the back page of this booklet. 
IITJEE-2011-Paper 1-CPM-2 
PAPER-1 [Code – 8] 
   
IITJEE 2012 
 
SECTION I : Single Correct Answer Type 
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of 
which ONLY ONE is correct. 
1. In the determination of Young’s modulus
2
4MLg
Y
d
? ?
=
? ?
p
? ?
l
 by using Searle’s method, a wire of length L = 2m 
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire 
is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They 
have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to 
the maximum probable error of the Y measurement  
(A)  due to the errors in the measurements of d and l are the same.  
(B)  due to the error in the measurement of d is twice that due to the error in the measurement of l. 
(C)  due to the error in the measurement of l is twice that due to the error in the measurement of d. 
(D)  due to the error in the measurement of d is four times that due to the error in the measurement of l. 
Sol. (A) 
0.5
L.C. 0.005
100
= = mm 
Y 2 (d)
Y d
? ? ?
= +
l
l
3
3
0.005 10 1
50 0.25 10
- - ? ×
= =
×
l
l
3
3
(d) 2 0.005 10 1
2
d 50 0.5 10
- - ? × ×
= =
×
2. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ?. If the
angular momentum of the system, calculated about O and P are denoted by 
O
L
r
 and 
P
L
r
 respectively, then
z
 
P
 
O
 
m
 
?
 
(A) 
O
L
r
 and 
P
L
r
 do not vary with time. 
(B) 
O
L
r
 varies with time while 
P
L
r
 remains constant. 
(C) 
O
L
r
 remains constant while 
P
L
r
 varies with time. 
(D) 
O
L
r
 and 
P
L
r
 both vary with time. 
Sol. (C) 
PART - I: PHYSICS  
IITJEE-2012-Paper 1-PCM-3 
P
L
r
O
 
m
 
?
 
O
L
r
3. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
R = 14 cm
 
n = 1.2
 
n = 1.5
 
(A) - 280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm 
Sol. (B) 
T
1 1
P (1.5 1) 0 (1.2 1) 0
14 14
? ? ? ?
= - - + - - ? ? ? ?
- ? ? ? ?
 = 
0.5 0.2 1
14 14 20
+ =
f = +20 cm 
1 1 1
v 40 20
- =
- 1 1 1 1
v 20 40 40
= - =
? v = 40 cm 
4. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with
constant angular speed ?, as shown in the figure.  At time t = 0, a small
insect starts from O and moves with constant speed v, with respect to the
rod towards the other end.  It reaches the end of the rod at t = T and stops.
The angular speed of the system remains ? throughout.  The magnitude of
the torque (| t
r
|) about O, as a function of time is best represented by which
plot?
? 
v ? 
O 
z 
(A)
O 
T 
t 
| t
r
| 
(B) 
O 
T 
t 
| t
r
| 
(C) 
O 
T 
t 
| t
r
| 
(D) 
O 
T 
t 
| t
r
| 
Sol. (B) 
t = ?
2 2
dI d
(C mv t )
dt dt
= ? +
= m?v
2
 2t. 
Page 4


        Solutions to IIT-JEE-2012 
CODE 
PAPER 1 
Time: 3 Hours      Maximum Marks: 210 
 
INSTRUCTIONS 
A.  General: 
1. This booklet is your Question paper. Do not break the seats of his booklet before being instructed to do so by the
invigilators. 
2. The question paper CODE is printed on the right hand top corner of this page and on the back page of this booklet.
3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
for rough work.
4 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are 
NOT allowed inside the examination hall.
5. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided
separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
impression is created on the bottom sheet.
7. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
8. On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
choices are legible. Read carefully the instructions printed at the beginning of each section.
B. Filling the Right Part of the ORS: 
9. The ORS also has a CODES printed on its left and right parts.
10. Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
same.
11. Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble
UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
darken the paper CODE given on the right side of ORS(R
4
).
C. Question paper format and Marking scheme: 
The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections. 
12. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. 
13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
ONE or MORE are correct. 
14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both
inclusive).  
D. Marking Scheme 
15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (-- - - 1) mark will be awarded in 
this section.  
16. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for 
incorrect answer in this section.  
17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
answer ONLY.  In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect 
answer in this section.  
8 
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 
Write your Name, Registration Number and sign in the space provided on the back page of this booklet. 
IITJEE-2011-Paper 1-CPM-2 
PAPER-1 [Code – 8] 
   
IITJEE 2012 
 
SECTION I : Single Correct Answer Type 
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of 
which ONLY ONE is correct. 
1. In the determination of Young’s modulus
2
4MLg
Y
d
? ?
=
? ?
p
? ?
l
 by using Searle’s method, a wire of length L = 2m 
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire 
is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They 
have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to 
the maximum probable error of the Y measurement  
(A)  due to the errors in the measurements of d and l are the same.  
(B)  due to the error in the measurement of d is twice that due to the error in the measurement of l. 
(C)  due to the error in the measurement of l is twice that due to the error in the measurement of d. 
(D)  due to the error in the measurement of d is four times that due to the error in the measurement of l. 
Sol. (A) 
0.5
L.C. 0.005
100
= = mm 
Y 2 (d)
Y d
? ? ?
= +
l
l
3
3
0.005 10 1
50 0.25 10
- - ? ×
= =
×
l
l
3
3
(d) 2 0.005 10 1
2
d 50 0.5 10
- - ? × ×
= =
×
2. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ?. If the
angular momentum of the system, calculated about O and P are denoted by 
O
L
r
 and 
P
L
r
 respectively, then
z
 
P
 
O
 
m
 
?
 
(A) 
O
L
r
 and 
P
L
r
 do not vary with time. 
(B) 
O
L
r
 varies with time while 
P
L
r
 remains constant. 
(C) 
O
L
r
 remains constant while 
P
L
r
 varies with time. 
(D) 
O
L
r
 and 
P
L
r
 both vary with time. 
Sol. (C) 
PART - I: PHYSICS  
IITJEE-2012-Paper 1-PCM-3 
P
L
r
O
 
m
 
?
 
O
L
r
3. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
R = 14 cm
 
n = 1.2
 
n = 1.5
 
(A) - 280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm 
Sol. (B) 
T
1 1
P (1.5 1) 0 (1.2 1) 0
14 14
? ? ? ?
= - - + - - ? ? ? ?
- ? ? ? ?
 = 
0.5 0.2 1
14 14 20
+ =
f = +20 cm 
1 1 1
v 40 20
- =
- 1 1 1 1
v 20 40 40
= - =
? v = 40 cm 
4. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with
constant angular speed ?, as shown in the figure.  At time t = 0, a small
insect starts from O and moves with constant speed v, with respect to the
rod towards the other end.  It reaches the end of the rod at t = T and stops.
The angular speed of the system remains ? throughout.  The magnitude of
the torque (| t
r
|) about O, as a function of time is best represented by which
plot?
? 
v ? 
O 
z 
(A)
O 
T 
t 
| t
r
| 
(B) 
O 
T 
t 
| t
r
| 
(C) 
O 
T 
t 
| t
r
| 
(D) 
O 
T 
t 
| t
r
| 
Sol. (B) 
t = ?
2 2
dI d
(C mv t )
dt dt
= ? +
= m?v
2
 2t. 
IITJEE-2011-Paper 1-CPM-4 
5. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40
amu) is kept at 300 K in a container.  The ratio of the rms speeds 
rms
rms
v (helium)
v (argon )
? ?
? ?
? ?
 is
(A) 0.32  (B) 0.45 (C) 2.24 (D) 3.16 
Sol. (D)
v
rms
 =
3RT
M
Required ratio = 
Ar
He
M 40
10
M 4
= =
= 3.16. 
6. Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage
source of potential difference X.  A proton is released at rest midway between the two plates.  It is found to
move at 45
0
 to the vertical JUST after release.  Then X is nearly
(A) 1 × 10
-5
 V (B) 1 × 10
-7
 V  (C) 1 × 10
-9
 V (D) 1 × 10
-10
 V
Sol. (C)
qE = mg
q(V/d) = mg
V =
mgd
q
 = 
27 2
19
1.67 10 10 10
1.6 10
- - - × × ×
×
 = 
28
9
19
10
10 V
10
- - - =
7. Three very large plates of same area are kept parallel and close to each other.  They are considered as ideal
black surfaces and have very high thermal conductivity.  The first and third plates are maintained at
temperatures 2T and 3T respectively.  The temperature of the middle (i.e. second) plate under steady state
condition is
(A) 
1/4
65
T
2
? ?
? ?
? ?
 (B) 
1/4
97
4
? ?
? ?
? ?
T (C) 
1/4
97
2
? ?
? ?
? ?
T (D) 
1/4
(97) T
Sol. (C)  
sA (2T)
4
 + sA (3T)
4
 = s 2A(T')
4
 
16T
4
 + 81T
4
 = 2 (T')
4
  
97 T
4
 = 2 (T')
4
  
(T')
4
 = 
97
2
 T
4
 
?  T' = 
1/4
97
T
2
? ?
? ?
? ?
3T 
2T 
Page 5


        Solutions to IIT-JEE-2012 
CODE 
PAPER 1 
Time: 3 Hours      Maximum Marks: 210 
 
INSTRUCTIONS 
A.  General: 
1. This booklet is your Question paper. Do not break the seats of his booklet before being instructed to do so by the
invigilators. 
2. The question paper CODE is printed on the right hand top corner of this page and on the back page of this booklet.
3. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
for rough work.
4 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are 
NOT allowed inside the examination hall.
5. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided
separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
6. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
impression is created on the bottom sheet.
7. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
8. On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
choices are legible. Read carefully the instructions printed at the beginning of each section.
B. Filling the Right Part of the ORS: 
9. The ORS also has a CODES printed on its left and right parts.
10. Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
same.
11. Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
the right part of the ORS. Do not write any of this information anywhere else. Darken the appropriate bubble
UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
darken the paper CODE given on the right side of ORS(R
4
).
C. Question paper format and Marking scheme: 
The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections. 
12. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. 
13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
ONE or MORE are correct. 
14. Section III contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both
inclusive).  
D. Marking Scheme 
15. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (-- - - 1) mark will be awarded in 
this section.  
16. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for 
incorrect answer in this section.  
17. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
answer ONLY.  In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect 
answer in this section.  
8 
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 
Write your Name, Registration Number and sign in the space provided on the back page of this booklet. 
IITJEE-2011-Paper 1-CPM-2 
PAPER-1 [Code – 8] 
   
IITJEE 2012 
 
SECTION I : Single Correct Answer Type 
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of 
which ONLY ONE is correct. 
1. In the determination of Young’s modulus
2
4MLg
Y
d
? ?
=
? ?
p
? ?
l
 by using Searle’s method, a wire of length L = 2m 
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire 
is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They 
have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to 
the maximum probable error of the Y measurement  
(A)  due to the errors in the measurements of d and l are the same.  
(B)  due to the error in the measurement of d is twice that due to the error in the measurement of l. 
(C)  due to the error in the measurement of l is twice that due to the error in the measurement of d. 
(D)  due to the error in the measurement of d is four times that due to the error in the measurement of l. 
Sol. (A) 
0.5
L.C. 0.005
100
= = mm 
Y 2 (d)
Y d
? ? ?
= +
l
l
3
3
0.005 10 1
50 0.25 10
- - ? ×
= =
×
l
l
3
3
(d) 2 0.005 10 1
2
d 50 0.5 10
- - ? × ×
= =
×
2. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ?. If the
angular momentum of the system, calculated about O and P are denoted by 
O
L
r
 and 
P
L
r
 respectively, then
z
 
P
 
O
 
m
 
?
 
(A) 
O
L
r
 and 
P
L
r
 do not vary with time. 
(B) 
O
L
r
 varies with time while 
P
L
r
 remains constant. 
(C) 
O
L
r
 remains constant while 
P
L
r
 varies with time. 
(D) 
O
L
r
 and 
P
L
r
 both vary with time. 
Sol. (C) 
PART - I: PHYSICS  
IITJEE-2012-Paper 1-PCM-3 
P
L
r
O
 
m
 
?
 
O
L
r
3. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
R = 14 cm
 
n = 1.2
 
n = 1.5
 
(A) - 280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm 
Sol. (B) 
T
1 1
P (1.5 1) 0 (1.2 1) 0
14 14
? ? ? ?
= - - + - - ? ? ? ?
- ? ? ? ?
 = 
0.5 0.2 1
14 14 20
+ =
f = +20 cm 
1 1 1
v 40 20
- =
- 1 1 1 1
v 20 40 40
= - =
? v = 40 cm 
4. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with
constant angular speed ?, as shown in the figure.  At time t = 0, a small
insect starts from O and moves with constant speed v, with respect to the
rod towards the other end.  It reaches the end of the rod at t = T and stops.
The angular speed of the system remains ? throughout.  The magnitude of
the torque (| t
r
|) about O, as a function of time is best represented by which
plot?
? 
v ? 
O 
z 
(A)
O 
T 
t 
| t
r
| 
(B) 
O 
T 
t 
| t
r
| 
(C) 
O 
T 
t 
| t
r
| 
(D) 
O 
T 
t 
| t
r
| 
Sol. (B) 
t = ?
2 2
dI d
(C mv t )
dt dt
= ? +
= m?v
2
 2t. 
IITJEE-2011-Paper 1-CPM-4 
5. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40
amu) is kept at 300 K in a container.  The ratio of the rms speeds 
rms
rms
v (helium)
v (argon )
? ?
? ?
? ?
 is
(A) 0.32  (B) 0.45 (C) 2.24 (D) 3.16 
Sol. (D)
v
rms
 =
3RT
M
Required ratio = 
Ar
He
M 40
10
M 4
= =
= 3.16. 
6. Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage
source of potential difference X.  A proton is released at rest midway between the two plates.  It is found to
move at 45
0
 to the vertical JUST after release.  Then X is nearly
(A) 1 × 10
-5
 V (B) 1 × 10
-7
 V  (C) 1 × 10
-9
 V (D) 1 × 10
-10
 V
Sol. (C)
qE = mg
q(V/d) = mg
V =
mgd
q
 = 
27 2
19
1.67 10 10 10
1.6 10
- - - × × ×
×
 = 
28
9
19
10
10 V
10
- - - =
7. Three very large plates of same area are kept parallel and close to each other.  They are considered as ideal
black surfaces and have very high thermal conductivity.  The first and third plates are maintained at
temperatures 2T and 3T respectively.  The temperature of the middle (i.e. second) plate under steady state
condition is
(A) 
1/4
65
T
2
? ?
? ?
? ?
 (B) 
1/4
97
4
? ?
? ?
? ?
T (C) 
1/4
97
2
? ?
? ?
? ?
T (D) 
1/4
(97) T
Sol. (C)  
sA (2T)
4
 + sA (3T)
4
 = s 2A(T')
4
 
16T
4
 + 81T
4
 = 2 (T')
4
  
97 T
4
 = 2 (T')
4
  
(T')
4
 = 
97
2
 T
4
 
?  T' = 
1/4
97
T
2
? ?
? ?
? ?
3T 
2T 
IITJEE-2012-Paper 1-PCM-5 
8. A small block is connected to one end of a massless spring of un-stretched length 4.9 m.  The other end of
the spring (see the figure) is fixed.  The system lies on a horizontal frictionless surface.  The block is
stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular
frequency ? = p/3 rad/s.  Simultaneously at t = 0, a small pebble is projected with speed v form point P at
an angle of 45
0
 as shown in the figure.  Point P is at a horizontal distance of 10 m from O.  If the pebble hits
the block at t = 1 s, the value of v is (take g = 10 m/s
2
)
45
0
v
 
x
 
P
 
10 m
 
O
 
z
 
(A) 50 m / s (B) 51 m / s (C) 52 m / s (D) 53 m / s 
Sol. (A) 
0
2vsin 45
1
g
= 
? v = 50 m / s . 
9. Young’s double slit experiment is carried out by using green, red and blue light, one color at a time.  The
fringe widths recorded are ß
G
, ß
R
 and ß
B
, respectively.  Then,
(A) ß
G
 > ß
B
 > ß
R
 (B) ß
B
 > ß
G
 > ß
R
  (C) ß
R
 > ß
B
 > ß
G
 (D) ß
R
 > ß
G
 > ß
B
Sol. (D)
?
R
 > ?
G
 > ?
B
? ß
R
 > ß
G
 > ß
B 
10. Consider a thin spherical shell of radius R with centre at the origin, carrying uniform positive surface
charge density.  The variation of the magnitude of the electric field | E(r)
r
| and the electric potential V(r) 
with the distance r from the centre, is best represented by which graph?  
(A)  
O
 
r
 
R
V(r)
 
|E(r)|
 
? 
(B) 
O
 
r
 
R
V(r)
 
|E(r)|
 
? 
(C)  
O
 
r
 
R
V(r)
 
|E(r)|
 
? 
(D)  
O
 
r
 
R
V(r)
 
|E(r)|
 
? 
Sol. (D) 
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