JEE Advanced 2017 paper II
Q. 1 Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density (dρ/ρdt) is constant. The velocity v of any point on the surface of the expanding sphere is proportional to
A. R
B. R³
C. 1/R
D. R²/³
Q. 2 Consider regular polygons with number of sides n = 3, 4, 5…… as shown in the figure. The center of mass of all the polygons is at height ℎ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is Δ. Then Δ depends on n and ℎ as
A. Δ=h sin²(Π/n)
B. Δ=h ((1/cos(Π/n)-1)
C. Δ=h sin(2Π/n)
D. Δ=h tan²(Π/2n)
Q. 3 A photoelectric material having work-function φ∘ is illuminated with light of wavelength λ(λ < hc/φ∘)The fastest photoelectron has a de Broglie wavelength λd A change in wavelength of the incident light by λd results in a change Δλd in λd. Then the ratio Δλd/Δλ is proportional to
A. λd/λ
B. (λd)²/λ²
C. (λd)³/λ
D. (λd)³/λ²
Q. 4 A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is
A. A
B. B
C. C
D. D
Q. 5 Three vectors P̅, Q̅ and R̅ are shown in the figure. Let S be any point on the vector R̅. The distance between the points P and S is b|R̅|. The general relation among vectors P̅, Q̅ and R̅ is
A. A
B. B
C. C
D. D
Q. 6 A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3×10⁵ times heavier than the Earth and is at a distance 2.5×10⁴ times larger than the radius of the Earth. The escape velocity from Earth’s gravitational field is vₑ = 11.2 km/s⁻¹. The minimum initial velocity (vₛ) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)
A. vs=22 km/s⁻¹
B. vs=42 km/s⁻¹
C. vs=62 km/s⁻¹
D. vs=72 km/s⁻¹
Q. 7 A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT=0.01 seconds and he measures the depth of the well to be L= 20 meters. Take the acceleration due to gravity g= 10 m/s² and the velocity of sound is 300 m/s⁻¹. Then the fractional error in the measurement, δL/L is closest to
A. 0.2%
B. 1%
C. 3%
D. 5%
Q. 8 A uniform magnetic field B exists in the region between x = 0 and x =3R/2(region 2 in the figure) pointing normally into the plane of the paper. A particle with charge +Q and momentum p directed along x-axis enters region 2 from region 1 at point P₁(y = −R). Which of the following option(s) is/are correct?
A. For B > 2p/3QR , the particle will re-enter region 1
B. For B=8p/13QR, the particle will enter region 3 through the point P₂ on x-axis
C. When the particle re-enters region 1 through the longest possible path in region 2,
the magnitude of the change in its linear momentum between point P₁ and the
farthest point from y-axis is p/√2
D. For a fixed B, particles of same charge Q and same velocity v, the distance between
the point P1 and the point of re-entry into region 1 is inversely proportional to the
mass of the particle
Q. 9 The instantaneous voltages at three terminals marked X, Y and Z are given by
Vₓ = V∘sin ωt,
Vᵧ = V∘sin (ωt+2Π/3) and
V = V∘sin (ωt+4Π/3)
An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. The reading(s) of the voltmeter will be
A. A
B. B
C. C
D. D
Q. 10 A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?
A. The electric flux passing through the curved surface of the hemisphere is -Q/2ε∘(1-1/ √2)
B. Total flux through the curved and the flat surfaces is Q/ε∘
C. The component of the electric field normal to the flat surface is constant over the
surface
D. The circumference of the flat surface is an equipotential
Q. 11 Two coherent monochromatic point sources S₁ and S₂ of wavelength λ = 600 nm are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is Δθ. Which of the following options is/are correct?
A. A dark spot will be formed at the point P₂
B. At P₂ the order of the fringe will be maximum
C. The total number of fringes produced between P₁ and P₂ in the first quadrant is close to 3000
D. The angular separation between two consecutive bright spots decreases as we move
from P₁ to P₂ along the first quadrant
Q. 12 A source of constant voltage V is connected to a resistance R and two ideal inductors L₁ and L₂ through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?
A. After a long time, the current through L₁ will be VL₂/R(L₁+L₂)
B. After a long time, the current through L₂ will be VL₁/R(L₁+L₂)
C. The ratio of the currents through L₁ and L₂ is fixed at all times (t > 0)
D. At t = 0, the current through the resistance R is V/R
Q. 13 A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is θ. Which of the following statements about its motion is/are correct?
A. The midpoint of the bar will fall vertically downward
B. The trajectory of the point A is a parabola
C. Instantaneous torque about the point in contact with the floor is proportional to sinθ
D. When the bar makes an angle θ with the vertical, the displacement of its midpoint
from the initial position is proportional to (1 − cosθ)
Q. 14 A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?
A. If the force is applied at point P tangentially then τ decreases continuously as the
wheel climbs
B. If the force is applied normal to the circumference at point X then τ is constant
C. If the force is applied normal to the circumference at point P then τ is zero
D. If the force is applied tangentially at point S then τ≠ 0 but the wheel never climbs the step
Questions: 15 – 16
Consider a simple RC circuit as shown in Figure 1.
Process 1: In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V₀(i.e., charging continues for time T >> RC). In the process some dissipation (Ed) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is Ec. Process 2: In a different process the voltage isfirst set to V₀/3 and maintained for a charging time T >> RC. Then the voltage is raised to 2V₀/3 without discharging the capacitor and again maintained for a time T>> RC. The process is repeated one more time by raising the voltage to V₀ and the capacitor is charged to the same final voltage V₀ as in Process 1. These two processes are depicted in Figure 2.
Q. 15 In Process 1, the energy stored in the capacitor Ec and heat dissipated across resistance ED are related by:
A. Ec=ED
B. Ec=ED ln 2
C. Ec=1/2ED
D. Ec=2ED
Q. 16 In Process 2, total energy dissipated across the resistance ED is:
A. ED=1/2 CV₀²
B. Ed=3(1/2 CV₀²)
C. ED=1/3(1/2CV₀²)
D. ED=3 CV₀²
Questions: 17 – 18
One twirls a circular ring (of mass M and radius R) near the tip of one’s finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r. The finger rotates with an angular velocity ω₀. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is μ and the acceleration due to gravity is g.
Q. 17 The total kinetic energy of the ring is
A. Mω₀²R²
B. 1/2Mω₀²(R-r)²
C. Mω₀²(R-r)²
D. 3/2Mω₀²(R-r)²
Q. 18 The minimum value of ω₀ below which the ring will drop down is
A. √(g/μ(R-r))
B. √(2g/μ(R-r))
C. √(3g/2μ(R-r))
D. √(g/2μ(R-r))
Q. 19 Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg/mol⁻¹. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is 46 g/mol⁻¹ ] Among the following, the option representing change in the freezing point is
A. A
B. B
C. C
D. D
Q. 20 For the following cell in the figure, when the concentration of Zn²⁺ is 10 times the concentration of Cu²⁺ , the expression for ΔG (in J/mol⁻¹ ) is
[F is Faraday constant; R is gas constant; T is temperature; E° (cell) =1.1V ]
A. 1.1F
B. 2.303RT − 2.2F
C. 2.303RT + 1.1F
D. −2.2F
Q. 21 The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are in figure.The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by 2 x 10⁻⁶ m³ /mol⁻¹. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is [Useful information: 1 J = 1 kg m²s⁻² ; 1 Pa = 1 kg m⁻¹s⁻²; 1 bar = 10⁵ Pa]
A. 14501 bar
B. 58001 bar
C. 1450 bar
D. 29001 bar
Q. 22 Which of the following combination will produce H₂ gas?
A. Fe metal and conc. HNO₃
B. Cu metal and conc.HNO₃
C. Zn metal and NaOH(aq)
D. Au metal and NaCN(aq) in the presence of air
Q. 23 The order of the oxidation state of the phosphorus atom in H₃PO₂, H₃PO₄, H₃PO₃, and H₄P₂O₆ is
A. H₃PO₃ > H₃PO₂ > H₃PO₄ > H₄P₂O₆
B. H₃PO₄ > H₃PO₂ > H₃PO₃ > H₄P₂O₆
C. H₃PO₄ > H₄P₂O₆ >H₃PO₃ > H₃PO₂
D. H₃PO₂ > H₃PO₃ > H₄P₂O₆ >H₃PO₄
Q. 24 The major product of the following reaction is
A. A
B. B
C. C
D. D
Q. 25 The order of basicity among the following compounds is
A. II > I > IV > III
B. IV > II > III > I
C. IV > I > II > III
D. I > IV > III > II
Q. 26 The correct statement(s) about surface properties is(are)
A. Adsorption is accompanied by decrease in enthalpy and decrease in entropy of the
system
B. The critical temperatures of ethane and nitrogen are 563 K and 126 K, respectively.
The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature
C. Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is
dispersion medium
D. Brownian motion of colloidal particles does not depend on the size of the particles
but depends on viscosity of the solution
Q. 27 For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by
A. With increase in temperature, the value of K for exothermic reaction decreases
because the entropy change of the system is positive
B. With increase in temperature, the value of K for endothermic reaction increases
because unfavourable change in entropy of the surroundings decreases
C. With increase in temperature, the value of K for endothermic reaction increases
because the entropy change of the system is negative
D. With increase in temperature, the value of K for exothermic reaction decreases
because favourable change in entropy of the surroundings decreases
Q. 28 In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)
A. The activation energy of the reaction is unaffected by the value of the steric factor
B. Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation
C. Since P = 4.5, the reaction will not proceed unless an effective catalyst is used
D. The value of frequency factor predicted by Arrhenius equation is higher than that
determined experimentally
Q. 29 For the following compounds, the correct statement(s) with respect to nucleophilic substitution reactions is(are)
A. I and III follow SN₁ mechanism
B. I and II follow SN₂ mechanism
C. Compound IV undergoes inversion of configuration
D. The order of reactivity for I, III and IV is: IV > I > III
Q. 30 Among the following, the correct statement(s) is(are)
A. Al(CH₃)₃ has the three-centre two-electron bonds in its dimeric structure
B. BH₃ has the three-centre two-electron bonds in its dimeric structure
C. AlCl₃ has the three-centre two-electron bonds in its dimeric structure
D. The Lewis acidity of BCl₃ is greater than that of AlCl₃
Q. 31 The option(s) with only amphoteric oxides is(are)
A. Cr₂O₃, BeO, SnO, SnO₂
B. Cr₂O₃, CrO, SnO, PbO
C. NO, B₂O₃, PbO, SnO₂
D. ZnO, Al₂O₃, PbO, PbO₂
Q. 32 Compounds P and R upon ozonolysis produce Q and S, respectively. The molecular formula of Q and S is C₈H₈O. Q undergoes Cannizzaro reaction but not haloform reaction, whereas S undergoes haloform reaction but not Cannizzaro reaction. The option(s) with suitable combination of P and R, respectively, is(are)
A. A
B. B
C. C
D. D
Questions: 33 – 34
Upon heating KClO3 in the presence of catalytic amount of MnO2, a gas W is formed. Excess amount of W reacts with white phosphorus to give X. The reaction of X with pure HNO3 gives Y and Z.
Q. 33 W and X are, respectively
A. O₃ and P₄O₆
B. O₂ and P₄O₆
C. O₂ and P₄O₁₀
D. O₃ and P₄O₁₀
Q. 34 Y and Z are, respectively
A. N₂O₃ and H₃PO₄
B. N₂O₅ and HPO₃
C. N₂O₄ and HPO₃
D. N₂O₄ and H₃PO₃
Questions: 35 – 36
Q. 35 The reaction of compound P with CH₃MgBr (excess) in (C₂H₅)₂O followed by addition of H₂O gives Q. The compound Q on treatment with H₂SO₄ at 0°C gives R. The reaction of R with CH₃COCl in the presence of anhydrous AlCl₃ in CH₂Cl₂ followed by treatment with H₂O roduces compound S. [Et in compound P is ethyl group]
A. A
B. B
C. C
D. D
Q. 36 The reactions, Q to R and R to S, are
A. Dehydration and Friedel-Crafts acylation
B. Aromatic sulfonation and Friedel-Crafts acylation
C. Friedel-Crafts alkylation, dehydration and Friedel-Crafts acylation
D. Friedel-Crafts alkylation and Friedel-Crafts acylation
Q. 37 The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y-2z=5 and 3x – 6y – 2z=7 is
A. 14x + 2y – 15z = 1
B. 14x – 2y + 15z = 27
C. 14x + 2y + 15z = 31
D. -14x + 2y + 15z = 3
Q. 38 Let O be the origin and let PQR be an arbitrary triangle. The point S is such that(in figure) Then the triangle PQR has S as its
A. centroid
B. circumcentre
C. incentre
D. orthocenter
Q. 39 If y=y(x) satisfies the differential equation(in figure) and y(0) =√7, then y(256)=
A. 3
B. 9
C. 16
D. 80
Q. 40 If f: ℝ → ℝ is a twice differentiable function such that f″(x)>0 for all x ∈ ℝ, and f(1/2)=1/2, f(1)=1, then
A. f′(1)≤0
B. 0<f′(1)<1/2
C. 1/2<f′(1)≤1
D. f′(1)>1
Q. 41 How many 3×3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MᵀM is 5?
A. 126
B. 198
C. 162
D. 135
Q. 42 Let S = {1, 2, 3, … , 9} . For k = 1, 2, … ,5, let Nₖ be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N₁+N₂+N₃+N₄+N₅=
A. 210
B. 252
C. 125
D. 126
Q. 43 Three randomly chosen nonnegative integers x,y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is
A. 36/55
B. 6/11
C. 1/2
D. 5/11
Q. 44 choose the correct answer from options:
A. g′(Π/2)=-2Π
B. g′(-Π/2)=2Π
C. g′(Π/2)=2Π
D. g′(-Π/2)=-2Π
Q. 45 Let α and β be nonzero real numbers such that 2 cosβ − cosα)+ cos α cos β = 1. Then which of the following is/are true?
A. A
B. B
C. C
D. D
Q. 46 If f: ℝ → ℝ is a differentiable function such that f′(x) > 2f(x) for all x ∈ ℝ, and f(0) = 1, then
A. f(x) is increasing in (0, ∞)
B. f(x) is decreasing in (0, ∞)
C. f(x) > e²ˣ in (0, ∞)
D. f(x) < e²ˣ in (0, ∞)
Q. 47 choose the correct option:
A. A
B. B
C. C
D. D
Q. 48 choose the correct option:
A. f′(x) = 0 at exactly three points in (-Π,Π)
B. f′(x) = 0 at more than three points in (-Π,Π)
C. f(x) attains its maximum at x = 0
D. f(x) attains its minimum at x = 0
Q. 49 If the line x=α divides the area of region R = { (x,y)∈R²: x³≤y≤x,0≤x ≤ 1} into two equal parts, then
A. 0 < α ≤ 1/2
B. 1/2 < α < 1
C. 2a⁴ – 4α² + 1=0
D. a⁴ + 4α² – 1=0
Q. 50 choose the correct option:
A. I > logₑ 99
B. I < logₑ 99
C. I < 49/50
D. I > 49/50
Questions: 51 – 52
Let O be the origin, and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ, respectively, of a triangle PQR
Q. 51 |OX x OY|=
A. sin(P+Q)
B. sin2R
C. sin(P+R)
D. sin(Q+R)
Q. 52 If the triangle PQR varies, then the minimum value of cos (P+Q) +cos (Q+R) +cos(R+P) is
A. -5/3
B. -3/2
C. 3/2
D. 5/3
Questions: 53 – 54
Let p,q be integers and let α, β be the roots of the equation, x²- x − 1 = 0, where α≠β. For n = 0, 1, 2, … , let aₙ = pαⁿ+qβⁿ (FACT: If a and b are rational numbers and a+b√5 = 0, then a = 0 = b).
Q. 53 value of a₁₂ is:
A. a₁₁ – a₁₀
B. a₁₁ + a₁₀
C. 2a₁₁ – a₁₀
D. a₁₁ – 2a₁₀
Q. 54 If a₄ = 28, then p+ 2q =
A. 21
B. 14
C. 7
D. 12
Answer Sheet | ||||||||||
Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Answer | A | B | D | A | A | B | B | AB | AD | AD |
Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Answer | BC | ABC | ACD | CD | A | C | D | A | C | B |
Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Answer | A | C | C | C | C | AB | BD | AB | ABCD | ABD |
Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
Answer | AD | AB | C | B | A | D | C | D | A | D |
Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
Answer | B | D | B | ABCD | ABCD | AC | AD | BC | BC | BD |
Question | 51 | 52 | 53 | 54 | ||||||
Answer | A | B | B | D |