JEE Advanced 2017 Paper I
Q. 1 A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true? one or more than 1 correct answer.
A. The pressure difference between the leading and trailing faces of the plate is
proportional to uv
B. The pressure difference between the leading and trailing faces of the plate is
proportional to uv
C. The plate will continue to move with constant non-zero acceleration, at all times
D. At a later time the external force F balances the resistive force
Q. 2 A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct?
A. A
B. B
C. C
D. D
Q. 3 A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct?
A. The time Tₐₒ = Tₒₐ
B. The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
C. The wavelength of Pulse 1 becomes longer when it reaches point A
D. The velocity of any pulse along the rope is independent of its frequency and
wavelength
Q. 4 A human body has a surface area of approximately 1 m². The normal body temperature is 10 K above the surrounding room temperature T₀. Take the room temperature to be T₀= 300 K. For T₀ = 300 K, the value of σT₀⁴ = 460 Wm⁻² (where σ is the Stefan Boltzmann constant). Which of the following options is/are correct?
A. The amount of energy radiated by the body in 1 second is close to 60 Joule
B. If the surrounding temperature reduces by a small amount ΔT₀ ≪ T₀, then to
maintain the same body temperature the same (living) human being needs to radiate
ΔW = 4σT₀³ΔT₀ more energy per unit time
C. Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation
D. If the body temperature rises significantly then the peak in the spectrum of
electromagnetic radiation emitted by the body would shift to longer wavelengths
Q. 5 A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field B points into the plane of the paper. At t= 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options is/are correct?
A. The emf induced in the loop is proportional to the sum of the areas of the two loops
B. The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone
C. The net emf induced due to both the loops is proportional to cos ωt
D. The rate of change of the flux is maximum when the plane of the loops is
perpendicular to plane of the paper
Q. 6 In the circuit shown, L= 1 μH , C= 1 μF and R = 1kΩ. They are connected in series with an a.c. source V = V₀ sin wt as shown. Which of the following options is/are correct?
A. The current will be in phase with the voltage if ω = 10⁴ rad. s⁻¹
B. The frequency at which the current will be in phase with the voltage is independent of R
C. At ω~0 the current flowing through the circuit becomes nearly zero
D. At ω≫ 10⁶ rad. s⁻¹, the circuit behaves like a capacitor
Q. 7 For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm=A. Which of the following options is/are correct?
A. A
B. B
C. C
D. D
Q. 8 A drop of liquid of radius R = 10⁻² m having surface tension S = 0.1/4π Nm-1 divides itself into K identical drops. In this process the total change in the surface energy ΔU = 10⁻³ J.If K = 10ᵃ then the value of α is
Q. 9 An electron in a hydrogen atom undergoes a transition from an orbit with a quantum number into another with quantum number nf. Vᵢ and Vf are respectively the initial and final potential energies of the electron. If Vᵢ/Vf = 6.25, then the smallest possible nf is
Q. 10 A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle θ = 30°. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as nm = n – mΔn, where nm is the refractive index of the mth slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m – 1)th and mth slabs from the right side of the stack. What is the value of m?
Q. 11 A stationary source emits sound of frequency f₀ = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2 ms⁻¹. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330 ms!! and the car reflects the sound at the frequency it has received)
Q. 12 131I is an isotope of Iodine that β decays to an isotope of Xenon with a half-life of 8 days.A small amount of a serum labelled with 131I is injected into the blood of a person. The activity of the amount of 131I injected was 2.4 ×10! Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the bloodstream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the person’s body, and gives an activity of 115 Bq. The total volume of blood in the person’s body, in liters is approximately (you may use e^x ≈ 1 + x for |x| ≪ 1 and ln 2 ≈ 0.7).
Questions: 13 – 15
Answer Q.13, Q.14 and Q.15 by appropriately matching the information given in
the three columns of the following table.
Q. 13 In which case will the particle move in a straight line with constant velocity?
A. (III) (ii) (R)
B. (III) (ii) (R)
C. (III) (iii) (P)
D. (II) (iii) (S)
Q. 14 In which case will the particle describe a helical path with axis along the positive z direction?
A. (IV) (i) (S)
B. (II) (ii) (R)
C. (III) (iii) (P)
D. (IV) (ii) (R)
Q. 15 In which case would the particle move in a straight line along the negative direction of yaxis (i.e., move along – ŷ)?
A. (II) (iii) (Q)
B. (III) (ii) (R)
C. (IV) (ii) (S)
D. (III) (ii) (P)
Questions: 16 – 18
Answer Q.16, Q.17 and Q.18 by appropriately matching the information given in
the three columns of the following table.
Q. 16 Which of the following options is the only correct representation of a process in which ΔU = ΔQ – PΔV ?
A. (II) (iv) (R)
B. (III) (iii) (P)
C. (II) (iii) (S)
D. (II) (iii) (P)
Q. 17 Which one of the following options is the correct combination?
A. (IV) (ii) (S)
B. (III) (ii) (S)
C. (II) (iv) (P)
D. (II) (iv) (R)
Q. 18 Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
A. (I) (ii) (Q)
B. (IV) (ii) (R)
C. (III) (iv) (R)
D. (I) (iv) (Q)
Q. 19 An ideal gas is expanded from (p₁, V₁, T₁) to (p₂, V₂, T₂) under different conditions. The correct statement(s) among the following is(are)
A. The work done on the gas is maximum when it is compressed irreversibly from (p2, V2) to (p1, V1) against constant pressure p1
B. If the expansion is carried out freely, it is simultaneously both isothermal as well as
adiabatic
C. The work done by the gas is less when it is expanded reversibly from V₁ to V₂ under
D. The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T₁ = T₂, and (ii) positive, if it is expanded reversibly under adiabatic conditions with T₁ ≠ T₂
Q. 20 For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here xL and xM represent mole fractions of L and M, respectively, in the solution. The correct statement(s) applicable to this system is(are)
A. The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed from xL = 0 to xL = 1
B. The point Z represents vapour pressure of pure liquid L and Raoult’s law is obeyed
when xL → 1 C. The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed when xL→ 0
D. Attractive intermolecular interactions between L-L in pure liquid L and M-M in pure liquid M are stronger than those between L-M when mixed in solution
Q. 21 The correct statement(s) about the oxoacids, HClO₄ and HClO, is(are)
A. The central atom in both HClO₄ and HClO is sp³ hybridized
B. HClO₃ is more acidic than HClO because of the resonance stabilization of its anion
C. HClO₄ is formed in the reaction between Cl₂ and H₂O
D. The conjugate base of HClO₄ is weaker base than H₂O
Q. 22 The colour of the X₂ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to
A. the physical state of X₂ at room temperature changes from gas to solid down the
group
B. decrease in ionization energy down the group
C. decrease in π*-σ* gap down the group
D. decrease in HOMO-LUMO gap down the group
Q. 23 Addition of excess aqueous ammonia to a pink coloured aqueous solution of MCl₂·6H₂O (X) and NH₄Cl gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1:3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y. Among the following options, which statement(s) is(are) correct?
A. Addition of silver nitrate to Y gives only two equivalents of silver chloride
B. The hybridization of the central metal ion in Y is d²sp³
C. Z is a tetrahedral complex
D. When X and Z are in equilibrium at 0°C, the colour of the solution is pink
Q. 24 The IUPAC name(s) of the following compound is(are)
A. 1-chloro-4-methylbenzene
B. ] 4-chlorotoluene
C. 4-methylchlorobenzene
D. 1-methyl-4-chlorobenzene
Q. 25 The correct statement(s) for the following addition reactions is(are)
A. O and P are identical molecules
B. (M and O) and (N and P) are two pairs of diastereomers
C. (M and O) and (N and P) are two pairs of enantiomers
D. Bromination proceeds through trans-addition in both the reactions
Q. 26 A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm⁻³, then the number of atoms present in 256 g of the crystal is N * 10²⁴ . The value of N is
Q. 27 The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized Pt electrodes. The distance between the electrodes is 120 cm with an area of cross section of 1 cm². The conductance of this solution was found to be 5 * 10⁻⁷ S. The pH of the solution is 4. The value of limiting molar conductivity (Λ°m) of this weak monobasic acid in aqueous solution is Z * 10² S cm⁻¹ mol⁻¹. The value of Z is
Q. 28 The sum of the number of lone pairs of electrons on each central atom in the following species is [TeBr₆]²⁻, [BrF₂]⁺, SNF₃, and [XeF₃]⁻ (Atomic numbers: N = 7, F = 9, S = 16, Br = 35, Te = 52, Xe = 54)
Q. 29 Among H₂, He₂⁺, Li₂, Be₂, B₂, C₂, N₂, O₂⁻, and F₂, the number of diamagnetic species is (Atomic numbers: H = 1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7, O = 8, F = 9)
Q. 30 Among the following, the number of aromatic compound(s) is
Questions: 31 – 33
Answer Q.31, Q.32 and Q.33 by appropriately matching the information given in
the three columns of the following table.
Q. 31 For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is
A. (I) (ii) (S)
B. (IV) (iv) (R)
C. (II) (ii) (P)
D. (III) (iii) (P)
Q. 32 For hydrogen atom, the only CORRECT combination is
A. (I) (i) (S)
B. (II) (i) (Q)
C. (I) (i) (P)
D. (I) (iv) (R)
Q. 33 For He+ ion, the only INCORRECT combination is
A. (I) (i) (R)
B. (II) (ii) (Q)
C. (I) (iii) (R)
D. (I) (i) (S)
Q. 34 For the synthesis of benzoic acid, the only CORRECT combination is
A. (II) (i) (S)
B. (IV) (ii) (P)
C. (I) (iv) (Q)
D. (III) (iv) (R)
Q. 35 The only CORRECT combination that gives two different carboxylic acids is
A. (II) (iv) (R)
B. (IV) (iii) (Q)
C. (III) (iii) (P)
D. (I) (i) (S)
Q. 36 The only CORRECT combination in which the reaction proceeds through radical mechanism is
A. (III) (ii) (P)
B. (IV) (i) (Q)
C. (II) (iii) (R)
D. (I) (ii) (R)
Q. 37 If 2x − y + 1 = 0 is a tangent to the hyperbola , then which of the following CANNOT be sides of a right angled triangle?
A. a, 4, 1
B. a, 4, 2
C. 2a, 8, 1
D. 2a, 4, 1
Q. 38 If a chord, which is not a tangent, of the parabola y² = 16x has the equation 2x + y = p, and midpoint (ℎ, k), then which of the following is(are) possible value(s) of p, ℎ and k
A. p = -2 , h =2 ,k = -4
B. p = -1 , h =1 , k = -3
C. p=2, h=3 ,k = -4
D. p=5 , h=4 , k=-3
Q. 39 Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)= x cos(π(x + [x])) is discontinuous?
A. x = −1
B. x = 0
C. x = 1
D. x = 2
Q. 40 Let f: ℝ → (0, 1) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0, 1)?
A. A
B. B
C. C
D. D
Q. 41 Which of the following is(are) NOT the square of a 3×3 matrix with real entries?
A. A
B. B
C. C
D. D
Q. 42 then which of the following is(are) possible value(s) of x?
A. A
B. B
C. C
D. D
Q. 43 Let X and Y be two events such that P(X) = 1/3 , P(X|Y) = 1/2 and P(Y|X) = 2/5. Then
A. P(Y)= 4/15
B. P(X′|Y) = 1/2
C. P(X∩Y)= 1/5
D. P(XUY)= 2/5
Q. 44 For how many values of p, the circle x² + y² +2x + 4y – p = 0 and the coordinate axes have exactly three common points?
Q. 45 Choose the correct option
Q. 46 For a real number α, if the system of linear equations, has infinitely many solutions, then 1 + α + α² =
Q. 47 Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/9x=
Q. 48 The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
Questions: 49 – 51
Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the following table.
Q. 49 For a = √2, if a tangent is drawn to a suitable conic (Column 1) at the point of contact (−1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?
A. (I) (i) (P)
B. (I) (ii) (Q)
C. (II) (ii) (Q)
D. (III) (i) (P)
Q. 50 If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination?
A. (I) (ii) (Q)
B. (II) (iv) (R)
C. (III) (i) (P)
D. (III) (ii) (Q)
Q. 51 The tangent to a suitable conic (Column 1) at ( √3, 1/2) is found to be √3x + 2u = 4, then which of the following options is the only CORRECT combination?
A. (IV) (iii) (S)
B. (IV) (iv) (S)
C. (II) (iii) (R)
D. (II) (iv) (R)
Questions: 52 – 54
Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three columns of the following table.
Q. 52 Which of the following options is the only CORRECT combination?
A. (I) (i) (P)
B. (II) (ii) (Q)
C. (III) (iii) (R)
D. (IV) (iv) (S)
Q. 53 Which of the following options is the only CORRECT combination?
A. (I) (ii) (R)
B. (II) (iii) (S)
C. (III) (iv) (P)
D. (IV) (i) (S)
Q. 54 Which of the following options is the only INCORRECT combination?
A. (I) (iii) (P)
B. (II) (iv) (Q)
C. (III) (i) (R)
D. (II) (iii) (P)
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | ABD | BC | AD | C | BD | BC | ACD | 6 | 5 | 8 |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | 6 | 5 | D | A | B | D | B | D | ABC | BD |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | ABD | CD | BCD | AB | BD | 2 | 6 | 6 | 6 | 5 |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | C | A | C | A | C | D | ABC | C | ABCD | AB |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | BD | AB | AB | 2 | 2 | 1 | 5 | 6 | B | C |
| Question | 51 | 52 | 53 | 54 | ||||||
| Answer | D | B | B | C |