PAPER 1
Time: 3 Hours Maximum Marks: 210
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
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
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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.
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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.
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choices are legible. Read carefully the instructions printed at the beginning of each section.
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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(R4).
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.
Write your Name, Registration Number and sign in the space provided on the back page of this booklet.
PAPER-1 [Code – 8]
IITJEE 2012
PART - I: PHYSICS
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.
4MLg
1. In the determination of Young’s modulusY = 2 by using Searle’s method, a wire of length L = 2m
πld
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 mm
100
∆Y ∆l 2∆(d)
= +
Y l d
∆l 0.005×10−3 1
= =
l 0.25×10−3 50
∆(d) 2× 0.005×10−3 1
2 = =
d 0.5×10−3 50
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 ω. If the
r r
angular momentum of the system, calculated about O and P are denoted by LO and LP respectively, then
z
P
O m
ω
r r
(A) LO and LP do not vary with time.
r r
(B) LO varies with time while LP remains constant.
r r
(C) LO remains constant while LP varies with time.
r r
(D) LO and LP both vary with time.
Sol. (C)
IITJEE-2012-Paper 1-PCM-3
r
L
P
r
L
O
O m
ω
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
n = 1.5 n = 1.2
R = 14 cm
(A) −280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm
Sol. (B)
1 1 0.5 0.2 1
P = (1.5 −1) − 0 + (1.2 −1) 0 − = + =
T
14 −14 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 z
constant angular speed ω, 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 ω
rod towards the other end. It reaches the end of the rod at t = T and stops.
The angular speed of the system remains ω throughout. The magnitude of v →
r
the torque (| τ |) about O, as a function of time is best represented by which
O
plot?
(A) (B)
r r
| τ | | τ |
O t O t
T T
(C) (D)
r r
| τ | | τ |
O t O t
T T
Sol. (B)
dI d 2 2
τ = ω = ω (C + mv t )
dt dt
2
= mωv 2t.
IITJEE-2012-Paper 1-PCM-3
r
L
P
r
L
O
O m
ω
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
n = 1.5 n = 1.2
R = 14 cm
(A) −280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm
Sol. (B)
1 1 0.5 0.2 1
P = (1.5 −1) − 0 + (1.2 −1) 0 − = + =
T
14 −14 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 z
constant angular speed ω, 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 ω
rod towards the other end. It reaches the end of the rod at t = T and stops.
The angular speed of the system remains ω throughout. The magnitude of v →
r
the torque (| τ |) about O, as a function of time is best represented by which
O
plot?
(A) (B)
r r
| τ | | τ |
O t O t
T T
(C) (D)
r r
| τ | | τ |
O t O t
T T
Sol. (B)
dI d 2 2
τ = ω = ω (C + mv t )
dt dt
2
= mωv 2t.
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