Answers & Solutions For JEE MAIN- 2015
(Code-A)
Time Duration : 3 hrs. Maximum Marks : 360
(Physics, Chemistry and Mathematics)
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. Each
question is allotted 4 (four) marks for each correct response.
4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response
of each question. 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. Filling up more than one response
in each question will be treated as wrong response and marks for wrong response will be
deducted accordingly as per instruction 4 above.
6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and
Side-2 of the Answer Sheet. Use of pencil is strictly prohibited.
7. No candidate is allowed to carry any textual material, printed or written, bits of papers,
pager, mobile phone, any electronic device, etc. except the Admit Card inside the
examination room/hall.
8. The CODE for this Booklet is A. Make sure that the CODE printed on Side-2 of the
Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are
the same as that on this booklet. In case of discrepancy, the candidate should immediately
report the matter to the Invigilator for replacement of both the Test Booklet and the Answer
Sheet.
, PART–A : PHYSICS
1. Two stones are thrown up simultaneously from the 2. The period of oscillation of a simple pendulum is
edge of a cliff 240 m high with initial speed of L
T 2
10 m/s and 40 m/s respectively. Which of the g . Measured value of L is 20.0 cm known
following graph best represents the time variation of to 1 mm accuracy and time for 100 oscillations of
relative position of the second stone with respect to
the pendulum is found to be 90 s using a wrist
the first?
watch of 1 s resolution. The accuracy in the
(Assume stones do not rebound after hitting the determination of g is
ground and neglect air resistance, take g = 10 m/s2)
(1) 2% (2) 3%
(The figures are schematic and not drawn to scale)
(3) 1% (4) 5%
(y2 – y1) m Answer (2)
240
2 l
Sol. g 4 .
T2
(1) g l T
100 100 2 100
t (s) g l T
t 8 12
l t
= 100 2. 100
(y2 – y1) m l t
240 0.1 1
= 100 2 100
20.0 90
100 200 1 20
(2) = 3%
200 90 2 9
t (s)
12
F
3. A B
(y2 – y1) m
240
(3) Given in the figure are two blocks A and B of
t (s) weight 20 N and 100 N, respectively. These are
8 12 being pressed against a wall by a force F as shown.
If the coefficient of friction between the blocks is 0.1
and between block B and the wall is 0.15, the
(y2 – y1) m frictional force applied by the wall on block B is
240
(1) 100 N (2) 80 N
(3) 120 N (4) 150 N
(4)
Answer (3)
t (s)
8 12
fs
Answer (3)
A B
Sol. Till both are in air (From t = 0 to t = 8 sec) Sol. F N
x = x2 – x1 = 30t
20 N 100 N
x t
When second stone hits ground and first stone is in Clearly fs = 120 N (for vertical equilibrium of the
air x decreases. system)
2
, 4. A particle of mass m moving in the x direction with 6. From a solid sphere of mass M and radius R a cube
speed 2v is hit by another particle of mass 2m of maximum possible volume is cut. Moment of
moving in the y direction wth speed v. If the
inertia of cube about an axis passing through its
collision is perfectly inelastic, the percentage loss in
the energy during the collision is close to center and perpendicular to one of its faces is
(1) 44% (2) 50% MR 2 MR 2
(1) (2)
(3) 56% (4) 62% 32 2 16 2
Answer (3) 4 MR 2 4 MR 2
(3) (4)
Sol. m 2v 9 3 3 3
v v' Answer (3)
= 2mv 2
v'
3m Sol. d 2 R a 3
2m
1 1
m 2 v 2m v 2
2
KE loss =
2 2
2
1 ⎛ 2mv 2 ⎞ 5 2
3m ⎜⎜ ⎟⎟ mv
2 ⎝ 3m ⎠ 3
2
5 a R
mv 2 3
Required % = 3 100 56%
2mv 2 mv 2
4 3
R
M 3
3
5. Distance of the centre of mass of a solid uniform
cone from its vertex is z0. If the radius of its base is M ⎛ 2 ⎞3 2
R and its height is h then z0 is equal to ⎜ R⎟
⎝ 3 ⎠
h2 3h
(1) (2) 2M
4R 4 M'
3
5h 3h 2
(3) (4)
8 8R M ' a2 2 M 4 2 1
I R
6 3 3 6
Answer (2)
Sol. dm r 2 .dy. 4 MR 2
I
9 3
7. From a solid sphere of mass M and radius R, a
R
y spherical portion of radius is removed, as
2
r h shown in the figure. Taking gravitational potential
V = 0 at r = , the potential at the centre of the
cavity thus formed is
(G = gravitational constant)
R
h
yCM
∫ ydm ∫ 0
r 2 dy y
1 2
∫ dm 3
R h GM GM
(1) (2)
2R R
3h
2GM 2GM
4 (3)
3R
(4)
R
3
(Code-A)
Time Duration : 3 hrs. Maximum Marks : 360
(Physics, Chemistry and Mathematics)
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. Each
question is allotted 4 (four) marks for each correct response.
4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response
of each question. 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. Filling up more than one response
in each question will be treated as wrong response and marks for wrong response will be
deducted accordingly as per instruction 4 above.
6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and
Side-2 of the Answer Sheet. Use of pencil is strictly prohibited.
7. No candidate is allowed to carry any textual material, printed or written, bits of papers,
pager, mobile phone, any electronic device, etc. except the Admit Card inside the
examination room/hall.
8. The CODE for this Booklet is A. Make sure that the CODE printed on Side-2 of the
Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are
the same as that on this booklet. In case of discrepancy, the candidate should immediately
report the matter to the Invigilator for replacement of both the Test Booklet and the Answer
Sheet.
, PART–A : PHYSICS
1. Two stones are thrown up simultaneously from the 2. The period of oscillation of a simple pendulum is
edge of a cliff 240 m high with initial speed of L
T 2
10 m/s and 40 m/s respectively. Which of the g . Measured value of L is 20.0 cm known
following graph best represents the time variation of to 1 mm accuracy and time for 100 oscillations of
relative position of the second stone with respect to
the pendulum is found to be 90 s using a wrist
the first?
watch of 1 s resolution. The accuracy in the
(Assume stones do not rebound after hitting the determination of g is
ground and neglect air resistance, take g = 10 m/s2)
(1) 2% (2) 3%
(The figures are schematic and not drawn to scale)
(3) 1% (4) 5%
(y2 – y1) m Answer (2)
240
2 l
Sol. g 4 .
T2
(1) g l T
100 100 2 100
t (s) g l T
t 8 12
l t
= 100 2. 100
(y2 – y1) m l t
240 0.1 1
= 100 2 100
20.0 90
100 200 1 20
(2) = 3%
200 90 2 9
t (s)
12
F
3. A B
(y2 – y1) m
240
(3) Given in the figure are two blocks A and B of
t (s) weight 20 N and 100 N, respectively. These are
8 12 being pressed against a wall by a force F as shown.
If the coefficient of friction between the blocks is 0.1
and between block B and the wall is 0.15, the
(y2 – y1) m frictional force applied by the wall on block B is
240
(1) 100 N (2) 80 N
(3) 120 N (4) 150 N
(4)
Answer (3)
t (s)
8 12
fs
Answer (3)
A B
Sol. Till both are in air (From t = 0 to t = 8 sec) Sol. F N
x = x2 – x1 = 30t
20 N 100 N
x t
When second stone hits ground and first stone is in Clearly fs = 120 N (for vertical equilibrium of the
air x decreases. system)
2
, 4. A particle of mass m moving in the x direction with 6. From a solid sphere of mass M and radius R a cube
speed 2v is hit by another particle of mass 2m of maximum possible volume is cut. Moment of
moving in the y direction wth speed v. If the
inertia of cube about an axis passing through its
collision is perfectly inelastic, the percentage loss in
the energy during the collision is close to center and perpendicular to one of its faces is
(1) 44% (2) 50% MR 2 MR 2
(1) (2)
(3) 56% (4) 62% 32 2 16 2
Answer (3) 4 MR 2 4 MR 2
(3) (4)
Sol. m 2v 9 3 3 3
v v' Answer (3)
= 2mv 2
v'
3m Sol. d 2 R a 3
2m
1 1
m 2 v 2m v 2
2
KE loss =
2 2
2
1 ⎛ 2mv 2 ⎞ 5 2
3m ⎜⎜ ⎟⎟ mv
2 ⎝ 3m ⎠ 3
2
5 a R
mv 2 3
Required % = 3 100 56%
2mv 2 mv 2
4 3
R
M 3
3
5. Distance of the centre of mass of a solid uniform
cone from its vertex is z0. If the radius of its base is M ⎛ 2 ⎞3 2
R and its height is h then z0 is equal to ⎜ R⎟
⎝ 3 ⎠
h2 3h
(1) (2) 2M
4R 4 M'
3
5h 3h 2
(3) (4)
8 8R M ' a2 2 M 4 2 1
I R
6 3 3 6
Answer (2)
Sol. dm r 2 .dy. 4 MR 2
I
9 3
7. From a solid sphere of mass M and radius R, a
R
y spherical portion of radius is removed, as
2
r h shown in the figure. Taking gravitational potential
V = 0 at r = , the potential at the centre of the
cavity thus formed is
(G = gravitational constant)
R
h
yCM
∫ ydm ∫ 0
r 2 dy y
1 2
∫ dm 3
R h GM GM
(1) (2)
2R R
3h
2GM 2GM
4 (3)
3R
(4)
R
3
