JEE Advanced - Vidhyarthi Darpan

JEE Advanced 2018 Paper II Previous Year Paper

JEE Advanced 2018 Paper II

Q. 1 A particle of mass ݉ is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = γ , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A. The force applied on the particle is constant

B. The speed of the particle is proportional to time

C. The distance of the particle from the origin increases linearly with time

D. The force is conservative

Q. 2 Consider a thin square plate floating on a viscous liquid in a large tank. The height ݄h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u₀ .Which of the following statements is (are) true?

A. The resistive force of liquid on the plate is inversely proportional to ݄h

B. The resistive force of liquid on the plate is independent of the area of the plate

C. The tangential (shear) stress on the floor of the tank increases with u₀

D. The tangential (shear) stress on the plate varies linearly with the viscosity η of the

liquid

Q. 3 An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density λ. It pierces a thin non-conducting spherical shell of radius ܴ in such a way that the arc ܼܳܿPQ subtends an angle of 120° at the centre ܱO of the spherical shell, as shown in the figure. The permittivity of free space is ∈₀. Which of the following statements is (are) true?

A. The electric flux through the shell is √3 Rλ⁄ε₀

B. The Z- component of the electric field is zero at all the points on the surface of the

shell

C. The electric flux through the shell is √2 Rλ⁄ε₀

D. The electric field is normal to the surface of the shell at all points

Q. 4 A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

A. A

B. B

C. C

D. D

Q. 5 In a radioactive decay chain, ²³²₉₀Th nucleus decays to ²¹²₈₂Pb nucleus. Let ܰNα and ܰNβ be the number of α and β⁻ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

A. N(α) = 5

B. N(α) = 6

C. N(β) = 2

D. N(β) = 4

Q. 6 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube.Two successive resonances are heard at air columns of length 50.7݉ܿ cm and 83.9݉ܿ cm . Which of the following statements is (are) true?

A. The speed of sound determined from this experiment is 332 ݉m/s⁻¹

B. The end correction in this experiment is 0.9 ݉ܿcm

C. The wavelength of the sound wave is 66.4 ݉ܿcm

D. The resonance at 50.7݉ܿ cm corresponds to the fundamental harmonic

Q. 7 A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4kg ݇i݃ s at rest on this surface. An impulse of 1.0 N is applied to the block at time t= 0 so that it starts moving along the x- axis with a velocity v(t) = v₀e⁻ᵗ/ᵀ, where v₀ is a constant and τ = 4s.The displacement of the block, in ݁݉meters t = τ is_________.

Take e⁻¹ = 0.37

Q. 8 A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in meters ,is

Q. 9 A particle, of mass 10⁻³ kg and charge 1.0 C ,is initially at rest. At time t=0, the particle comes under the influence of an electric field E̅=E₀sin ωtî, where Eₒ=1.0 N/C⁻¹ and ω=10³rad/s⁻¹. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉m/s⁻¹ , attained by the particle at subsequent times is

Q. 10 A moving coil galvanometer has 50 turns and each turn has an area 2 x 10⁻⁴ m². The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is 10⁻⁴ N m rad⁻¹. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad.݀ The resistance of the coil of the galvanometer is 50 Ω .This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 – 1.0A .For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in Ω ,is __________.

Q. 11 A steel wire of diameter 0.5 ݉mm and Young’s modulus 2 x 10⁻¹¹ N m⁻² carries a load of mass ܯ .The length of the wire with the load is 1.0 ݉m A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 ݇kg, the vernier scale division which coincides with a main scale division is __________. Take g = 10 ms⁻² and π = 3.2

Q. 12 One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant 8.0 J/mol⁻¹ K⁻¹, the decrease in its internal energy, in joule is__________.

Q. 13 In a photoelectric experiment a parallel beam of monochromatic light with power of 200 ܹ is incident on a perfectly absorbing cathode of work function 6.25 ܸ݁eV The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F= n x 10 N⁻⁴ due to the impact of the electrons. The value of ݊ is __________.Mass of the electron ݉9 x 10⁻³¹ kg and 1.0 eV = 1.6 x 10⁻¹⁹ J

Q. 14 Consider a hydrogen-like ionized atom with atomic number ܼ with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n =1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 ܸ݁eV The value of Z ܼ is __________

Q. 15 The electric field E is measured at a point ܼܿ(0, 0, ݀d) generated due to various charge distributions and the dependence of E on ݀d is found to be different for different charge distributions. List-I contains different relations between E and ݀d List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

A. A

B. B

C. C

D. D

Q. 16 A planet of mass M ,has two natural satellites with masses ݉m₁ and ݉m₂. The radii of their circular orbits are ܴR₁ and ܴR₂ respectively. Ignore the gravitational force between the satellites. Define v₁ , L₁ , K₁ and T₁ to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v₂ , L₂ , K₂ and ܶT₂ to be the corresponding quantities of satellite 2. Given ݉m₁/m₂ = 2 and ܴR₁/R₂ = 1/4, match the ratios in List-I to the numbers in List-II.

A. A

B. B

C. C

D. D

Q. 17 One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the ܸܿPܼ V-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

A. A

B. B

C. C

D. D

Q. 18 In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimensions and α ≠ β .In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: p̅ is the linear momentum,L is the angular momentum about the origin, K is the kinetic energy, ܷU is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

A. A

B. B

C. C

D. D

Q. 19 The correct option(s) regarding the complex [Co(en)(NH₃)₃(H₂O)]³⁺ (en = H₂NCH₂CH₂NH₂) is (are)

A. It has two geometrical isomers

B. It will have three geometrical isomers if bidentate ‘en’ is replaced be two cyanide

ligands.

C. It is paramagnetic

D. It absorbs light at longer wavelength as compared to [Co(en)(NH₃)₄]³⁺

Q. 20 The correct option(s) to distinguish nitrate salts of Mn⁺² and Cu⁺² taken separately is (are)

A. Mn⁺² shows the characteristic green colour in the flame test

B. Only Cu⁺² shows the formation of precipitate by passing H₂S in acidic medium

C. Only Mn⁺² shows the formation of precipitate by passing H₂S in faintly basic medium

D. Cu⁺²/Cu has higher reduction potential than Mn⁺²/Mn (measured under similar

conditions)

Q. 21 Aniline reacts with mixed acid (conc. HNO₃ and conc. H₂SO₄) at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are)

A. A

B. B

C. C

D. D

Q. 22 The Fischer presentation of D-glucose is given below. The correct structure(s) of β-

Lglucopyranose is (are)

A. A

B. B

C. C

D. D

Q. 23 For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (u=0) and at time u are ܼܿP₀ and ܼܿPᵤ, respectively. Initially, only A is present with concentration [A]₀, and t₁/₃ is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

A. A

B. B

C. C

D. D

Q. 24 For a reaction, A ⇌ P the plots of [A] and [P] with time at temperatures T₁ and T₂ are given below.

If ܶT₂ > ܶT₁ , the correct statement(s) is (are)

A. A

B. B

C. C

D. D

Q. 25 The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

N₂O₃, N₂O₅, P₄O₆, P₄O₇, H₄P₂O₅, H₅P₃O₁₀, H₂S₂O₃, H₂S₂O₅

Q. 26 Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of O2 consumed is ____.

(Atomic weights in g/mol: O = 16, S = 32, Pb = 207)

Q. 27 To measure the quantity of MnCl₂ dissolved in an aqueous solution, it was completely converted to KMnO₄ using the reaction, MnCl₂ + K₂S₂O₈ + H₂O —> KMnO₄ + H₂SO₄ + HCl (equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl₂ (in mg) present in the initial solution is ____.

(Atomic weights in g/mol: Mn = 55, Cl = 35.5)

Q. 28 For the given compound X, the total number of optically active stereoisomers is ____.

Q. 29 In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.

(Atomic weights in g/mol : H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%)

corresponding to the product in each step is given in the parenthesis)

Q. 30 The surface of copper gets tarnished by the formation of copper oxide. N₂ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the N₂ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below: 2Cu(s) + H₂O(g) —> Cu₂O(s) + H₂(g), pH₂ is the minimum partial pressure of H₂ (in bar) needed to prevent the oxidation at 1250 K. The value of pH₂ is ____.

(Given: total pressure = 1 bar, R (universal gas constant) = 8 J /K.mol , ln(10) = 2.3. Cu(s) and Cu₂O(s) are mutually immiscible.

Q. 31 Consider the following reversible reaction,

A(g) + B(g) ⇌ AB(g).

The activation energy of the backward reaction exceeds that of the forward reaction by 2ܴܶ ( in J/mol⁻¹ ). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔGθ ( in J/mol⁻¹ ) for the reaction at 300 K is ____. (Given; ln(2) = 0.7, ܴܶ = 2500 J/mol⁻¹ at 300 K and G is the Gibbs energy)

Q. 32 Consider an electrochemical cell: A(s) | Aⁿ⁺ (aq, 2 M) || B²ⁿ⁺ (aq, 1 M) | B(s). The value of ΔH^Ɵ for the cell reaction is twice that of ΔG^Ɵ at 300 K. If the emf of the cell is zero, the ΔS^Ɵ (in J/K.mol⁻¹) of the cell reaction per mole of B formed at 300 K is ____.

(Given: ln(2) = 0.7, ܴ (universal gas constant) = 8.3 J/K⁻¹mol⁻¹. H, S and G are enthalpy,

entropy and Gibbs energy, respectively.)

Q. 33 Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

A. A

B. B

C. C

D. D

Q. 34 The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.

(given, order of migratory aptitude: aryl > alkyl > hydrogen)

A. A

B. B

C. C

D. D

Q. 35 LIST-I contains reactions and LIST-II contains major products.

A. A

B. B

C. C

D. D

Q. 36 Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [H⁺] are given in LIST-II. (Note: Degree of dissociation (α) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [H⁺] represents the concentration of H⁺ ions)

A. A

B. B

C. C

D. D

Q. 37 For any positive integer ݊, define ݂f (n): (0, ∞) → R as Here, the inverse trigonometric function tan x assumes values in (-π/2, π/2)

Then, which of the following statement(s) is (are) TRUE?

A. A

B. B

C. C

D. D

Q. 38 Let ܶ be the line passing through the points ܼܿP(-2, 7) and ܳQ(2, -5). Let F be the set of all pairs of circles (S₁,S₂) such that ܶ is tangent to T at ܼܿ and tangent to ܵS₁ at P ܳ, and also such that ܵS₂ and ܵQ touch each other at a point, say, M .Let E₁ be the set representing the locus of M as the pair (S₁,S₂) varies in F₁. Let the set of all straight line segments joining a pair of distinct points of E₁ and passing through the point ܴR (1, 1) be F₂ Let E₂ be the set of the mid-points of the line segments in the set F₂ Then, which of the following statement(s) is (are) TRUE?

A. The point (-2,7) lies in E₁

B. The point (4/5,7/5) does not lie in E₂

C. The point (1/2, 1) lie in E₂

D. The point (0,3/2) does not lie in E₂

Q. 39 Find the equation

A. A

B. B

C. C

D. D

Q. 40 Consider two straight lines, each of which is tangent to both the circle x² + y² = 1/2 and the parabola y² = 4x. Let these lines intersect at the point Q ܳ. Consider the ellipse whose center is at the origin ܱ(0,0) and whose semi-major axis is OQ ܱܳ. If the length of the minor axis of this ellipse is √2 , then which of the following statement(s) is (are) TRUE?

A. (A) For the ellipse, the eccentricity is 1/√2 and the length of the latus rectum is 1

B. (B) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2

C. (C) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/4√2. (π-2)

D. (D) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/16 . (π-2)

Q. 41 Let s,t,r be non-zero complex numbers and L be the set of solutions z = xi + y where, x,y∈ R, ݅i =√-1 of the equation sz + tz̅+r = 0, where z̅ = x – iy .Then, which of the following statement(s) is (are) TRUE?

A. If L has exactly one element, then |sI ≠ ItI

B. If |sI = ItI then L has infinitely many elements

C. The number of elements in L ∩ {z : I z-i+1I = 5} is at most 2

D. If L has more than one element, then L has infinitely many elements

Q. 42 Let ݂f : (0,π) → R be a twice differentiable function such that

A. A

B. B

C. C

D. D

Q. 43 The value of the integral is_____________

Q. 44 Let ܼܿ be a matrix of order 3 x 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the maximum possible value of the determinant of ܼܿP is _____ .

Q. 45 Let ܺX be a set with exactly 5 elements and ܻ be a set Y with exactly 7 elements. If α is the number of one-one functions from ܺX to Y ܻand β is the number of onto functions from ܻ to ܺ, then the value of 1/5!(β-α) is _____ .

Q. 46 Let ݂f: R—> R be a differentiable function with ݂f(0)=0. If y = f(x) satisfies the differential equation dy/dx = (2+5y)(5y-2) then the value of lim x–>∞ f(x) is _____.

Q. 47 Let f: R—> R be a differentiable function with ݂f(0)=1 and satisfying the equation f(x+y) = f(x).f'(y) + f'(x).f(y) Then, the value of log(e) f(4) is _____.

Q. 48 Let ܼܿ be a point P in the first octant, whose image ܳQ in the plane x+y=3 (that is, the line segment PQ ܼܳܿ is perpendicular to the plane x+y=3 and the mid-point of ܼܳܿ PQ lies in the plane x+y=3) lies on the z-axis. Let the distance of ܼܿP from the x-axis be 5. If R ܴ is the image of ܼܿR in the xy-plane, then the length of ܴܿ ܼ is _____

Q. 49 Consider the cube in the first octant with sides ܱܿOܼ P, OQ and ܱOܴ R of length 1, along the x-axis, y-axis and z-axis, respectively, where ܱO(0,0,0) is the origin. Let ܵS(1/2,1/2,1/2) be the centre of the cube and ܶ be the vertex of the cube opposite to the origin ܱ such that ܵ lies on the diagonal

Q. 50 Let 1(¹⁰C₁)² + 2(¹⁰C₂)² +….+10(¹⁰C₁₀)² where , ¹⁰Cᵣ , r ε {1, 2, ⋯ , 10} denote binomial coefficients. Then, the value of is _____ .

Q. 51 Match the following with the lists given below.

A. A

B. B

C. C

D. D

Q. 52 In a high school, a committee has to be formed from a group of 6 boys M₁, M₂, M₃, M₄, M₅ and M₆ and 5 girls G₁,G₂,G₃,G₄ and G₅

(i) Let α₁ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.

(ii) Let α₂ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.

(iii) Let α₃ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.

(iv) Let α₄ be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M₁ and G₁ are NOT in the committee together.

A. A

B. B

C. C

D. D

Q. 53 Let H: x²/a² – y²/b² = 1, where a>b>0, be a hyperbola in the xy- plane whose conjugate ax is LM subtends an angle of 60° at one of its vertices N. Let the area of triangle LNM be 4√3. Match the correct option from List – 1 to List -2

A. P -> 4; Q -> 2; R -> 1; S-> 3

B. P -> 4; Q -> 3; R -> 1; S-> 2

C. P -> 4; Q -> 1; R -> 3; S-> 2

D. P -> 3; Q -> 4; R -> 2; S-> 1

Q. 54 Match them by observing the lists given in figure carefully.

A. A

B. B

C. C

D. D

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	ABD	ACD	AB	B	AC	AC	6.30	30.00	3.00	5.55/5.56
Question	11	12	13	14	15	16	17	18	19	20
Answer	3.0	900.00	24.00	3.00	B	B	C	A	ABD	BD
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	D	ACD	BCD	6	6.47	126	7	495	-14.6
Question	31	32	33	34	35	36	37	38	39	40
Answer	-8500	-11.62	C	D	B	D	ABD	AD	ACD	ACD
Question	41	42	43	44	45	46	47	48	49	50
Answer	ACD	BCD	2	4	11 9	0.4	2	8	0.5	646
Question	51	52	53	54
Answer	A	C	B	D

JEE Advanced 2018 Paper I Previous Year Paper

JEE Advanced 2018 Paper I

Q. 1 The potential energy of a particle of mass m at a distance r from a fixed point 0 is given byV(r) = kr2/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point 0. If is the speed of the particle and 0 is the magnitude of its angular momentum about 0, which of the following statements is (are) true?

A. v=(k/2m)R

B. v=(k/m)R

C. L=(mk)R2

D. v=[(mk)/2]R2

Q. 2 Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force F=(t i+ j) is applied on the body, where = 1.0 N/s and = 1.0 N. The torque acting on the body about the origin at time t = 1.0 s is . Which of the following statements is (are) true?

A. = 1/3 N m

B. The torque is in the direction of the unit vector + k

C. The velocity of the body at t = 1 s is v = 1/2 (i + 2 j) m/s

D. The magnitude of displacement of the body at t= 1 s is 1/6 m

Q. 3 A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The surface tension of water is o. The angle of contact between water and the wall of the capillary tube is 8. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A. For a given material of the capillary tube, ℎ decreases with increase in 􀀂

B. For a given material of the capillary tube, ℎ is independent of 􀀔

C. If this experiment is performed in a lift going up with a constant acceleration, then ℎ

decreases

D. ℎ is proportional to contact angle θ

Q. 4 In the figure below, the switches S₁ and S₂ are closed simultaneously at t = 0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wire reaches its maximum magnitude I(nax) at time t = v. Which of the following statements is (are) true?

A. I(nax) =V/2R

B. I(nax) =V/4R

C. v = L/R ln 2

D. v = 2L/R ln 2

Question 5 This section contains SIX (06) questions.

Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). For each question, choose the correct option(s) to answer the question. Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +4 If only (all) the correct option(s) is (are) chosen.

Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.

Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options.

Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option.

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : −2 In all other cases.

For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option) ,without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in -2 marks.

Q. 5 Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I1 and the wire located at x = −R carries a constant current I₂. A circular loop of radius R is suspended with its centre at (0, 0, √3R) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the +j true?

Direction. Which of the following statements regarding the magnetic ﬁeld B⃗⃗ is (are)

A. If I₁ = I₂, then B cannot be equal to zero at the origin (0, 0, 0)

B. If I₁ > 0 and I₂ < 0, then Bcan be equal to zero at the origin (0, 0, 0)

C. If I₁ < 0 and I₂ > 0, thenB can be equal to zero at the origin (0, 0, 0)

D. If I₁ = I₂, then the z-component of the magnetic field at the centre of the loop is (−µ₀ I/2R)

Q. 6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

A. Process I is an isochoric process

B. In process II, gas absorbs heat

C. In process IV, gas releases heat

D. Processes I and III are not isobaric

Q. 7 Two vectorsA and B are deﬁned as A = a îand B = a (cos mtî+ sin mtĵ), where a is a constant and m = n/6 rad/s. If |A + B| = √3|A − B | at time t = v for the ﬁrst time, the value of v, in seconds, is _______

Q. 8 Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 n/s and the man behind walks at a speed 2.0 n/s. A third man is standing at a height 12 n above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 n/s. At the instant, when the moving men are 10 n apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is .

Q. 9 A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is (2 − √3) /√10 s, then the height of the top of the inclined plane, in meters, is__________Take g = 10 n s⁻².

Q. 10 A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 N/n and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 n/s collides elastically with the first block. The collision is such that the 2.0 kg block does not hit the wall. The distance, in meters, between the two blocks when the spring returns to its unstretched position for the first time after the collision is .

Q. 11 Three identical capacitors C₁, C₂ and C₃ have a capacitance of 1.0 µF each and they are uncharged initially. They are connected in a circuit as shown in the figure and C₁ is then filled completely with a dielectric material of relative permittivity cᵣ . The cell electromotive force (emf) V₀ = 8 V. First the switch S₁ is closed while the switch S₂ is kept open. When the capacitor C₃ is fully charged, S₁ is opened and S₂ is closed simultaneously. When all the capacitors reach equilibrium, the charge on C₃ is found to be 5 µC. The value of cᵣ = ________

Q. 12 In the xy-plane, the region y > 0 has a uniform magnetic ﬁeld B1k̂ and the region y < 0 has another uniform magnetic ﬁeld B₂k̂. A positively charged particle is projected from the origin along the positive y-axis with speed v₀ = n n/s at t = 0, as shown in the figure. Neglect gravity in this problem. Let t = T be the time when the particle crosses the x-axis from below for the first time. If B₂ = 4B₁, the average speed of the particle, in n/s, along the x- axis in the time interval T is

Q. 13 Sunlight of intensity 1.3 kW n⁻² is incident normally on a thin convex lens of focal length 20cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kW n⁻² , at a distance 22 cn from the lens on the other side is _____.

Q. 14 Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T₂ = 300 K and T₂ = 100 K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K₁ and K₂ respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K₁/K₂ = .

Questions: 15 – 16

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E] and [B] stand for dimensions of electric and magnetic fields respectively, while [c₀] and [µ₀] stand for dimensions of the permittivity and permeability of free space respectively. [L] and [T] are dimensions of length and time respectively. All the quantities are given in SI units. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 15 The relation between [E] and [B] is

A. [E] = [B] [L] [T]

B.[E] = [B] [L]⁻¹[T]

C. [E] = [B] [L] [T]⁻¹

D. [E] = [B] [L]⁻¹[T]⁻

Q. 16 The relation between [c₀] and [µ₀] is

A. [µ₀] = [c₀] [L]²[T]⁻²

B. [µ₀] = [c₀] [L]⁻²[T]²

C. [µ₀] = [c₀]⁻¹[L]²[T]⁻²

D. [µ₀] = [c₀]⁻¹[L]⁻²[T]²

Questions: 17 – 18

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then z ± Δz = (x±Δx)/(y±Δy) =x/y (1 ± (Δx/x)) (1 ± (Δy/y))⁻¹.

The series expansion for (1 ± Δy/y)⁻¹, to first power in Δy/y, is 1 ∓ (Δy/y). The relative errors in independent variables are always added. So the error in z will be Δz = z (Δx/x + Δy/y). The above derivation makes the assumption that Δx/x ≪1, Δy/y ≪1. Therefore, the higher powers of these quantities are neglected.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 17 Consider the ratio r =(1−a)/(1+a) to be determined by measuring a dimensionless quantity

a. If the error in the measurement of a is Δa (Δa/a ≪ 1) , then what is the error Δr in determining r?

A. Δa/(1+a)²

B. 2Δa/(1+a)²

C. 2Δa/(1−a²)

D. 2aΔa/(1−a²)

Q. 18 In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0 s. For |x| ≪ 1, ln(1 + x) = x up to first power in x. The error Δh, in the determination of the decay constant h, in s⁻¹, is

A. 0.04

B. 0.03

C. 0.02

D. 0.01

Q. 19 The compound(s) which generate(s) N₂ gas upon thermal decomposition below 300⁰C is (are)

A. NH₄NO₃

B. (NH₄)₂Cr₂O₇

C. Ba(N₃)₂

D. Mg₃N₂

Q. 20 The correct statement(s) regarding the binary transition metal carbonyl compounds is

(are) (Atomic numbers: Fe = 26, Ni = 28)

A. Total number of valence shell electrons at metal centre in Fe(CO)₅ or Ni(CO)₄ is 16

B. These are predominantly low spin in nature

C. Metal–carbon bond strengthens when the oxidation state of the metal is lowered

D. The carbonyl C−O bond weakens when the oxidation state of the metal is increased

Q. 21 Based on the compounds of group 15 elements, the correct statement(s) is (are)

A. Bi₂O₅ is more basic than N₂O₅

B. NF₃ is more covalent than BiF₃

C. PH₃ boils at lower temperature than NH₃

D. The N−N single bond is stronger than the P−P single bond

Q. 22 In the following reaction sequence, the correct structure(s) of X is (are)

A. A

B. B

C. C

D. D

Q. 23 The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)

A. A

B. B

C. C

D. D

Q. 24 A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively. The correct option(s) is (are)

A. A

B. B

C. C

D. D

Q. 25 Among the species given below, the total number of diamagnetic species is ___.

H atom, NO₂ monomer, O₂⁻(superoxide), dimeric sulphur in vapour phase, Mn₃O₄, (NH₄)₂[FeCl₄], (NH₄)₂[NiCl₄], K₂MnO₄, K₂CrO₄

Q. 26 The ammonia prepared by treating ammonium sulphate with calcium hydroxide is

completely used by NiCl₂.6H₂O to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl₂.6H₂O are used in the preparation, the combined weight (in grams) of gypsum and the nickel ammonia coordination compound thus produced is ____.(Atomic weights in g/mol : H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

Q. 27 Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of (number of anions/number of cations) in Z is ____.

Q. 28 For the electrochemical cell, Mg(s) I Mg⁺² (aq, 1 M) II Cu⁺² (aq, 1 M) I Cu(s), the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg⁺² is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is . (given, F/R= 11500 K V⁻¹, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

Q. 29 closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m³ ) of the compartment A after the system attains equilibrium is ____.

Q. 30 Liquids u and v form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids u and v has vapour pressure 45 Torr. At the same temperature, a new solution of u and v having mole fractions xᵤ and xᵥ, respectively, has vapour pressure of 22.5 Torr. The value of xᵤ/xᵥ in the new solution is (given that the vapour pressure of pure liquid u is 20 Torr at temperature T)

Q. 31 The solubility of a salt of weak acid (AB) at pH 3 is Y×10⁻³ mol/L. The value of Y is .(Given that the value of solubility product of AB (Ksp) = 2×10⁻¹⁰ and the value of ionization constant of HB (Kₐ) = 1×10⁻⁸)

Q. 32 The plot given below shows P − T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolar solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is .

Questions: 33 – 34

Treatment of benzene with CO/HCl in the presence of anhydrous AlCl₃/CuCl followed by reaction with Ac₂O/NaOAc gives compound X as the major product. Compound X upon reaction with Br₂/Na₂CO₃, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with H₂/Pd-C, followed by H₃PO₄ treatment gives Z as the major product. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 33 The compound Y is

A. A

B. B

C. C

D. D

Q. 34 The compound Z is

A. A

B. B

C. C

D. D

Questions: 35 – 36

An organic acid P (C₁₁H₁₂O₂) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 35 The compound R is

A. A

B. B

C. C

D. D

Q. 36 The compound S is

A. A

B. B

C. C

D. D

Q. 37 For a non-zero complex number z, let arg(z) denote the principal argument with − n < arg(z) ≤ n. Then, which of the following statement(s) is (are) FALSE?

A. arg(−1 − i) =n/4, where i = √−1

B. The function ƒ: ℝ → (−n, n], defined by ƒ(t) = arg(−1 + it) for all t ∈ ℝ, is continuous at all points of ℝ, where i = √−1

C. For any two non-zero complex numbers z₁ and z₂, arg (z₁/z₂) − arg( z₁) + arg( z₂) is an integer multiple of 2n

D. For any three given distinct complex numbers z₁, z₂ and z₃, the locus of the point z

satisfying the condition arg ((z−z₁) (z₂−z₃)/(z−z₃) (z₂−z₁)) = n,lies on a straight line

Q. 38 In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10√3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE?

A. ∠QPR = 45°

B. The area of the triangle PQR is 25√3 and ∠QRP = 120°

C. The radius of the incircle of the triangle PQR is 10√3 − 15

D. The area of the circumcircle of the triangle PQR is 100

Q. 39 Let P₁: 2x + y − z = 3 and P₂: x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?

A. The line of intersection of P₁ and P₂ has direction ratios 1, 2, −1

B. The line (3x − 4)/9=(1 − 3y)/9= z/3 is perpendicular to the line of intersection of P₁ and P₂

C. The acute angle between P₁ and P₂ is 60°

D. If P₃ is the plane passing through the point (4, 2, −2) and perpendicular to the line of intersection of P₁ and P₂, then the distance of the point (2, 1, 1) from the plane P₃ is 2/√3

Q. 40 For every twice differentiable function ƒ: ℝ → [−2, 2] with (ƒ(0))² + (ƒ′(0))² = 85, which of the following statement(s) is (are) TRUE?

A. There exist r, s ∈ ℝ, where r < s, such that ƒ is one-one on the open interval (r, s)

B. There exists x0 ∈ (−4, 0) such that |ƒ′(x₀)| ≤ 1

C. limx→∞ ƒ(x) = 1

D. There exists α ∈ (−4, 4) such that ƒ(α) + ƒ′′(α) = 0 and ƒ′(α) ≠ 0

Q. 41 Let ƒ: ℝ → ℝ and g: ℝ → ℝ be two non-constant differentiable functions. If ƒ′(x) = (e(ƒ(x) −g(x)))g′(x) for all x ∈ ℝ, and ƒ(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?

A. A

B. B

C. C

D. D

Q. 42 Let ƒ:[0, ∞) → ℝ be a continuous function such that x0 for all x ∈ [0, ∞). Then, which of the following statement(s) is (are) TRUE?

A. The curve y = ƒ(x) passes through the point (1, 2)

B. The curve y = ƒ(x) passes through the point (2, −1)

C. The area of the region {(x, y) ∈ [0, 1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−2)/4

D. The area of the region {(x, y) ∈ [0,1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−1)/4

Q. 43 The value of the given equation is ______ .

Q. 44 The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .

Q. 45 Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, … , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, … . Then, the number of elements in the set X ∪ Y is

Q. 46 The number of real solutions of the equation lying in the interval (-1/2,1/2).(Here, the inverse trigonometric functions sin−1x and cos−1x assume values in [−n/2,n/2] and [0, n], respectively.)

Q. 47 For each positive integer n, let For x ∈ ℝ, let [x] be the greatest integer less than or equal to x. If the limit is given then the value of [L] is ________.

Q. 48 Let a and b be two unit vectors such thata ⋅ b = 0. For some x, y ∈ ℝ, let c = x a + y b + (a × b ) . If |c = 2 and the vector c⃗ is inclined at the same angle α to both a and b , then the value

of 8 cos² α is

Q. 49 Let a, b, c be three non-zero real numbers such that the equation √3 a cos x + 2 b sin x = c, x ∈ [−n/2,n/2], has two distinct real roots α and þ with α + þ = n/3. Then, the value of ba is_____ .

Q. 50 4 A farmer F₁ has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F₂ takes away the region which lies between the side PQ and a curve of the form y = xⁿ (n > 1). If the area of the region taken away by the farmer F₂ is exactly 30% of the area of ∆PQR, then the value of n is .

Questions: 51 – 52

Let S be the circle in the xy-plane defined by the equation x Let S be the circle in the xy-plane defined by the equation x² + y² = 4. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 51 Let E₁E₂ and F₁F₂ be the chords of S passing through the point P₀ (1, 1) and parallel to the x-axis and the y-axis, respectively. Let G₁G₂ be the chord of S passing through P₀ and having slope −1. Let the tangents to S at E₁ and E₂ meet at E₃, the tangents to S at F₁ and F₂ meet at F₃, and the tangents to S at G₀ and G₂ meet at G₃. Then, the points E₃, F₂, and G₃ lie on the curve

(A) (B)

A. x + y = 4

B. (x − 4)² + (y − 4)²= 16 (C) (D)

C. (x − 4)(y − 4) = 4

D. xy = 4

Q. 52 Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

A. (x + y)² = 3xy

B. x^2/3 + y^2/3 = 2^4/3

C. x² + y² = 2xy

D. x² + y² = x² y²

Questions: 53 – 54

There are five students S₁, S₂, S₃, S₄ and S₅ in a music class and for them there are five seats R₁, R₂, R₃, R₄ and R₅ arranged in a row, where initially the seat Rᵢ is allotted to the student Sᵢ, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 53 The probability that, on the examination day, the student S₁ gets the previously allotted seat Rᵢ, and NONE of the remaining students gets the seat previously allotted to him/her is

A. 3/40

B. 1/8

C. 7/40

D. 1/5

Q. 54 For i = 1, 2, 3, 4, let Tᵢ denote the event that the students Sᵢ and Sᵢ₊₁ do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T₁ ∩ T₂ ∩ T₃ ∩ T₄ is

A. 1/15

B. 1/10

C. 7/60

D. 1

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	ABD	BCD	CD	ABD	ABD	BCD	2.00	5.00	2.00	2.09
Question	11	12	13	14	15	16	17	18	19	20
Answer	1.50	2.00	130.00	4.00	C	D	B	C	BC	BC
Question	21	22	23	24	25	26	27	28	29	30
Answer	ABC	B	ABD	BC1	1	2992	3	10	2.22	19
Question	31	32	33	34	35	36	37	38	39	40
Answer	4.47	0.05	C	A	A	B	ABD	BCD	CD	ABD
Question	41	42	43	44	45	46	47	48	49	50
Answer	BC	BC	8	625	3748	2	1	3	0.5	4
Question	51	52	53	54
Answer	A	D	A	C

JEE Advanced 2017 Paper II Previous Year Paper

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

JEE Advanced 2017 Paper I Previous Year Paper

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
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

JEE Advanced 2016 Paper II Previous Year Paper

JEE Advanced 2016 Paper 2

Q. 1 The electrostatic energy of Z protons uniformly distributed uniformly throughout a spherical nucleus of radius R is given in the picture. Thea measured masses of the neutron, ¹H₁, ¹⁵N₇ and ¹⁵O₈ are 1.008665 u, 1.0077825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the ¹⁵N₇ and ¹⁵O₈ are same, 1 u = 931.5 MeV/c² (c is the speed of light) and e²/(4Πε0) = 1.44 MeV fm. Assuming that the difference between the binding energies of ¹⁵N₇ ¹⁵O₈ is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10⁻¹⁵ m)

E=35Z (Z-1) e24 0R

A. 2.85 fm

B. 3.03 fm

C. 3.42 fm

D. 3.80 fm

Q. 2 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 permissible level required for safe operation of the laboratory. What is the maximum number of days after which the laboratory can be considered safe for use?

A. 64

B. 90

C. 108

D. 120

Q. 3 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 m³ changes to a final state at P􀀁 = (1/32) x 10⁵ Pa and V􀀁 = 8 x 10⁻³ m³ in an adiabatic quasi-static process, such that P³.V⁵ = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pᵢ followed by an isochoric (isovolumetric) process at volume V􀀁. The amount 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

Q. 4 The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a lenght of 1 m at 10 ⁰C. Now the end P is maintained at 10 ⁰C, while the end S is heated and maintained at 400 ⁰C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 x 10⁻⁵K⁻¹, the change in lenght of the wire PQ is

A. 0.78 mm

B. 0.90 mm

C. 1.56 mm

D. 2.34 mm

Q. 5 A small object is placed 50 cm to the left of a thin convex lens of focal lenght 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle of θ = 30⁰ 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 the point (x,y) at which the image is formed are

A. (0, 0)

B. (50 – 25√3, 25)

C. (25, 25√3)

D. (125/3, 25/√3)

Q. 6 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 scale divisions. The Vernier scale of the other caliper (C₂) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C₁ and C₂, respectively, are

A. 2.85 and 2.82

B. 2.87 and 2.83

C. 2.87 and 2.86

D. 2.87 and 2.87

Q. 7 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 lenght l = √24a through their centres. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is ω . The angular momentum of the entire assembly about the point ‘O’ is L (see the figure). Which of the following statements(s) is (are) true?

A. The center of mass of the assembly rotates about the z – axis with an angular speed of ω/5

B. The magnitude of an angular momentum of center of mass of the assembly about the point O is 81ma²ω

C. The magnitude of angular momentum of the assembly about its center of mass is

17ma²ω/2

D. The magnitude of the z – component of L is 55 ma²ω

Q. 8 Light of wavelenght λₚₕ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is Φ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelenght of the electrons passing through the anode is λₑ, which of the following statements(s) is (are) true?

A. λₑ, decreases with increase in Φ and λₚₕ

B. λₑ is approximately halved, if d is doubled

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

D. λₑ increases at the same rate as λₚₕ for λₚₕ <he/Φ

Q. 9 In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a period motion is T = (2π) √7(R – r)/ 5g. 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%

Q. 10 Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc < R/2, which of the following statement(s) about any one of the galvanometers is (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 connected in series, and the second galvanometer is connected in parallel to the first galvanometer.

C. The maximum current range is obtained when all the components in parallel

D. The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors.

Q. 11 In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true?

A. The volunteer 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

Q. 12 A block with mass M is connected by a massless spring with stiffness constant ƙ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x₀. Consider two cases : (i) when the block is at x₀ ; and (ii) when then block is at x = x₀ + A. In both the cases, a particle with mass m (

A. The amplitude of oscillation in the first case changes by a factor of √[(M/(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

Q. 13 While conducting the Young’s double slit experiment, a student replaced the two slits with a large opaque plate in the x- y plane containing two small holes that act as two coherent point sources (S₁,S₂) emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0) at a distance D = 3 m from the mid -point of S₁S₂ , as shown schematically in the figure. The distance between the sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S₁S₂. Which of the following is(are) true of the intensity pattern on the screen?

A. Straight bright and dark bands parallel to the x – axis

B. The region very close to the point O will be dark

C. Hyberbolic bright and dark bands with foci symmetrically placed about O in the x –

direction

D. Semi circular bright and dark bands centered at point 0

Q. 14 A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity v₀ in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B₀ into the plane of the paper, as shown in the question figure. For sufficiently large v₀, the loop eventually crosses the region. Let x be the location of the right edge of the loop. 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 given schematic plot(s) is/are correct? (Ignore gravity)

A. A

B. B

C. C

D. D

Questions: 15 – 16

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

A. (R/4) [ eʷᵗ+ e⁻ʷᵗ ]

B. (R/2) cos ωt

C. (R/4) [ e²ʷᵗ + e⁻²ʷᵗ ]

D. (R/2) cos 2ωt

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

A. (1/2) mω²R ( e²ʷᵗ – e⁻²ʷᵗ ) ĵ + mgk̂

B. (1/2) mω²R ( eʷᵗ – e²ʷᵗ ) ĵ + mgk̂

C. -mω²R cos ωt ĵ – mgk̂

D. mω²R sin ωt ĵ – mgk̂

Questions: 17 – 18

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

Q. 17 Which one of the following statements is correct?

A. The balls will stick to the top plate and remain there

B. The balls will bounce back to the bottom plate carrying the same charge they went up with

C. The balls will bounce back to the bottom plate carrying the opposite charge they went up with

D. The balls will execute simple harmonic motion between the two plates

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

A. zero

B. proportional to the potential V₀

C. proportional to V

D. proportional to V

Q. 19 For the following electrochemical cell at 298 K ,

Pt (s) | H₂ (g,1 bar) | H⁺ (aq, 1 M) || M⁴⁺ (aq), M²⁺ (aq) | Pt (s)

E_cell = 0.092 V when [M²⁺ (aq)] / [M⁴⁺ (aq)] = 10ˣ

Given: E⁰ [M⁴⁺ / M²⁺)] = 0.151 V; 2.303 (RT/V) = 0.059 V.

The value of x is

A. -2

B. -1

C. 1

D. 2

Q. 20 The given qualitative sketches I, II and III shows the variation of surface tension with a molar concentration of three different aqueous solutions of KC₁, CH₃OH and CH₃(CH₂)₁₁OSO₃⁻Na⁺ at room temperature. The correct assignment of the sketches is

A. A

B. B

C. C

D. D

Q. 21 In the given reaction sequence in aqueous solution, the species X Y and Z, respectively, are

A. A

B. B

C. C

D. D

Q. 22 The geometries of the ammonia complexes of Ni²⁺ , Pt²⁺ 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

Q. 23 The correct order of acidity for the given compounds is

A. I > II >I II > IV

B. III > I > II >I V

C. III > IV > II > I

D. I >I II > IV > II

Q. 24 The major product of the given reaction sequence is

A. A

B. B

C. C

D. D

Q. 25 According to Molecular Orbital Theory,

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

Q. 26 Mixture(s) showing positive deviation from Raoult’s law at 35 ᵒC is (are)

A. carbon tetrachloride + methanol

B. carbon disulphide + acetone

C. benzene + toluene

D. phenol + aniline

Question 27 ONE OR MORE THAN ONE of the four given options is (are) correct.

Q. 27 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

Q. 28 Extraction of copper from copper pyrite (CuFeS₂) 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

Q. 29 The nitrogen containing compound produced in the reaction of HNO₃ with P₄O₁₀

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

Q. 30 For “invert sugar”, the correct statement(s) is(are)

(Given : specific rotations of (+) -sucrose, (+)-maltose, L-(-)glucose and L-(+)-fructose in aqueous solution are +66⁰ , +140⁰ , -52⁰ and +92⁰ , respectively)

A. ‘ínvert sugar’ is prepared by acid catalyzed hydrolysis of maltose

B. ‘ínvert sugar’ is an equimolar mixture of D-(+)- glucose and D-(-)- fructose

C. specific rotation of ‘invert sugar’ is -20⁰

D. on reaction with Br₂ water, ‘invert sugar’ forms saccharic acids as one of the products

Q. 31 Reagent(s) which can be used to bring about the given transformation is (are)

A. LiAlH₄ in (C₂H₅)₂O

B. BH₃ in THF

C. NaBH₄ in C₂H₅OH

D. Raney Ni/H₂ in THF

Q. 32 Among the given, reaction(s) which give(s) tert-butyl benzene as the major product is(are)

A. A

B. B

C. C

D. D

Questions: 33 – 34

•Read the paragraph and answer the following questions

•Each question has ONE correct option

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

X₂ (g) ⇄ 2X (g)

The standard reaction Gibbs energy, ΔᵣG°, 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 β. Thus, β(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 gasses to behave ideally. (Given: R = 0.083L bar K⁻¹mol⁻¹)

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

A. 8(β_equilibrium)² / (2 – β_equilibrium)

B. 8(β_equilibrium)² / (4 – β_equilibrium)

C. 4(β_equilibrium)² / (2 – β_equilibrium)

D. 4(β_equilibrium)² / (4 – β_equilibrium)

Q. 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 spontaneusly

C. β_equilibrium = 0.7

D. K_C < 1

Question 35

Treatment of compound O with KMnO₄/H+ gave P, which on heating with ammonia gave P. The compound Q on treatment with Br₂/NaOH produced R. On strong heating, Q gave S, which on further treatment with ethyl 2- bromopropanoate in the presence of KOH followed by acidification gave a compound T.

Q. 35 The compound R is

A. A

B. B

C. C

D. D

Question 36

Q. 36 The compound T is

A. glycine

B. alanine

C. valine

D. serine

Q. 37 Let P be the given lower triangular matrix and I be the identity matrix of order 3. If Q = [qᵥ ] is a matrix such that P⁵⁰ – Q = I, then (q₃₁ + q₃₂) / q₂₁ equals

A. 52

B. 103

C. 201

D. 205

Q. 38 Let bᵢ > 1 for i = 1, 2, …, 101. Suppose loge b₁, loge b₂, …, loge b₁₀₁ are in Arithmetic Progression (A. P.) with the common difference logₑ2. Suppose a₁, a₂, …, a₁₀₁ are in A. P. such that a₁ = b₁ and a₅₁ = b₅₁. If t = b₁ + b₂ + … + b₅₁ and s = a₁ + a₂ + … + a₅₁, then

A. s > t and a₁₀₁ > b₁₀₁

B. s > t and a₁₀₁ < b₁₀₁

C. s < t and a₁₀₁ > b₁₀₁

D. s < t and a₁₀₁ < b₁₀₁

Q. 39 The value of the given summation is equal to

K=1121sin 4+(k – 1) 6 sin 4 + k6

A. 3 – √3

B. 2(3 – √3)

C. 2(√3 – 1)

D. 2(2 + √3)

Q. 40 The value of the given integral is

A. Π²/4 – 2

B. Π²/4 + 2

C. Π² – e^(Π/2)

D. Π² + e^(Π/2)

Q. 41 Area of the region { (x, y) ∈ R² : y ≥ √ (|x + 3|), 5y ≤ x + 9 ≤ 15 } is equal to

A. 1/6

B. 4/3

C. 3/2

D. 5/3

Q. 42 Let P be the image of the point (3, 1, 7) with respect to the plane x – y + z = 3. The the equation of the plane passing through P and containing the straight line x/1 = y/2 = z/1 is

A. x + y – 3z = 0

B. 3x + z = 0

C. x – 4y + 7z = 0

D. 2x – y = 0

Q. 43 Let the given equality be true for all x > 0. Then

A. f(1/2) ≥ f(1)

B. f(1/3) ≤ f(2/3)

C. f'(2) ≤ 0

D. f'(3)/f(3) ≥ f'(2)/f(2)

Q. 44 Let a, b ∈ R and f : R → R be defined by f(x) = a cos (|x³ – x|) + b sin (|x³ + 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 = 0

D. NOT differentiable at x = 1 if a = 1 and b = 1

Q. 45 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 limit_(x → 2) [f(x) g(x)] / [f'(x) g'(x)] = 1, 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

Q. 46 Let f : [-1/2, 2] → R and g : [-1/2, 2] → R be functions defined by f(x) = [x² – 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 ∈ R. Then

A. f is discontinuous exactly at three points in [-1/2, 2]

B. f is discontinuous exactly at four points in [-1/2, 2]

C. g is NOT differentiable exactly at four points in (-1/2, 2)

D. g is NOT differentiable exactly at five points in (-1/2, 2)

Q. 47 Let a, b ∈ R and a² + b² ≠ 0. Suppose S = { z ∈ C : z = 1/(a + ibt), t ∈ R, t ≠ 0 }, where i = √-1. If z = x + iy and z ∈ S, then (x, y) lies on

A. the circle with radius 1/2a and centre (1/2a, 0) for a > 0, b ≠ 0

B. the circle with radius -1/2a and centre (-1/2a, 0) for a < 0, b ≠ 0

C. the x-axis for a ≠ 0, b = 0

D. the y-axis for a = 0, b ≠ 0

Q. 48 Let P be the point on the parabola y² = 4x which is at the shortest distance from the center S of the circle x² + y² – 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 is 1/2

Q. 49 Let a, λ, μ ∈ R. Consider the system of liner equations

ax + 2y = λ

3x – 2y = μ

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

A. If a = -3, then the system has infinitely many solutions for all values of λ and μ

B. If a ≠ -3, then the system has a unique solution for all values of λ and μ

C. If λ + μ = 0, then the system has infinitely many solutions for a = -3

D. If λ + μ ≠ 0, then the system has no solution for a = -3

Q. 50 Let û = u_1 î + u_2 ĵ + u_3 k̂ be a unit vector in R³ and ŵ = (1/√6)(î + ĵ + 2k̂). Given that there exists a vector v in R³ such that |û x v̂| = 1 and ŵ . (û x v̂) = 1. Which of the following statement(s) is(are correct?

A. There is exactly one choice for such vector v

B. There are indefinitely many choices for such vector v

C. If û lies in the xy-plane then |u_1| = |u_2|

D. If û lies in the xz-plane then 2 |u_1| = |u_3|

Questions: 51 – 52

Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.

Q. 51 P(X > Y) is

A. 1/4

B. 5/12

C. 1/2

D. 7/12

Q. 52 P(X = Y) is

A. 11/36

B. 1/3

C. 13/36

D. 1/2

Questions: 53 – 54

Let F₁(x₁, 0) and F₂(x₂, 0), for x₁ < 0 and x₂ > 0, be the foci of the ellipse x²/9 + y²/8 = 1. Suppose a parabola having vertex at the origin and focus at F₂ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.

Q. 53 The orthocentre of the triangle F₁MN is

A. (-9/10, 0)

B. (2/3, 0)

C. (9/10, 0)

D. (2/3, √6)

Q. 54 If the 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 MF₁NF₂ is

A. 3 : 4

B. 4 : 5

C. 5 : 8

D. 2 : 3

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	C	C	A	C	B	AC	C	ABD	BC
Question	11	12	13	14	15	16	17	18	19	20
Answer	ABCD	ABD	BD	AB	A	B	C	D	D	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	A	A	A	A	AC	AB	BCD	ABC	BD	BC
Question	31	32	33	34	35	36	37	38	39	40
Answer	CD	BCD	B	C	A	B	B	B	C	A
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	C	BC	AB	AD	BC	ACD	ACD	BCD	BC
Question	51	52	53	54
Answer	B	C	A	C

JEE Advanced 2016 Paper I Previous Year Paper

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
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