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JEE ADVANCED - 2016 PAPER - 1 22- MAY-2016
PART I - PHYSICS
SECTION - 1 (Maximum Marks 15)

C
(Only One Correct Type)
This section contains 5 questions. Each question has FOUR option (A), (B), (C) and (D). ONLY
ONE of these four option is correct.
1.
A parallel beam of light is incident from air at an angle  on the side PQ of a right angled
triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at
the face PR when  has a minimum value of 45°, The angle  of the prism is
P


Q
1.
n=2
R
(A)
15°
(B)
(A)
180° –  +  = 360° – 135° 
using snell’s law
22.5°
(C) 30°
 = 45° + 
sin 45
2


sin45  
1
(D) 45°

' = 45° – 
sin (45°– ) = (1 / 2) 
 = 15°
2.
In a historical experiment to determine Planck’s constant, a metal surface was irradiated with
light of different wavelengths. The emitted photoelectron energies were measured by applying a
stopping potential. The relevant data for the wavelength () of incident light and the corresponding
stopping potential (V0) are given below :
(m)
V0 (Volt)
0.3
2.0
0.4
1.0
0.5
0.4
Given that c = 3 × 108 m s–1 and e = 1.6 × 10–19C, Planck’s constant (in units of J s) found from
such an experiment is
(A) 6.0 × 10–34
(B) 6.4 × 10–34
(C) 6.6 × 10–34
(D) 6.8 × 10–34
2.
(B)
hc
   e.V0

and,



h  (3  10 8 )
   2  1.6  10 19
0.3  10  6
…(i)
h  3  10 8
   1.0  1.6  10  9
0.4  10 6

h  3  10 8  1
1 
9


  1.6  10
10 6
0
.
3
0
.
4


JEE Advanced 2016 (22-May-16)
…(ii)
h  3  10 8  1 
9

  1.6  10 h = 6.4 ×10–34Js
10 6
1
.
2


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3.
A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a
closed circulation system (as shown schematically in the figure), the water from the cooler is
used to cool an external device that generates constantly 3 kW of heat (thermal load). The
temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of
water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of
P (in watts) for which the device can be operated for 3 hours is
(Specific heat of water is 4.2 kJ kg–1 K–1 and the density of water is 1000 kg m–3)
Cooler
Device
Hot

C
cold
(A)
1600
(B)
2067
(C) 2533
3.
(B)
120 × 4200 ×20 = (3000 – P) × 3600 × 3
4.
An infinite line charge of uniform electric charge density lies along the axis of an electrically
conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled
with a material of permittivity  and electrical conductivity. The electrical conduction in the
material follows Ohm’s law. Which one of the following graphs best describes he subsequent
variation of the magnitude of current density j(t) at any point in the material?
j (t)
(0,0)
P = 2067 W
(B)
t
t
(0,0)
j (t)
j (t)
(C)
(D)
(0,0)
(A)

j (t)
(A)
4.
(D) 3933
E

2  .r
t
t
(0,0)
v 
r 

ln 2 
2 0  r1 
also J =  × E, i = i0e–(t)  (A) is correct.
JEE Advanced 2016 (22-May-16)
Question & Solutions Paper-I
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5.
A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth,
vertical wall of height h(<l) such that a small portion of the stick extends beyond the wall. The
reaction force of the wall on the stick is perpendicular to the sick. The stick makes an angle of
30° with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the
stick is equal in magnitude to the reaction of the floor on the stick. The ratio h/l and the frictional
force f at the bottom of the stick are (g = 10 ms–2)
(A)
h
3
16 3

,f 
N
l
16
3
(B)
h 3
16 3

,f 
N
l 16
3
(C)
h 3 3
8 3

,f 
N
l
16
3
(D)
h 3 3
16 3

,f 
N
l
16
3

C
5.
(D) or (No Answer is correct).
If we consider reaction at floor is
fs 2  N22 then No option matches.
If we consider reaction at floor is N2 then option (D) matches.
N1 : normal reaction by vertical wall.
N2 : normal reaction by horizontal surface.
 N1 cos 30° = fs
…(i)
 N1 = N2
…(ii)
for vertical eqlb :  N1 sin 30° + N2 = 16
 N1 = N2 = (32 / 3) Newton
 fs = [163 / 3]
net
ground  0
For rotational eqlb
mg
l 1
24
  N1
2 2
3
JEE Advanced 2016 (22-May-16)

h 3 3

l
16
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SECTION - 2 (Maximum Marks 32)
(One or More Than One Options Correct Type)
This section contains 8 questions. Each question has FOUR options (A), (B), (C) and (D).
ONE OR MORE THAN ONE of these four option(s) is (are) correct.
6.

The position vector r of a particle of mass m is given by the following equation

r (t )  t 3 iˆ   t 2 ˆj ,
where  = 10/3 ms–3,  = 5 ms–2 and m = 0.14 kg. At t = 1 s which of the following statement(s)
is (are) true about the particle?

(A) The velocity v is given by v  (10 iˆ  10 ˆj ) ms -1


(B) The angular momentum L with respect to the origin is given by L  (5 / 3)kˆ N m


(C) The force F is given by F  (iˆ  2 ˆj ) N


(D) The torque  with respect to the origin is given by   ( 20 / 3)kˆ N m

C

 dr
v
 (3t 2 )iˆ  ( 2 t ) ˆj
dt


 dv

a
 (6t )iˆ  (2) ˆj , F  ma
dt
 
   
L  r  mv ,   r  F
6.
(ABD)
7.
A transparent slab of thickness d has a refractive index n(z) that increases with z, Here z is the
vertical distance inside the slab, measured from the top. The slab is placed between two media
with uniform refractive indices n1 and n2 (>n1), as shown in the figure . A ray of light is incident
with angle i from medium 1 and emerges in medium 2 with refraction angle f with a lateral
displacement l.
i
1
n1=constant
n(z)
z
n2=constant
d
2
l
f
Which of the following statement(s) is (are) true?
(A) l is independent of n2
(B) n1sin i  = n2 sin f
(C) l is dependent of n(z)
(D) n1sin i  =( n2 – n1)sin f
7.
(ABC)
nsin n = constant for parallel interfaces, l depends on n (z) & independent of n2.
JEE Advanced 2016 (22-May-16)
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8.
A plano-convex lens is made of a material of refractive index n. When a small object is placed
30 cm away in front of the curved surface of the lens, an image of double the size of the object is
produced. Due to reflection from the convex surface of the lens, another faint image is observed
at a distance of 10 cm away from the lens. Which of the following statement(s) is (are) true?
(A) The refractive index of the lens is 2.5
(B) The radius of curvature of the convex surface is 45 cm
(C) The faint image is erect and real.
(D) The focal length of the lens is 20 cm.
8.
(AD)
Lens : m = 2
 v = 60 m  1/ f = (1/30) + (1/60)
Mirror : convex  v = –10 cm
 (1/30) – (1/10) = 2 / (–R) R = 30 cm
 (1/flens) =(n–1) (1/30)  n = 2.5
f = 20 cm

C
9.
Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge
Ze are defined by their principal quantum number n, where n>>1. Which of the following
statement(s) is (are) true?
A) Relative change in the radii of two consecutive orbitals does not depend on Z
(B) Relative change in the radii of two consecutive orbitals varies as 1/n
(C) Relative change in the energy of two consecutive orbitals varies as 1/n3
(D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n.
9.
(ABD)
r = a0n2 / z
dr =(a0 / z)× 2n . dn
dr (a0 z )  2n  1 1


r
(a0 n 2 z )
n
(B)
E = E0(z2/n2)
dE = E0z2 (–2/n3) × dn
dE E0 z2 (2 / n3 )  1 1


E
(E0z2 n2 )
n
L = nh / 2
dL = (h / 2) .dn
dL (h / 2 )  1 1


L
(h / 2 )
n
dL (h / 2 )  1 1


L
(nh / 2 )
n
JEE Advanced 2016 (22-May-16)
(D)
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10. A length-scale (l) depends on the permittivity () of a dielectric material. Boltzmann constant
(kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles,
and the charge (q) carried by each of the particles. Which of the following expression(s) for l is
(are) dimensionally correct?
(A)
 nq 2
l  
 kBT
(C)

q2
l   2/3
 n k BT








(B)
 k T 
l   B2 
 nq 
(D)

q2
l   1/3
 n k BT





C
10. (BD)
b
 q2 
c
l  K bT    n  

 
a+b=0
…(i)
–2a – 2b =0
…(ii)
2a + 3b – 3c = 2
…(iii)
c = –1/ 3, b = –1, a = 1
q2
K bT , , n 

JEE Advanced 2016 (22-May-16)
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

[L2] = ML2T 2 a ML3T 2
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 L 
b
3 c
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11.
Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and
121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line
MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It
crosses Q and eventually reaches a point R, 1800 m away from Q. Let (t) represent the beat
frequency measured by a person sitting in the car at time t. Let P, Q and R be the beat
frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330
ms–1. Which of the following statement(s) is (are) true regarding the sound heard by the person?
(A)
The plot below represents schematically the variation of beat frequency with time
 (t)
P

C
Q
Q
R
t
(B) P + R = 2Q
(C) The plot below represents schematically the variation of beat frequency with time
 (t)
P
Q
Q
R
t
(D) The rate of change in beat frequency is maximum when the car passes through Q
R
M
Q

11.
N

(ABD)
P1 (t)
P
'= [(330 + v) / 330] .f
(t)= (121 –118) + (v cos/330) (121–118)
= 3 + (v cos/330)× 3
So, option A, B and D are correct.
JEE Advanced 2016 (22-May-16)
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12. A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such
that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is
electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The
current in the triangular loop is in counterclockwise direction and increased at a constant rate of
10 A s–1. Which of the following statement(s) is (are) true?
10cm
(A)
(B)
(C)
(D)
90°
The induced current in the wire is in opposite direction to the current along the hypotenuse
The magnitude of induced emf in the wire is (µ0 / ) volt
There is a repulsive force between the wire and the loop
If the loop is rotated at a constant angular speed about the wire, an additional emf of
(µ0 /) volt is induced in the wire

C
C
12. (BC)
A
B
Due to section (AB), current in wire will be as shown (from Lenz's law).
Due to AB section force is attractive, where as due to (BC–CA) section force is
repulsive. (BC–CA) section being closer repulsive force will dominate.
x
dx
l
0 i
And ,   
.2 xdx

 2x
0
(l = 0.1 m)
= (0i /)(l)
M = (0i /10)
  M
di

 0 .volt
dt

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13. An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing
an electric current. The hot filament emits black-body radiation. The filament is observed to
break up at random locations after a sufficiently long time of operation due to non-uniform
evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the
following statement(s) is (are) true?
(A) The temperature distribution over the filament is uniform
(B) The resistance over small sections of the filament decreases with time
(C) The filament emits more light at higher band of frequencies before it breaks up
(D) The filament consumes less electrical power towards the end of the life of the bulb
13. (CD)
P = V2 / R
as frequency increases  energy increases.  (C) is correct.
due to evapouration of tungsten, power consume will be less at the end
 (D) is correct.

C
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SECTION - 3 (Maximum Marks 15)
(One Integer Value Correct Type)
This section contains 5 questions. The answer to each question is SINGLE DIGIT INTEGER
ranging from 0 to 9, both inclusive.
14. Two inductors L1(inductance 1 mH, internal resistance 3 ) and L2 (inductance 2 mH, internal
resistance 4 ), and a resistor R (resistance 12 ) are all connected in parallel across a 5 V
battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum
current (Imax / Imin) drawn from the battery is

C
1mH
3
2mH
4
12
I min 
14. (8)
5
12
I max 
I max
 1 3  4  8
I min
5 5 5
 
12 4 3
5V
15. A metal is heated in a furnace where a sensor is kept above the metal surface to read the power
radiated (P) by the metal. The sensor has a scale that displays log2 (P / P0), where P0 is a
constant. When the metal surface is at a temperature of 487 °C, the sensor shows a value 1.
Assume that the emissivity of the metallic surface remains constant. What is the value displayed
by the sensor when the temperature of the metal surface is raised to 2767 °C?
15. (9)
Reading = wg2 (P / P0)
T1 = 760
T2= 3040 = 4T1
1 = 4 log2 (T1 / T0)
and m = 4 log2 (4T1 / T0)
 m – 1 = 4 [log2 (4)]
m–1=8
m=9
16. A hydrogen atom in its ground state is irradiated by light of wavelength 970 Å. Taking hc / e =
1.237 × 10–6 eV m and the ground state energy of hydrogen atom as – 13.6 eV, the number of
lines present in the emission spectrum is
16. (6)
E = (hc / e) = [(1.237 × 10–6) / (970 / 10–10)] = 12.75 eV
So, e– jumps to n = 3 (3rd excited state)
no. of  = [(3 × 4) / 2] = 6
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17. Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and
0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity
 = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm–3 and viscosity  = 2
poiseulles. The ratio of the terminal velocities of P and Q is
17. (3)
V = (2 / 9) r2
[{(S – l) g} / ]
2
VP  rP  S  l P  Q
  .
.
VQ  rQ  S   l Q  P
2
 2 .



8  0.8  .  2 
 
8  1.6  3 

C
 4
97 .2 2
 3
6.4 3
18. The isotope 125B having a mass 12.014 u undergoes –decay to 126C. 126C has an excited state
of the nucleus (126 C * ) at 4.041 MeV above its ground state. If 125 B decays at 126C * , the maximum
kinetic energy of the –particle in units of MeV is
(1 u = 931.5 MeV/c2, where c is the speed of light in vacuum).
18. (9)
12
5
0
B  12
6 C *  1e  Q.value
Q–value = Kmax = {(12.014 – 12) × 031 – 4.041} MeV
= 8.993 MeV  9 MeV = 9
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