JEE Advanced 2016 Paper 1
Q. 1 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 in the image below. 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
Q. 2 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(
A. h/l = √3/16, f = (16√3/3)N
B. h/l = 3/16, f = (16√3/3)N
C. h/l = 3√3/16, f = (8√3/3)N
D. h/l = 3√3/16, f = (16√3/3)N
Q. 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 at 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
Q. 4 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°
Q. 5 An infinite line charge of uniform electric density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time = 0, the space inside the cylinder is filled with a material of permittivity ε 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?
A. I
B. II
C. III
D. IV
Q. 6 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 changes 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
Q. 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 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 v(t) represent the beat frequency measured by a person sitting in the car at time t. Let Vₚ, Vᵩ and Vᵣ be 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 sound heard by the person?
A. Vₚ + Vᵣ = 2Vᵩ
B. The rate of change in beat frequency is maximum when the car passes through Q
C. The plot in image I. represents schematically the variation of beat frequency with time
D. The plot in image II. represents schematically the variation of beat frequency with time
Q. 8 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
Q. 9 A piano-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 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 cm
B. The radius 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
Q. 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 expression(s) for l is(are) dimensionally correct?
A. I
B. II
C. III
D. IV
Q. 11 A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that 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?
A. The magnitude of induced emf in the wire is (μ₀/π) volt
B. If the loop is rotated at a constant angular speed about the wire, an additional emf of
(μ₀/π) 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
Q. 12 The position vector r ⃗ of a particle of mass m is given by the following equation
r ⃗(t)-at³iˆ+βt²jˆ, where a=10/3 m s⁻³, β=5 m s⁻² and m=0.1 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 ⃗ =(10iˆ+10jˆ)m s⁻¹
B. The angular momentum L ⃗ with respect to the origin is given by L ⃗ =-(5/3)kˆ N m s
C. The force F ⃗ is given by F ⃗ =(iˆ+2jˆ)N
D. The torque r ⃗ with respect to the origin is given by r ⃗ = -(20/3)kˆ N m
Q. 13 A transparent slab of thickness d hhas 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 θ₁ from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement l. Which of the following statement(s) is(are) true?
A. n₁sinθ₁= n₂sinθ
B. n₁sinθ₁=(n₂-n₁)sinθf
C. l is independent of n₂
D. l is independent on n(z)
Q. 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 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?
Q. 15 The isotope ¹²₅B having a mass 12.014 u undergoes β-decay to ¹²₆C, ¹²₆C has an excited state of the nucleus (¹²₆C*) at 4.041 MeV above its ground state. If ¹²₅B decays to ¹²₆C*, the maximum kinetic energy of the β-particle in units of MeV is –
(1 u = 931.5 MeV/c², where c is the speed of light in vaccum)
Q. 16 A hydrogen atom in its ground state is irradiated by light of wavelength 970. Taking hc l e = 1.237 x 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?
Q. 17 Consider two solid spheres P and Q each of density 8 gm cm⁻³ and diameter 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm⁻³ and viscosity n=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm⁻³ and viscosity n=2 poiseulles. The ratio of the terminal velocities of P and Q is?
Q. 18 Two inductors L₁ (inductance 1 mH, internal resistance 3Ω) and L₂ (inductance 2 mH, internal resistance 4Ω), and a resistor R (resistance 12Ω) 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 (I₁/I₂) drawn from the battery is?
(I₁ = maximum, I₂ = minimum)
Q. 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 4πr²dr. The qualitative sketch of the dependence of P on r is –
A. I
B. II
C. III
D. IV
Q. 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 (ΔS) in JK⁻¹ is (1 L atm = 101.3 J)
A. 5.763
B. 1.013
C. -1.013
D. -5.763
Q. 21 The increasing order of atomic radii of the following group 13 element is
A. Al<Ga<In<Tl
B. Ga<Al<In<Tl
C. Al<In<Ga<Tl
D. Al<Ga<Tl<In
Q. 22 Among [Ni(co₄)], [NiCl₄]²⁻, [Co(NH₃)₄Cl₂]Cl, Na₃[CoF₆], Na₂O₂ and CsO₂, the total number if paramagnetic compound is
A. 2
B. 3
C. 4
D. 5
Q. 23 On complete hydrogenation, natural rubber produces
A. Ethylene-propylene copolymer
B. Vulcanised rubber
C. Polypropylene
D. Polybutylene
Q. 24 Choose the correct option(s)
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 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
Q. 25 A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward 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)
Q. 26 The crystalline form of borax has
A. Tetranuclear [B₄O₅(OH₄)²⁻] unit
B. All boron atoms in the same place
C. Equal number of sp² and sp³ hybridised boron atoms
D. One terminal hydroxide per boron atom
Q. 27 The compound(s) with TWO lone pairs of electrons on the central atom is(are)
A. BrF₅
B. CIF₃
C. XeF₄
D. SF₄
Q. 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)₂
D. Na₂[Fe(CN)₅ NO]
Q. 29 Positive Tollen’s test is observed for
A. I
B. II
C. III
D. IV
Q. 30 The product(s) of the following reaction is(are)
A. I
B. II
C. III
D. IV
Q. 31 The correct statement(s) about the filtering reaction sequence is(are)
A. R is steam volatile
B. Q gives dark bullet 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
Q. 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, (MW₁/MW₂), is – (MW₁= solute, MW₂=solvent)
Q. 33 The diffusion coefficient of an ideal gas is proportional to its mean free path and means speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion of this gas increases x times. The value of x is –
Q. 34 In neutral or fairly alkaline solution, 8 moles of permanganate anion quantitatively oxidise thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is –
Q. 35 The number of geometric isomers possible for the complex [CoL₂Cl₂]⁻ (L=H₂NCH₂CH₂O⁻) is –
Q. 36 In the following monobromination reaction, the number of possible chiral products is
Q. 37 Let –π/6 < θ<-π/12. 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. If α₁ > β₁ and α₂ > β₂, then α₁+ β₂ equals
A. 2(secθ-tanθ)
B. 2secθ
C. -2tanθ
D. 0
Q. 38 A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of days of selecting the team is
A. 380
B. 320
C. 260
D. 95
Q. 39 Let S={xϵ(-π,π):x≠0, ±π/2}. The sum of all distinct solutions of the equation
√3secx+cosecx+2(tanx-cotx)=0 in the set S is equal to
A. -7π/9
B. -2π/9
C. 0
D. 5π/9
Q. 40 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 are produced in the factory turn out to be defective. It is known that p(computer turns out to be defective given that it 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 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 T₂ is
A. 36/73
B. 47/79
C. 78/93
D. 75/83
Q. 41 The least value of a ϵ R for which 4ax²+1/x≥1, for all x>0 is
A. 1/64
B. 1/32
C. 1/27
D. 1/25
Q. 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 of OPQR of the pyramid is a square with OP – 3. The point S is directly above the midpoint 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
Q. 43 Let f:(0,∞) → R be a differentiable functions such that f’(x) =2-f(x)/2 for all x ϵ (0,∞) and f(1)≠1. Then
A. I
B. II
C. III
D. IV
Q. 44 P is a matrix where a ϵ R. Suppose Q=[qᵢ] is a matrix such that PQ =kI, where k ϵ R and k≠0 and I is the identity matrix of order 3. If q₂₃=-k/8 and det(Q) =k²/2, then
A. a=0, k=8
B. 4a-k+8=0
C. det(P adj(Q)) =2⁹
D. det(Q adj(P))=2¹³
Q. 45 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 incircle of the triangle XYZ is 8π/3, then
A. Area of the triangle is 6√6
B. The radius of the circumference of the triangle XYZ is (35/6)√6
C. (sinX/2)(sinY/2)(sinZ/2)= 4/35
D. sin²(X+Y/2)= 35
Q. 46 A solution curve of the differentials equation (x²+xy+4x+2y+4)dy/dx-y²=0, 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 y=(x+2)²
D. Does NOT intersect y=(x+3)²
Q. 47 Let f:R→R, g:R→R and h:R→R be differentiable functions such that f(x) =x³+3x+2, g(f(x)) =x and h(g(g(x))) =x for all x ϵ R. Then
A. g’(2)=1/15
B. h’(1)=666
C. h(0)=16
D. h(g(3)) =36
Q. 48 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
A. Q₂Q₃=12
B. R₂R₃=4√6
C. area of the triangle OR₂R₃ is 6√2
D. Area of the triangle PQ₂Q₃ is 4√2
Q. 49 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 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)
Q. 50 The total number of distinct x ϵ R for the following matrix is
Q. 51 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)⁵¹C₃ for some positive integer n. Then the value of n is
Q. 52 The total number of distinct x ϵ [0,1] for which the following is
Q. 53 Let α, β ϵ R be such that (refer image). Then 6(α+β) equals
Q. 54 Let z=-1+√3i/2, where i=√-1, and r, s ϵ {1,2,3}. Let P(refer image) and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P² = -I is
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | B | D | B | A | C | ABD | ABC | CD | AC | BD |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | AD | ABD | ACD | 9 | 8 OR 9 | 6 | 3 | 8 | D | C |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | B | B | A | BCD | BD | ACD | BC | AC | ABC | B |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | BC | 9 | 4 | 6 | 5 | 5 | C | A | C | C |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | C | BCD | A | BC | ACD | AD | BC | ABC | AC | 2 |
| Question | 51 | 52 | 53 | 54 | ||||||
| Answer | 5 | 1 | 7 | 1 |