IIT JEE Advanced exam successfully conducted by Indian Institutes of Technology (IITs) on 22nd May 2016This exam held in seven IIT zones across the country. Around two Laks Students attend the JEE Advanced examination. We are providing you a tentative and reliable Answer Key. Through this Answer Sheet you can Review and Analysis your performance in the examination. You can also check Answer Sheet from official Website jeeadv.nic.in.

PART-I : PHYSICS

SECTION–1 : (Maximum Marks : 15)
-> This section contains Five questions.
-> Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct
->For each question, darken the bubble corresponding to the correct option in the ORS
-> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –1 In all other cases

1. A parallel beam of light is incident from air at an angle α 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 α has a minimum value of 45°. The angle θ of the prism is:

(a) 15°
(b) 22.5°
(c) 30°
(d) 45°
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 (λ) of incident light and the corresponding stopping potential (V0) are given below:

Given that c = 3 × 10^8 ms^–1 and e = 1.6 × 10^–19 C, 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
3. 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 stick. 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)

4. A water cooler of storage capacity 120 litres can cool water at 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)
(a) 1600
(b) 2067
(c) 2533
(d) 3933
5. An infinite line charge of uniform electric charge density λ 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 σ. The electrical conduction in the material follows Ohm’s law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

SECTION–2 : (Maximum Marks : 32)
-> This section contains EIGHT questions.
-> Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four option(s) is (are) correct.
-> For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
-> For each question, marks will be awarded in one of the following categories :
Full Marks : +4 If only the bubble(s) corresponding to the correct option(s) is (are) darkened.
Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –2 In all other cases

6. 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 θi from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement θ.
Which of the following statement(s) is(are) true ?

7. A conducting loop in the shape of 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 constant rate of 10 A s^–1. Which of the following statement(s) is(are) true?

(a) The induced current in the wire is in opposite direction to the current along the hypotenuse.
(b) There is a repulsive force between the wire and the loop
(c) If the loop is rotated at a constant angular speed about the wire, an additional emf of (μ⋅/π) volt is induced in the wire
(d) The magnitude of induced emf in the wire is (μ⋅/π) volt.
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.
9. 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
10. A length-scale (l) depends on the permittivity (ε) 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 expressions(s) for l is(are) dimensionally correct?

11. 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 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
12. The position vector r of a particle of mass m is given by the following equation   which of the following statement (s) is (are) true about the particle?

Answer is : A, B, D
13. Two loudspeakers M and N are located 20m 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 Iv(t) represent the beat frequency measured
by a person sitting in the car at time t. Let VP, VQ and VR 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

(b) The plot below represents schematically the variations of beat frequency with time

(c) The rate of change in beat frequency is maximum when the car passes through Q
(d)

SECTION–3 : (Maximum Marks : 15)
-> This section contains FIVE questions.
-> The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
-> For each question, darken the bubble corresponding to the correct integer in the ORS.
-> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened.
Zero Marks : 0 In all other cases.

14. 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 η = 3 poise lies.
Sphere Q is dropped into a liquid of density 1.6 gm cm^–3 and viscosity η = 2 poise lies. The ratio of the terminal velocities of P and Q is.
15. Two inductors L1 (inductance 1 mH, internal resistance 3 Ω) and L2 (inductance 2mH, internal resistance 4Ω), and a resistor R (resistance 12 Ω) are all connected in parallel across a 5V 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.
: 8
17. 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
18. 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?
PART – II : CHEMISTRY
SECTION–1 : (Maximum Marks : 15)
-> This section contains Five questions.
-> Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct
-> For each question, darken the bubble corresponding to the correct option in the ORS
-> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –1 In all other cases
19. P is the probability of finding the 1 s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4r2dr. The qualitative sketch
of the dependence of P on r is –

20. One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings (ΔSsurr) in J K–1 is –
(1 L atm = 101.3 J)
(a) 5.763
(b) 1.013
(c) -1.013
(d) -5.763
21. The increasing order of atomic radii of the following group 13 elements is
(a) Al < Ga < In < Tl
(b) Ga < Al < In < Tl
(c) Al < In < Ga < Tl
(d) Al < Ga < Tl < In
22. On complete hydrogenation, natural rubber produces
(a) ethylene-propylene copolymer
(b) vulcanised rubber
(c) polypropylene
(d) polybutylene
23. Among [Ni(CO)4], [NiCl4]2– , [Co(NH3)4Cl2]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compounds is –
(a) 2
(b) 3
(c) 4
(d) 5
SECTION–2 : (Maximum Marks : 32)
–> This section contains EIGHT questions.
–> Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four option(s) is (are) correct.
–> For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
–> For each question, marks will be awarded in one of the following categories :
Full Marks : +4 If only the bubble(s) corresponding to the correct option(s) is (are) darkened.
Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –2 In all other cases
for example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in -2 marks, as a wrong option is also darkened.
24. A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upwards deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is (are)-
(a) β¯ decay (β emission)
(b) orbital or K-electron capture
(c) Neutron emission
(d) β^+ decay (positron emission)
25. The correct statements(s) about of the following reaction sequence is(are)

(a) R is steam volatile
(b) Q gives dark violet coloration with 1% aqueous FeCl3 solution
(c) S gives yellow precipitate with 2, 4,-dinitrophenylhydrazine
(d) S gives dark violet coloration with 1% aqueous FeCl3 solution
26. Positive Tollen’s test is observed for

27. The product(s) of the following reaction sequence is(are)

28. The compound(s) with TWO lone pairs of electrons on the central atom is (are)
(a) BrF5
(b) ClF3
(c) XeF4
(d) SF4
29. The crystalline form of borax has
(a) Tetranuclear [B4O5(OH)4]^2– unit
(b) All boron atoms in the same plane
(c) Equal number of sp2 and sp3 hybridized boron atoms
(d) One terminal hydroxide per boron atom
30. The reagent(s) that can selectively precipitate S2– from a mixture of S2– and SO4^2– in aqueous solution is(are) :
(a) CuCl2
(b) BaCl2
(c) Pb(OOCCH3)2
(d) Na2[Fe(CN)5NO]
31. According to the Arrhenius equation,
(a) A high activation energy usually implies a fast reaction
(b) Rate constant increase with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy
(c) Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant
(d) The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.
SECTION–3 : (Maximum Marks : 15)
–> This section contains FIVE questions.
–>The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
–> For each question, darken the bubble corresponding to the correct integer in the ORS.
–> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened.
Zero Marks : 0 In all other cases.
32. The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm–3. The ratio of the molecular weights of
the solute and solvent,

33. In the following monobromination reaction, the number of possible chiral products is

34. The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a
result, the diffusion coefficient of this gas increases x times. The value of x is
35. The number of geometric isomers possible for the complex
36. In neutral or faintly alkaline solution, 8 moles permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of a sulphur containing product. the magnitude of X is
Part-III: Mathematics
SECTION–1 : (Maximum Marks : 15)
–> This section contains Five questions.
–> Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct
–> For each question, darken the bubble corresponding to the correct option in the ORS
–> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –1 In all other cases
37. A debate club consists of 6 girls and 4 body. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 member) for the team. If the team has to
include at most one boy, then the number of ways of selecting the team is
(a) 380
(b) 320
(c) 260
(d) 95
38. The least value of α ∈ R for which  for all x>0, is-
(a) 1/64
(b) 1/32
(c) 1/27
(d) 1/25
39. Let
Suppose α1 and β1 are the roots of the equation x2 – 2xsecθ + 1 = 0 and α2 and β2 are the roots of the equation x2 + 2xtanθ – 1 = 0.
(a) 2(secθ – tanθ)
(b) 2secθ
(c) –2tanθ
(d) 0
40.   The sum of all distinct solution of the equation  √sec x + cosecx + 2(tan x – cot x) = 0 in the set S is equal to –
(a) -(7π/9)
(b) -(2π/9)
(c) 0
(d) 5π/9
41. A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out
to be defective. It is known that
P(computer turns out to be defective given that is produced in plant T1)
= 10P(computer turns out to be defective given that it is produced in plant T2)
where P(E) denotes the probability of an event E. A computer produces in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2
is
(a) 36/73
(b) 47/79
(c) 78/93
(d) 75/83
SECTION–2 : (Maximum Marks : 32)
–> This section contains EIGHT questions.
–> Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is (are) correct.
–> For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
For each question, marks will be awarded in one of the following categories :
Full Marks : +4 If only the bubble(s) corresponding to the correct option(s) is (are) darkened.
Partial Marks:+1 For darkening a bubble corresponding to each correct option, Provided No incorrect option is darkened.
Zero Marks:  0 If None of the bubbles is darkened.
Negative Marks: -2 In all other cases
for example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in -2 marks, as a wrong option is also darkened.
42. A solution curve of the differential equation (x² + xy + 4x + 2y + 4)
(dy/dx)-y² = 0,x>0, passes through the point (1,3). The the solution curve-
(a) intersects y = x + 2 exactly at one point
(b) intersects y = x + 2 exactly at two points
(c) intersects y = (x + 2)²
(d) does NOT intersect y = (x + 3)²
43. Consider a pyramid OPQRS located in the first octant (x ≥> 0,y ≥ 0, z ≥> 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP= 3. The point S is directly above the mid-point T of diagonal OQ such that TS = 3. Then-
(a) the acute angle between OQ and OS is π/3
(b) the equation of the plane containing the triangle OQS is x – y = 0
(c) the length of the perpendicular from P to the plane containing the triangle OQS is 3/√2
(d) the perpendicular distance from O to the straight line containing RS is √(15/2)
44. In a triangle XYZ, let x,y,z be the lengths of sides opposite to the angles X,Y,Z, respectively and 2s = x + y + z. If (s-x)/4= s-y/3= s-z/2
and area of in circle of the triangle XYZ is 8π/3, then-
(a) area of the triangle XYZ is 6√6
(b) the radius of circumcircle of the triangle XYZ is (35/6) √6
(c) sin X/2 sin Y/2 sin Z/2 = 4/35
(d) sin²((X+Y)/2)=3/5
45. Let RS be the diameter of the circle x² + y² = 1, where S is the point (1,0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal
to the circle at P intersects a line drawn through Q parallel to RS at point E. then the locus of E passes through the point(s)-
(a) (1/3, 1/√3)
(b) (1/4, 1/2)
(c) (1/3, -1/√3)
(d) (1/4, -1/2)
46. The circle C1: x² + y² = 3, with centre at O, intersects the parabola x² = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2√3 and centres Q2 and Q3, respectively. If Q2 and Q3 lie on the y-axis, then-

47. Let ƒ : R –> R, g : R –> R and h : R –> R be differentiable functions such that ƒ(x) = x³ + 3x + 2, g(ƒ(x)) = x and h(g(g(x))) = x for all x ∈ R. Then-
(a) g'(2)=1/15
(b) h'(1)=666
(c) h(0)=16
(d) h(g(3))=36
48. Let ƒ : (0, ∞) –> R be a differentiable function such that f‘(x)=2-(ƒ(x)/x for all x ∈ (0,∞) and ƒ(1) ≠ 1. Then

49. Let P=(a) α=0, k=8
(b) 4α-k+8=0
SECTION–3 : (Maximum Marks : 15)
–> This section contains FIVE questions.
–> The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
–> For each question, darken the bubble corresponding to the correct integer in the ORS.
–> For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened.
Zero Marks : 0 In all other cases.
50. Let m be the smallest positive integer such that the coefficient of x2 in the expansion of
(1 + x)² + (1 + x)³ + ……. + (1 + x)^49 + (1 + mx)^50 is (3n + 1) ^51 C3 for some positive integer n.Then the value of n is
51.  The total number of distinct x ∈ R for which
=10 is
52. Let z =–1 +√3i /2, where i = √-1, and r, s ∈ {1, 2, 3}. Let P =
and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P² = –I is