PART I : PHYSICS SECTION 1 (Maximum Marks : 15)rgacademy.co.in/IIT JEE 2016.pdf · [1] IIT JEE –...

[1] IIT JEE – 2016 / Paper-1

PHYSICSPART 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. In a historical experiment to determine Planck's constant, a metal surface was irradiated with light ofdifferent wavelengths. The emitted photoelectron energies were measured by applying a stopping potential.The relavant data for the wavelength ( ) of incident light and the corresponding stopping potential (V

0)

are given below:

( )m V0 ( )Volt0.3 2.00.4 1.00.5 0.4

Given that c = 3 × 108 m s–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

2. A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wallof height h(< l) such that a small portion of the stick extends beyond the wall. The reaction force of thewall on the stick is perpendicular to the stick. The stick makes an angle of 30° with the wall and the bottomof the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction ofthe floor on the stick. The ratio h/l and the frictional force f at the bottom of the stick are (g = 10 m/s2)

(A)h

lf

3

16

6 3

3, N (B)

h

lf

3

16

6 3

3, N

(C)h

lf

3 3

16

8 3

3, N (D)

h

lf

3 3

16

16 3

3, N

[2] IIT JEE – 2016 / Paper-1

PHYSICS

3. A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closedcirculation system (as shown schematically in the figure), the water from the cooler is used to cool anexternal device that generates constantly 3 kW of heat (thermal load). The temperature of water fed intothe device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. Theentire system is thermally insulated. The minimum value ofP (in watts) for which the device can be operatedfor 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

4. A parallel beam of light is incident from air at an angle a 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 a has a

minimum value of 45°. The angle of the prism is

(A) 15° (B) 22.5° (C) 30° (D) 45°

5. An infinite line charge of uniform electric charge density lies along the axis of an electrically conductinginfinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material ofpermittivity and electrical conductivity . 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 currentdensity j(t) at any point in the material?

(A) (B) (C) (D)

[3] IIT JEE – 2016 / Paper-1

PHYSICS

6. Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear chargeZeare definedby their principal quantum numbern, 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

7. 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 movestowards Q constantly at 60 km / hr along the perpendicular bisector of MN. It crosses Q and eventuallyreaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a personsitting in the car at time t. Let v

P , v

Qand v

Rbe the beat frequencies measured at locations P , Q and R,

respectively.The speed of sound in air is 330 m s–1. Which of the following statement(s) is(are) true regarding the soundheard by the person?(A) v

P + v

R= 2 v

Q

(B) The rate of change in beat frequency is maximum when the car passes through Q(C) The plot below represents schematically the variation of beat frequency with time

(D) The plot below represents schematically the variation of beat frequency with time

8. An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing anelectric current. The hot filament emits black-body radiation. The filament is observed to break up atrandom locations after a sufficiently long time of operation due to non-uniform evaporation of tungstenfrom 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

[4] IIT JEE – 2016 / Paper-1

PHYSICSSECTION 2 (Maximum Marks : 32)

This section contains EIGHT questions.

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE OR MORE THAN ONE ofthese four options(s) is(are) correct.


For each question, marks will be awarded in one of the following categories:Full Marks : +4 If only the bubble(s) corresponding to all 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 willresult in +4 marks: darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will resultin –2 marks, as a wrong option is also darkened.

9. A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm awayin front of the curved surface of the lens, an image of double the size of the object is produced. Due toreflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm awayfrom the lens. Which of the following statements) 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

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) lnq

k TB

FHGIKJ

2

(B) l

k T

nqBFHGIKJ

2

(C) lq

n k TB

FHGIKJ

2

2 3 /(D) l

q

n k TB

FHGIKJ

2

1 3 /

[5] IIT JEE – 2016 / Paper-1

PHYSICS

11. 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 insulatedfrom the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is incounterclockwise direction and increased at a constant rate of 10 As–1. Which of the following statement(s)is(are) true?

(A) The magnitude of induced emfin the wire is

0FHGIKJ volt

(B) If the loop is rotated at a constant angular speed about the wire, an additional emf of

0FHGIKJ volt is

induced in the wire(C) The induced current in the wire is in opposite direction to the current along the hypotenuse(D) There is a repulsive force between the wire and the loop

12. The position vector r of a particle of mass m is given by the following equation :r t t i t j( ) , 3 2

where 10 3 53 2/ ,m s m s and m = 0.1 kg. At t =1 s, which of the following statement(s)

is(are) true about the particle?

(A) The velocity is given by ( )10 10 1i j m s

(B) The angular momentumL with respect to the origin is given by

L k ( / ) 5 3 N m s

(C) The forceF is given by

F i j ( )2 N

(D) The torque with respect to the origin is given by ( / ) 20 3 k N m

13. A transparent slab of thickness d has a refractive index n(z) that increases with z . Here z is the verticaldistance 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 ifrom

medium 1 and emerges in medium 2 with refraction angle f with a lateral displacement l.

Which of the following statement(s) is(are) true?

(A) n ni f1 2sin sin (B) n n ni f1 2 1sin ( ) sin

(C) l is independent of n2 (D) l is dependent on n(z)

[6] IIT JEE – 2016 / Paper-1

PHYSICSSECTION 3 (Maximum Marks : 15)


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. 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 log

2 (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 themetallic surface remains constant. What is the value displayed by the sensor when the temperature of themetal surface is raised to 2767 °C?

15. The isotope6

12 B having a mass 12.014 u undergoes -decay to6

12

6

12C C has an excited state of the

nucleus (6

12 C* ) at 4.041 MeV above its ground state. If6

12 B decays to6

12 C*, 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).

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 numberof lines present in the emission spectrum is

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 terminalvelocities of P and Q is

18. Two inductors L1(inductance 1 mH, internal resistance 3 Q) 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 isswitched on at time t = 0. The ratio of the maximum to the minimum current (Imax / Imin) drawn from thebattery is

CHEMISTRY

[9] IIT JEE – 2016 / Paper-1

PART II : CHEMISTRY






19. P is the probability of finding the 1s 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 2r dr . The qualitative sketch of thedependence of P on r is

(A) (B)

(C) (D)

CHEMISTRY

[10] IIT JEE – 2016 / Paper-1

20. One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 Lto 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings

Ssurrb g in JK1 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. Among Ni CO NiCl Co NH Cl Cl Na CoF Na Ob g b g4 4

2

3 4 2 3 6 2 2, , , ,

and CsO2 , the total number of

paramagnetic compounds is

(A) 2 (B) 3 (C) 4 (D) 5

23. On complete hydrogenation, natural rubber produces

(A) ethylene-propylene copolymer (B) vulcanised rubber

(C) polypropylene (D) polybutylene

CHEMISTRY

[11] IIT JEE – 2016 / Paper-1









24. According to the Arrhenius equation,

(A) a high activation energy usually implies a fast reaction.

(B) rate constant increases with increase in temperature. This is due to a greater number of collisionswhose 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 collision occur, irrespective of theirenergy

25. A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upwarddeviation 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) -decay ( emission) (B) orbital or K-electron capture

(C) neutron emission (D) -decay (positron emission)

26. The crystalline form of borax has

(A) tetranuclear B O OH4 5 4

2b g 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

CHEMISTRY

[12] IIT JEE – 2016 / Paper-1

27. The compound(s) with TWO lone pairs of electrons on the central atom is(are)

(A) BrF5 (B) ClF3 (C) XeF4 (D) SF4

28. The reagent(s) that can selectively precipitate S2 from a mixture of S2 and SO42 in aqueous solution

is(are)

(A) CuCl2 (B) BaCl2 (C) Pb OOCCH3 2b g (D) Na Fe CN NO2 5b g

29. Positive Tollen's test is observed for

(A) (B) (C) (D)

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

(A) (B) (C) (D)

31. The correct statement(s) about 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

CHEMISTRY

[13] IIT JEE – 2016 / Paper-1






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 3. g cm . The ratio of the molecular weights of the solute

and solvent,MW

MWsolute

solvent

FHG

IKJ , is

33. The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x is

34. In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphateanions to produce X moves of a sulphur containing product. The magnitude of X is

35. The number of geometric isomers possible for the complex CoL Cl L H NCH CH O2 2 2 2 2

is

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

MATHEMATICS

[14] IIT JEE – 2016 / Paper-1

PART III : MATHEMATICS






37. Let6 12

. Suppose 1 and 1 are the roots of the equation 2x 2x sec 1 0 and 2 and

2 are the roots of the equation 2x 2x tan 1 0 .If 1 1 and 2 2 , then 1 1 equals.

(A) 2 sec tan (B) 2sec (C) 2 tan (D) 0

38. A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club includingthe selection of a captain (from among these 4 members) for the team. If the team has to include at mostone boy, then the number of ways of selecting the team is

(A) 380 (B) 260 (C) 260 (D) 95

39. Let S x , : x 0,2

. The sum of all distinct solutions of the equation

3 sec x cos ecx 2 tan x cot x 0 in the set S is equal to

(A)7

9

(B)

2

9

(C) 0 (D)

5

9

MATHEMATICS

[15] IIT JEE – 2016 / Paper-1

40. A computer producing factory has only two plants 1T and 2T . Plant 1T produces 20% and plant 2T

produces 80% of the total computers produced. 7% of compouters produced in the factory turn out to bedefective. It is known that

P(computer turns out to be defective given that it is produced in plant 1T )

= 10 P (computer turns out to be defective given that it is produced in plant 2T )

where P E denotes the probability of an event E. A computer produced in the factory is randomly

selected and it does not turn out to be defective. Then the probability that it is produced in plant 2T is

(A)36

73 (B)

47

79(C)

78

93(D)

75

83

41. The least value of R for which 2 14 x 1

x , for all x 0 is

(A)1

64(B)

1

32(C)

1

27(D)

1

25

MATHEMATICS

[16] IIT JEE – 2016 / Paper-1









42. 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 is3

(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 is3

2

(D) the perpendicular distance from O to the straight line containing RS is 15

2

43. Let f : 0, be a differentiable function such that f x

f (x) 2x

for all x 0, and f 1 1 .

Then

(A)x 0

1lim f 1

x

(B)x 0

1lim x f 2

x

(C) 2

x 0lim x f x 0

(D) f x 2 for all x (0, 2)

MATHEMATICS

[17] IIT JEE – 2016 / Paper-1

44. Let

3 1 2

P 2 0

3 5 0

where a R . Suppose ijQ q is a matrix such that PQ kI , where

k R, k 0 and I is the identity matrix of order 3. If 23

kq

8 and

2kdet Q

2 , then

(A) 0, k 8 (B) 4 k 8 0 (C) 9det P adj Q 2 (D) 13det Q adj P 2

45. If a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X, Y, Z, respectively, and

2z x y z . Ifs x s y s z

4 3 2

and area of incircle of the triangle XYZ is

8

3

, then

(A) area of the triangle XYZ is 6 6

(B) the radius of circumcircle of the triangle XYZ is35

66

(C)X Y Z 4

sin sin sin2 2 2 35

(D) 2 x y 3sin

2 5

MATHEMATICS

[18] IIT JEE – 2016 / Paper-1

46. A solution curve of the differential equation 2 2dyx xy 4x 2y 4 y 0

dx , x 0 , passes through

the point (1, 3). Then the solution curve

(A) intersects y x 2 exactly at one point (B) intersects y x 2 exactly at two points

(C) intersects 2y x 2 (D) does NOT intersect 2

y x 3

47. Let f : , g : and h : be differentiable functions such that 3f x x 3x 2 ,

g f x x and h g g x x for all x . Then

(A) 1g 2

15 (B) h 1 666 (C) h 0 16 (D) h g 3 36

48. The circle 2 21C :x y 3 , with centre at O, intersects the parabola 2x 2y at the point P in the first

quadrnat. Let the tangent to the circle 1C at P touches other two circles 2C and 3C at 2R and 3R ,

respectively. Suppose 2C and 3C have equal radii 2 3 and centres 2Q and 3Q respectively. If 2Q and

3Q lie on the y-axis, then

(A) 2 3Q Q 12 (B) 2 3R R 4 6

(C) area of the triangle 2 3OR R is 6 2 (D) area of the triangle 2 3PQ Q is 4 2

49. Let RS be the diameter of the circle 2 2x y 1 , where S is the point (1, 0) . Let P be a varible 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 tothe circle at P intersects a line drawn through Q parallel to RS at point E.Then the locus of E passesthrough the point(s)

(A)1 1

,3 3

(B)1 1

,4 2

(C)1 1

,3 3

(D)1 1

,4 2

MATHEMATICS

[19] IIT JEE – 2016 / Paper-1






50. The total number of distinct x for which

2 3

2 3

2 3

x x 1 x

2x 4x 1 8x 10

3x 9x 1 27x

is

51. Let m be the smallest positive integer such that the coefficient of 2x in the expansion of

2 3 49 501 x 1 x ... 1 x 1 mx is 51

33x 1 C for some positive integer n. Then the value

of n is

52. The total number of distinct x 10,1 for whichx 2

40

tdt 2x 1

1 t

is

53. Let , be such that 2

x 0

x sin xlim 1

x sin x

. Then 6 equals

54. Let1 3i

z2

, where i 1 and r, s 1, 2, 3 . Let

r 2s

2s r

z zP

r z

and I be the indentity

matrix of order 2. Then the total number of ordered pairs (r, s) for which 2P I is

PHYSICS[1] IIT JEE – 2016 / Paper-2

PART I: PHYSICS


This section contains SIX questions.



For each question, marks will be awarded in one of the following categories:Full Marks : +3 If only the bubble coresponding to the corect option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases.

1. There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale.The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scaledivisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 mainscale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) bycalipers C1 and C2, respectively, are

(A) 2.87 and 2.83 (B) 2.87 and 2.87 (C) 2.87 and 2.86 (D) 2.85 and 2.82

2. A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex sphericalmirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror istilted such that the axis of the mirror is at an angle = 30° to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of thepoint (x,y) at which the image is formed are

(A) (50 – 25 3, 25) (B) (125 / 3,25 / 3) (C) (25, 25 3) (D) (0,0)


3. An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissiblelevel required for safe operation of the laboratory. What is the minimum number of days after which thelaboratory can be considered safe for use?(A) 64 (B) 90 (C) 108 (D) 120

4. The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of thewires has a length of 1 m at 10 °C. Now the end P is maintained at 10 °C, while the end S is heatedand maintained at 400 °C. The system is thermally insulated from its surroundings. If the thermalconductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion ofPQ is 1.2 × 10–5 K–1, the change in length of the wire PQ is(A) 0.78 mm (B) 0.90 mm (C) 1.56 mm (D) 2.34 mm

5. The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R isgiven by

EZ Z e

R=

3

5

1

4

2

0

( )

The measured masses of the neutron,1

1

7

15H, N and8

15O are 1.008665 u, 1.007825 u, 15.000109 u and

15.003065 u, respectively. Given that the radii of both the7

15 N and8

15O nuclei are same, 1 u = 931.5

MeV/c2 (c is the speed of light) and e2

04 144/ ( ) . MeV fm. Assuming that the difference between the

binding energies of7

15 N and8

15O is purely due to the electrostatic energy, the radius of either of the nuclei

is (1 fm = 10–15 m)(A) 2.85 fm (B) 3.03 fm (C) 3.42 fm (D) 3.80 fm

6. A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure

Pi 105 Pa and volume Vi 10 3 3m changes to a final state at Pf ( / )1 32 105 Pa and

V f 8 10 3 3m in an adiabatic quasi-static process, such that P V3 5 constant. Consider anotherthermodynamic process that brings the system from the same initial state to the same final state in twosteps: an isobaric expansion at Pi

followed by an isochoric (isovolumetric) process at volume V f . Theamount of heat supplied to the system in the two-step process is approximately(A) 112 J (B) 294 J (C) 588 J (D) 813 J


SECTION 2 (Maximum Marks : 40) This section contains EIGHT questions.


For each question, darken the bubble(s) corresponding to the correct option in the ORS.





7. In an experiment to determine the acceleration due to gravityg, the formula used for the time period of a

periodic motion is TR r

g

2

7

5

( ). The values of R and r are measured to be (60 ± 1) mm and

(10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s,0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s.Which of the following statement(s) is(are) true?(A) The error in the measurement of r is 10% (B) The error in the measurement of T is 3.57%(C) The error in the measurement of T is 2% (D) The error in the determined value of g is 11%

8. Consider two identical galvanometers and two identical resistors with resistanceR. If the internal resistanceof the galvanometers RC < R/2, which of the following statement(s) about any one of the galvanometersis(are) true?(A) The maximum voltage range is obtained when all the components are connected in series(B) The maximum voltage range is obtained when the two resistors and one galvanometer are connectedin series, and the second galvanometer is connected in parallel to the first galvanometer(C) The maximum current range is obtained when all the components are connected in parallel(D) The maximum current range is obtained when the two galvanometers are connected in series and thecombination is connected in parallel with both the resistors


9. In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are)true?

(A) The voltmeter displays –5 V as soon as the key is pressed, and displays + 5 V after a long time(B) The voltmeter will display 0 V at time t = In 2 seconds(C) The current in the ammeter becomes 1/e of the initial value after 1 second(D) The current in the ammeter becomes zero after a long time

10. Light of wavelength ph falls on a cathode plate inside a vacuum tube as shown in the figure. The work

function of the cathode surface is and the anode is a wire mesh of conducting material kept at a distanced from the cathode. A potential difference V is maintained between the electrodes. If the minimum de

Broglie wavelength of the electrons passing through the anode is e , which of the following statement(s)is(are) true?

(A) e is approximately halved, if d is doubled

(B) e increases at the same rate as ph for ph hc /

(C) For large potential difference ( / ),V e e is approximately halved if V is made four times

(D) e decreases with increase in and ph


11. A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis witha constant velocityv0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length3L where there is a uniform magnetic field B0 into the plane of the paper, as shown in the figure. Forsufficiently large v0, the loop eventually crosses the region. Let x be the location of the right edge of theloop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop,respectively, as a function of x. Counter-clockwise current is taken as positive.

Which of the following schematic plot(s) is(are) correct? (Ignore gravity)

(A) (B)

(C) (D)


12. A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moveswithout friction on a horizontal surface. The block oscillates with small amplitudeA about an equilibriumposition x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x =x0 + A . Inboth the cases, a particle with mass m(<M) is softly placed on the block after which they stick to eachother. Which of the following statement(s) is(are) true about the motion after the mass m is placed on themass M ?

(A) The amplitude of oscillation in the first case changes by a factor ofM

m M, whereas in the second

case it remains unchanged(B) The final time period of oscillation in both the cases is same(C) The total energy decreases in both the cases(D) The instantaneous speed at x0 of the combined masses decreases in both the cases

13. While conducting the Young’s double slit experiment, a student replaced the two slits with a large opaqueplate in the x-y plane containing two small holes that act as two coherent point sources (S1,S2) emitting lightof wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0 ) at adistance D = 3 m from the mid-point of S1,S2, as shown schematically in the figure. The distance betweenthe sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S1,S2.Which of the following is(are) true of the intensity pattern on the screen?

(A) The region very close to the point O will be dark(B) Semi circular bright and dark bands centered at point O(C) Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction(D) Straight bright and dark bands parallel to the x-axis


14. Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a

massless, rigid rod of length l 24 a through their centers. This assembly is laid on a firm and flatsurface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is

. The angular momentum of the entire assembly about the point ‘O’ isL (see the figure). Which of the

following statement(s) is(are) true?

(A) The magnitude of angular momentum of center of mass of the assembly about the point O is 81 2ma

(B) The magnitude of the z-component ofL is 55 2ma

(C) The magnitude of angular momentum of the assembly about its center of mass is 17 22ma /

(D) The center of mass of the assembly rotates about the z-axis with an angular speed of / 5



This section contains TWO paragraphs.

Based one each paragraph, there will be TWO questions.


For each question, darken the bubble corresponding to all the correct option in the ORS. For each question, markes will be awarded in one of the following categories:

Full Marks : +3 If only the bubble coresponding to the corect option is darkened.Zero Marks : 0 In all ther cases

PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frameof reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angularvelocity is an example of a non-inertial frame of reference.

The relationship between the forceFrot

experienced by a particle of mass m moving on the rotating disc and the

forceFin

experienced by the particle in an inertial frame of reference is F F m m rrot in rot 2 ( ) ( )

whererot

is the velocity of the particle in the rotating frame of reference andr is the position vector of the

particle with respect to the centre of the disc.Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constantangular speed about its vertical axis through its center. We assign a coordinate system with the origin at thecenter of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation

axis ( ). k A small block of mass m is gently placed in the slot at r R i ( / )2 at t = 0 and is constrained

to move only along the slot.

15. The distance r of the block at time t is

(A)R

t2

cos (B)R

t2

2cos (C)R

e et t

42 2( )

(D)R

e et t

4( )

16. The net reaction of the disc on the block is

(A)1

22m R e e j mgkt t ( )

(B) m R t j mgk 2 sin

(C) m R t j mgk 2 cos (D)1

22 2 2m R e e j mgkt t ( )


PARAGRAPH 2

Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and aninsulating curved surface as shown in the figure. A number of spherical balls made of a light weight and softmaterial and coated with a conducting material are placed on the bottom plate. The balls have a radiusr<<h. Now a high voltage source (HV) is connected across the conducting plates such that the bottomplate is at +V0 and the top plate at –V0. Due to their conducting surface, the balls will get charged, willbecome equipotential with the plate and are repelled by it. The balls will eventually collide with the topplate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of theballs. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assumethat there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

17. Which one of the following statements is correct?(A) The balls will bounce back to the bottom plate carrying the same charge they went up with(B) The balls will execute simple harmonic motion between the two plates(C) The balls will bounce back to the bottom plate carrying the opposite charge they went up with(D) The balls will stick to the top plate and remain there

18. The average current in the steady state registered by the ammeter in the circuit will be

(A) proportional to the potential V0 (B) proportional to V0

2

(C) proportional to V0

1/2 (D) zero

CHEMISTRY

[10] IIT JEE – 2016 / Paper-2

PART II : CHEMISTRY






19. In the following reaction sequence in aqueous solution, the species X, Y and Z, respectively, are

(A) Ag S O Ag S O Ag S2 3 2

3

2 2 3 2b g , , (B) Ag S O Ag SO Ag S2 3 3

5

2 3 2b g , ,

(C) Ag SO Ag S O Ag3 2

3

2 2 3b g , , (D) Ag SO Ag SO Ag3 3

3

2 4b g , ,

20. The correct order of acidity for the following compounds is

(A) I > II > III > IV (B) III > I > II > IV (C) III > IV > II > I (D) I > III > IV > II

21. For the following electrochemical cell at 298 K,

Pt s H g bar H aq M M aq M aq Pt sb g b g b g b g b g b g24 21 1, , ,

E Vcell 0 092. whenM aq

M aqx

2

410

b gb g

Given : E VRT

FV

M M4 20 0151 2 303 0 059

/. ; . .

The value of x is(A) –2 (B) –1 (C) 1 (D) 2

CHEMISTRY

[11] IIT JEE – 2016 / Paper-2

22. The major product of the following reaction sqeuence is

(A) (B)

(C) (D)

23. The geometries of the ammonia complexes of Ni Pt2 2 , and Zn2 , respectively, are

(A) octahedral, square planar and tetrahedral (B) square planar, octahedral and tetrahedral

(C) tetrahedral, square planar and octahedral (D) octahedral, tetrahedral and square planar

24. The qualitative sketches I, II and III given below show the variation of surface tension with molar concen-

tration of three different aqueous solutions of KCl, CH OH3 and CH CH OSO Na3 2 11 3b g at room tem-

perature. The correct assignment of the sketches is

(A) I : KCl II : CH OH3 III : CH CH OSO Na3 2 11 3b g

(B) I : CH CH OSO Na3 2 11 3b g II : CH OH3 III : KCl

(C) I : KCl II : CH CH OSO Na3 2 11 3b g III : CH OH3

(D) I : CH OH3 II : KCl III : CH CH OSO Na3 2 11 3b g

CHEMISTRY

[12] IIT JEE – 2016 / Paper-2









25. The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)(A) The number of the nearest neighbours of an atom present in the topmost layer is 12

(B) The efficiency of atom packing is 74%

(C) The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively

(D) The unit cell edge length is 2 2 times the radius of the atom

26. The nitrogen containing compound produced in the reaction of HNO3 with P O4 10

(A) can also be prepared by reaction of P4 and HNO3

(B) is diamagnetic

(C) contains one N-N bond

(D) reacts with Na metal producing a brown gas

27. For 'invert sugar', the correct statement(s) is(are)(Given: specific rotations of (+)-sucrose, (+)-maltose, L-(–)-glucose and L-(+)-fructose in aqueous solu-tion are +66°, +140°, –52° and +92°, respectively)(A) 'invert sugar' is prepared by acid catalyzed hydrolysis of maltose

(B) 'invert sugar' is an equimolar mixture of D-(+)-glucose and D-(–)-fructose(C) specific rotation of 'invert sugar' is –20°

(D) on reaction with Br2 water, 'invert sugar' forms saccharic acid as one of the products

CHEMISTRY

[13] IIT JEE – 2016 / Paper-2

28. Reagent(s) which can be used to bring about the following transformation is(are)

(A) LiAlH4 in C H O2 5 2b g (B) BH3 in THF

(C) NaBH4 in C H OH2 5 (D) Raney Ni H/ 2 in THF

29. Mixture(s) showing positive deviation from Raoult's law at 35°C is(are)(A) carbon tetrachloride + methanol (B) carbon disulphide + acetone

(C) benzene + toluene (D) phenol + aniline

30. Extraction of copper from copper pyrite CuFeS2b g involves(A) crushing followed by concentration of the ore by froth-flotation

(B) removal of iron as slag

(C) self-reduction step to produce 'blister copper' following evolution of SO2

(D) refining of 'blister copper' by carbon reduction

31. Among the following, reaction(s) which gives(give) tert-butyl benzene as the major product is(are)

(A) (B)

(C) (D)

32. According to Molecular Orbital Theoory,

(A) C22 is expected to be diamagnetic

(B) O22 is expected to have a longer bond length than O2

(C) N2 and N2

have the same bond order

(D) He2 has the same energy as two isolated He atoms

CHEMISTRY

[14] IIT JEE – 2016 / Paper-2







PARAGRAPH 1

Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equation:

2X g 2X g

The standard reaction Gibbs energy, rG , of this reaction is positive. At the start of the reaction, there is one

mole of X2 and no X. As the reaction proceeds, the number of moles of X formed is given by . Thus,

equilibrium is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total

pressure of 2 bar. Consider the gases to behave ideally.

(Given: R L bar K mol 0 083 1 1. )

33. The equilibrium constant KP for this reaction at 298 K, in terms of equilibrium , is

(A)8

2

2

equilibrium

equilibrium (B)8

4

2

2

equilibrium

equilibrium (C)4

2

2

equilibrium

equilibrium (D)4

4

2

2

equilibrium

equilibrium

34. The INCORRECT statement among the following, for this reaction, is(A) Decrease in the total pressure will result in formation of more moles of gaseous X

(B) At the start of the reaction, dissociation of gaseous X2 takes place spontaneously

(C) equilibrium 0 7.

(D) KC 1

CHEMISTRY

[15] IIT JEE – 2016 / Paper-2

PARAGRAPH 2

Treatment of compound O with KMnO H4 / gave P, which on heating with ammonia gaveQ. The compound

Q on treatment with Br NaOH2 / produced R. On strogn heating, Q gave S, which on further treatment withethyl 2-bromopropanoate int epresence of KOH followed by acidification, gave a compound T.

35. The compound R is

(A) (B) (C) (D)

36. The compound T is

(A) glycine (B) alanine (C) valine (D) serine

MATHEMATICS[16] IIT JEE – 2015 / Paper-2

PART III : MATHEMATICS






37. The value of

13

k 1

1

k 1 ksin sin

4 6 4 6

is equal to

(A) 3 3 (B) 2 3 3

(C) 2 3 1 (D) 2 2 3

38. Area of the region 2x, y R : y x 3 , 5y x 9 15 is equal to

(A)1

6(B)

4

3(C)

3

2(D)

3

2

39. Let

1 0 0

P 4 1 0

16 4 1

and I be the identity matrix of order 3. If ijQ q is a matrix such that 50P Q I ,

then31 32

21

q q

q

equals

(A) 52 (B) 103 (C) 201 (D) 205


40. The value of22

x

2

x cos xdx

1 e

is equal to

(A)2

24

(B)

2

24

(C) 2 2e

(D) 2 2e

41. Let P be the image of the point (3, 1, 7) with respect to the plane x y z 3 . Then the equation of the

plane passing through P and containing the straight linex y z

1 2 1 is

(A) x y 3z 0 (B) 3x z 0 (C) x 4y 7z 0 (D) 2x y 0

42. Let ib 1 for i 1, 2, ..., 101. Suppose e 1 e 2 e 101log b , log b , ..., log b are in Arithmetic progression (A.P)

with the common difference elog 2 . Suppose 1 2 101a , a , ..., a are in A.P. such that 1 1a b and 51 51a b .

If 1 2 51t b b ... b and 1 2 51s a a ...a , then

(A) s t and 101 101a b (B) s t and 101 101a b

(C) s t and 101 101a b (D) s t and 101 101a b


SECTION 2 (Maximum Marks : 32) This section contains EIGHT questions.







43. Let P be the point on the parabola 2y 4x which is at the shortest distance from the center S of the circle

2 2x y 4x 16y 64 0 . Let Q be the point on the circle dividing the line segment SP internally. Then

(A) SP 2 5 (B) SQ : QP 5 1 : 2

(C) the x-intercept of the normal to the parabola at P is 6.

(D) the slope of the tangent to the circle at Q is1

2.

44. Let1

f : , 22

and

1g : , 2

2

be functions defined by 2f x x 3 and

g x x f x 4x 7 f x , where [y] denotes the greatest integer less than or equal to y for y .

Then

(A) f is discontinuous exactly at three points in1

, 22

(B) f is discontinuouss exactly at four points in1

, 22

(C) g is not differentiable exactly at four points in1

, 22

(D) g is not differentiable exactly at five points in1

, 22


45. Let a, b and 2 2a b 0 . Suppose1

S z C : z , t , t 0a ibt

, where i 1 . If

z x iy and z s , then x, y lies on

(A) the circle with radius1

2a and centre

1, 0

2a

for a 0, b 0

(B) the circle with radius1

2a and centre

1, 0

2a

for a 0, b 0

(C) the x-axis for a 0, b 0

(D) the y-axis for a 0, b 0

46. Let a, b R and f : R R be defined by 3 3f x a cos x x b x sin x x . Then f is

(A) differentiable at x = 0 if a = 0 and b = 1

(B) differentiable at x 1 if a 1 and b 0

(C) NOT differentiable at x 0 if a 1 and b 1(D) NOT differentiable at x 1 if a 1 and b 1

47. Let f : R (0, ) and g : R R be twice differentiable functions such that f and g are continuous

functions on R. Suppose f (2) g 2 0 , f (2) 0 and g (2) 0 . If x 2

f x g xlim 1

f x g x

, then

(A) f has a local minimum at x 2

(B) f has a local maximum at x 2

(C) f (2) f (2)

(D) f x f x 0 for at least one x R


48. Let 1 2 3ˆ ˆ ˆu u i u j u k a unit vector in 3 and 1 ˆ ˆ ˆw i j 2k

6 . Given that there exists a vector v

in 3 such that u 1

and ˆ ˆw u v 1

.Which of the following statement(s) is (are) correct?

(A) There is exactly one choice for such v

(B) There are infinitely many choices for such v

(C) If u lies in the xy plane then 1 2u u

(D) If u lies in the xz plane then 1 32 u u

49. Let a, , . Consider the system of linear equations

ax 2y

3x 2y

Which of the following statement(s) is (are) correct?

(A) If a 3 , then the system has infinitely many solutions for all values of and

(B) If a 3 , then the system has a unqie solution for all values of and

(C) If 0 then the system has infinitely many solutions for a 3

(D) If 0 then the system has no solution for a 3

50. Let

n

2 2n2 2 2 2

2

n nn x n x ... x

2 nf x lim

n nn! x n x ... x

4 n

, for all x 0 . Then

(A) 1f f 1

2

(B)1 2

f f3 3

(C) f (2) 0 (D)

f 3 f (2)

f 3 f 2








PARAGRAPH 1

Football teams 1T and 2T have to play two games against each other. It is assumed that the outcomes

of the two games are independent. The probabilities of 1T winning, drawing and losing a game against

2T are1 1

,2 6

and1

3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for

a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams 1T and

2T , respectively, after two games

51. P X Y is

(A)1

4(B)

5

12(C)

1

2(D)

7

12

52. P X Y is

(A)11

36(B)

1

3(C)

13

36(D)

1

2


PARAGRAPH 2

Let 1 1F x , 0 and 2 2F x , 0 , for 1x 0 and 2x 0 , be the foci of the ellipse2 2x y

19 8

. Suppose

a parabola having vertex at the origin and focus at 2F intersects the ellipse at point M in the first quad-

rant and at point N in the fourth quadrant.

53. The orthocentre of the triangle 1F MN is

(A)9

, 010

(B)2

, 03

(C)9

, 010

(D)2

, 63

54. If th tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at

Q, then the ratio of area of the triangle MQR to area of the quadrilateral 1 2MF NF is

(A) 3 : 4 (B) 4 : 5 (C) 5 : 8 (D) 2 : 3

(Paper II)PHYSICS

1. [A] 2. [C] 3. [C] 4. [A] 5. [C] 6. [C] 7. [A,B,D] 8. [B,C]

9. [A,B,C,D] 10. [C] 11. [A, D] 12. [A,B,D] 13. [A,B] 14. [C,D] 15. [D] 16. [A]

17. [C] 18. [B]

CHEMISTRY19. [A] 20. [A] 21. [D] 22. [A] 23. [A] 24. [D] 25. [B,C,D] 26. [B,D]

27. [B,C] 28. [C,D] 29. [A,B] 30. [A,B,C,D] 31. [B,C,D] 32. [A, C] 33. [B] 34. [C]

35. [A] 36. [B]

MATHEMATICS37. [C] 38. [C] 39. [B] 40. [A] 41. [C] 42. [B] 43. [A,C,D] 44. [B,D]

45. [A,C,D] 46. [A,B] 47. [A,D] 48. [B,C] 49. [B,C,D] 50. [B,C] 51. [B] 52. [C]

53. [A] 54. [C]

IIT JEE - 2016(Paper I)

PHYSICS1. [B] 2. [D] 3. [B] 4. [A] 5. [C] 6. [A,B,D] 7. [A,B,C] 8. [C,D]

9. [A, D] 10. [B, D] 11. [A,D] 12. [A,B,D] 13. [A,C,D] 14. [9] 15. [6] 16. [6]

17. [3] 18. [8]

CHEMISTRY19. [D] 20. [C] 21. [B] 22. [B] 23. [A] 24. [B,C,D] 25 [B,D] 26. [A,C,D]

27. [B,C] 28. [A] 29. [A,B,C] 30. [B] 31. [B,C] 32. [9] 33. [4] 34. [6]

35. [5] 36. [5]

MATHEMATICS41. [2] 42. [0] 43. [4] 44. [3] 45. [8] 46. [4] 47. [8] 48. [5]

49. [ B, C] 50. [B, D] 51. [A, B] 52. [A, D] 53. [A, C] 54. [B, C] 55. [A, D] 56. [A, B, C]

57. [A, C, D] 58.[C, D] 59. [A] p,q; [B] p,q; [C] p,q,s,t [D] q, t

60. [A] p,r,s; [B] p; [C] p,q [D] s,t

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