JEE Advanced 2013 Paper 2
Q. 1 Using the expression 2d sinθ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°.
A. the absolute error in d remains constant
B. the absolute error in d increases
C. the fractional error in d remains constant
D. the fractional error in d decreases
Q. 2 Two non conducting spheres of radii R₁ and R₂ and carrying uniform volume charge densities +p and -p respectively, are placed such that they partially overlap, as shown in figure (1). At all points in the overlapping region
A. The electrostatic field is zero
B. The electrostatic potential is constant
C. The electrostatic field is constant in magnitude
D. The electrostatic field has same direction
Q. 3 The figure (1) shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.
A. the rate at which heat is absorbed in the range 0 – 100 K varies linearly with temperature (T).
B. heat absorbed in increasing the temperature from 0 – 100 K is less than the heat required for increasing the temperature from 400 – 500 K.
C. there is no change in the rate of heat absorption in the range 400 – 500 K.
D. the rate of heat absorption increases in the range 200 – 300 K
Q. 4 The radius of the orbit of an electron in a Hydrogen – like atom is 4.5 ao, where ao is the Bohr radius. Its orbital angular momentum is 3h / 2π. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)
A. 9 / 32R
B. 9 / 16R
C. 9 / 5R
D. 4 / 3R
Q. 5 Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)
A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4√GM/L
B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2√GM/L
C. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is √2GM/L
D. The energy of the mass m remains constant
Q. 6 A particle of mass m is attached to one end of a massless spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u₀. When the speed of the particle is 0.5 u₀, it collides elastically with a rigid wall. After this collision
A. the speed of the particle when it returns to its equilibrium position is u₀
B. the time at which the particle passes through the equilibrium position for the first time is t = π√m/k
C. the time at which the maximum compression of the spring occurs is t = 4π/3 √m/k
D. the time at which the particle passes through the equilibrium position for the second time is t = 5π/3√m/k
Q. 7 A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. The cylinder is placed co-axially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)
A. In the region 0 < r < R, the magnetic field is non-zero.
B. In the region R < r < 2R, the magnetic field is along the common axis.
C. In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
D. In the region r > 2R, the magnetic field is non-zero.
Q. 8 Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. A wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f₁. An observer in the other vehicle hears the frequency of the whistle to be f₂. The speed of sound in still air is V. The correct statement(s) is (are)
A. If the wind blows from the observer to the source, f₂ > f₁.
B. If the wind blows from the source to the observer,f₂ > f₁
C. If the wind blows from the observer to the source, f₂ < f₁
D. If the wind blows from the source to the observer, f₂ < f₁.
Questions: 9 – 10
A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current Qω / 2π. A uniform magnetic field along the positive z-axix is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.
Q. 9 The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
A. BR / 4
B. BR / 2
C. BR
D. 2BR
Q. 10 The charge in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is
A. -⋎BQR²
B. -⋎(BQR² / 2)
C. -⋎(BQR²/ 2)
D. -⋎BQR²
Questions: 11 – 12
The mass of a nucleus (A)(Z)X is less than the sum of masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into light nuclei of masses m₁ and m₂ only if (m₁ + m₂) < M. Also two light nuclei of masses m₃ and m₄ can undergo complete fusion and form a heavy nucleus of mass M’ only if (m₃ + m₄) > M’. The masses of some neutral atoms are given in table
Q. 11 The correct statement is
A. The nucleus (6)(3)Li can emit an alpha particle
B. The nucleus (210)(84)P0 can emit a proton
C. Deutron and alpha particle can undergo complete fusion
D. The nuclei (70)(30)Zn and (82)(34)Se can undergo complete fusion
Q. 12 The Kinetic energy (in keV) of alpha particle, when the nucleus (210)(84)Po at rest undergoes alpha decay, is
A. 5319
B. 522
C. 5707
D. 5818
Questions: 13 – 14
A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure (1), is 150 J. (Take the acceleration due to gravity, g =10ms⁻²).
Q. 13 The speed of the block when it reaches the point Q is:
A. 5 ms⁻¹
B. 10 ms⁻¹
C. 10√3 ms⁻¹
D. 20 ms⁻¹
Q. 14 The magnitude of the normal reaction that acts on the block at the point Q is:
A. 7.5 N
B. 8.6 N
C. 11.5 N
D. 22. 5 N
Questions: 15 – 16
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers’ usage. It can be transported either directly with a cable of large current carrying or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformer, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers’ end, a step-down transformer is used to supply power to the consumers ta the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformer are ideal with a power factor unity. All the currents and voltages mentioned are rms values.
Q. 15 If the direct transmission method with a cable of resistance 0.4 Ω km⁻¹ is used, the power dissipation (in %) during transmission is:
A. 20
B. 30
C. 40
D. 50
Q. 16 In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:
A. 200 : 1
B. 150 : 1
C. 100 : 1
D. 50 : 1
Q. 17 Match list I with list II (given in figure (1)) and select the correct answer using the codes given below:
| List I | List II | ||
| P. | Boltzamnn constant | 1. | ML2T-1 |
| Q. | Coefficient of viscosity | 2. | ML-1T-1 |
| R. | Planck constant | 3. | MLT-3K-1 |
| S. | Thermal conductivity | 4. | ML2T-2K-1 |
A. P3, Q1, R2, S4
B. P3, Q2, R1, S4
C. P4, Q2, R1, S3
D. P4, Q1, R2, S3
Q. 18 A right-angled prism of refractive index μ₁ is placed in a rectangular block of refractive index μ₂, which is surrounded by a medium of refractive index μ₃, as shown in figure (1). A ray of light ‘e’ enters the rectangular block at normal incidence. Depending upon the relationship between μ₁, μ₂ and μ₃, it takes one of the four possible paths ‘ef’, ‘eg’, ‘eh’ or ‘ei’. Match the paths in List I with conditions of refractive indices in List II (given in figure (2)) and select the correct answer using the codes given below:
A. P2, Q3, R1, S4
B. P1, Q2, R4, S3
C. P4, Q1, R2, S3
D. P2, Q3, R4, S1
Q. 19 Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process (given if figure (1)) and then select the correct answer using the codes given below the lists:
A. P4, Q2, R1, S3
B. P1, Q3, R2, S4
C. P2, Q1, R4, S3
D. P4, Q3, R2, S1
Q. 20 One mole of a monatomic ideal gas is taken along two cyclic processes E → F → G → E and E → F → H → E as shown in the PV diagram given in figure (1). The processes involved are purely isochoric, isobaric, isothermal or adiabatic. Match the paths in List I with the magnitudes of the work done in List II (given in figure (2)) and select the correct answer using the codes given below:
A. P4, Q3, R2, S1
B. P4, Q3, R1, S2
C. P3, Q1, R2, S4
D. P1, Q3, R2, S4
Q. 21 The correct statement(s) about O₃ is (are) :
A. O – O bond lengths are equal.
B. Thermal decomposition of O₃ is endothermic.
C. O₃ is diamagnetic in nature.
D. O₃ has a bent structure
Q. 22 In the nuclear transmutation given in figure (1), (X, Y) is (are) :
A. (γ, n)
B. (p, D)
C. (n, D)
D. (γ, p)
Q. 23 The carbon-based reduction method is NOT used for the extraction of:
A. tin from SnO₂
B. iron from Fe₂O₃
C. aluminium from Al₂O₃
D. magnesium from MgCO₃ . CaCO₃
Q. 24 The thermal dissociation equilibrium of CaCO₃(s) is studied under different conditions. CaCO₃(s) ⇔ CaO(s) + C0₂(g)
A. ΔH is dependent on T
B. K is independent of the initial amount of CaCO₃
C. K is dependent on the pressure of CO₂ at a given T
D. ΔH is independent of the catalyst, if any.
Q. 25 The Ksp of Ag2CrO4 is 1.1 x 10⁻¹² at 298 K. The solubility (in mol/L) of Ag₂CrO₄ in a 0.1 M AgNO₃ solution is
A. 1.1 x 10⁻¹¹
B. 1.1 x 10⁻¹⁰
C. 1.1 x 10⁻¹²
D. 1.1 x 10⁻⁹
Q. 26 In the following reactions given in figure (1), the product(s) formed is(are) (given in figure (2)):
A. P(major)
B. Q(minor)
C. R(minor)
D. S(major)
Q. 27 The major product(s) among the structure (P), (Q), (R), (S) (given in figure (1)) of the following reaction (given in figure (2)) is(are) :
A. P
B. Q
C. R
D. S
Q. 28 After completion of the reactions (I and II) (given in figure), the organic compound(s) in the reaction mixtures (given in figure (1)) is (are) :
A. Reaction I: P and Reaction II: P
B. Reaction I: U, acetone and Reaction II: Q, acetone
C. Reaction I: T, U, acetone and Reaction II: P
D. Reaction I: R, acetone and Reaction II: S, acetone
Questions: 29 – 30
A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in figure (1):
Q. 29 The succeeding operations that enable this transformation of states are:
A. Heating, cooling, heating, cooling
B. Cooling, heating, cooling, heating
C. Heating, cooling, cooling, heating
D. Cooling, heating, heating, cooling
Q. 30 The pair of isochoric processes among the transformation of states is
A. K to L and L to M
B. L to M and N to K
C. L to M and M to N
D. M to N and N to K
Questions: 31 – 32
The reactions of Cl₂ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The Cl₂ gas reacts with SO₂ gas, in presence of charcoal, to give a product R. R reacts with white phosphorous to give a compound S. On hydrolysis, S gives an oxoacid of phosphorous, T.
Q. 31 P and Q, respectively, are the sodium salts of
A. hypochlorus and chloric acids
B. hypochlorus and chlorus acids
C. chloric and perchloric acids
D. chloric and hypochlorus acids
Q. 32 R, S and T, respectively, are:
A. SO₂Cl₂, PCl₅ and H₃PO₄
B. SO₂Cl₂, PCl₃ and H₃PO₃
C. SOCl₂, PCl₃ and H₃PO₂
D. SOCl₂, PCl₅ and H₃PO₄
Questions: 33 – 34
An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged when treated with H₂S in a dilute mineral acid medium. However, it gave a precipitate (R) with H₂S in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with H₂0₂ in an aqueous NaOH medium.
Q. 33 The precipitate P contains
A. Pb²⁺
B. Hg₂²⁺
C. Ag⁺
D. Hg²⁺
Q. 34 The coloured solution S contains
A. Fe₂(SO₄)₃
B. CuSO₄
C. ZnSO₄
D. Na₂CrO₄
Questions: 35 – 36
P and Q are isomers of dicarboxylic acid C₄H₄O₄. Both decolourize Br₂ / H₂O. On heating, P forms the cyclic anhydride. Upon treatment with dilute alkaline KMnO₄, as well as Q, Q could produce one or more than one from S, T and U. (GivEn in figure(1)).
Q. 35 Compounds formed from P and Q are, respectively:
A. Optically active S and optically active pair (T, U)
B. Optically inactive S and optically inactive pair (T, U)
C. Optically active pair (T, U) and optically active S
D. Optically inactive pair (T, U) and optically inactive S
Q. 36 In the reaction sequences given in figure (2), V and W are, respectively (among the options (A), (B), (C), (D) given in figure (3)).
A. (A)
B. (B)
C. (C)
D. (D)
Q. 37 Match the chemical conversions in List I with the appropriate reagents in List II given in figure (1) and select the correct answer using the code given below:
Q. 38 The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in List II (Given in figure (1)). Match List I with List II and select the correct answer using the code given below:
A. P4, Q2, R3, S1
B. P3, Q2, R1, S4
C. P1, Q4, R2, S3
D. P3, Q4, R2, S1
Q. 39 The standard reduction potential data at 25° C is given below:
E° (Fe³⁺, Fe²⁺) = +0.77 V;
E° (Fe²⁺, Fe) = -0.44 V;
E° (Cu²⁺, Cu) = +0.34 V;
E° (Cu⁺, Cu) = +0.52 V
E° [O₂(g) + 4H⁺ + 4e⁻ → 2H₂O] = +1.23 V;
E° [O₂(g) + 2H₂0 + 4e⁻ → 4OH⁻] = +0.40 V;
E° (Cr³⁺, Cr) = -0.74 V;
E° (Cr²⁺, Cr) = -0.91 V;
Match E° of the redox pair in List I with the values given in List II (given in figure (1)) and select the correct answer using the code below:
A. P4, Q1, R2, S3
B. P2, Q3, R4, S1
C. P1, Q2, R3, S4
D. P3, Q4, R1, S2
Q. 40 An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II (Both the Lists are given in figure (1)). Match List I and List II and select the correct answer using the code given below.
Q. 41 Let w = √3 + i / 2 and P = {wⁿ : n = 1, 2, 3, …..}. Further H₁ = {z ∈ C : Re z > 1/2} and H₂ = {z ∈ C : Re z < -1/2}, where C is the set of all complex numbers. If z₁ ∈ P ∩ H₁, z₂ ∈ P ∩ H₂ and O represents the origin, then ∠ z₁ Oz₂ =
A. π / 2
B. π / 6
C. 2π / 3
D. 5π / 6
Q. 42 If 3ˣ = 4ˣ⁻¹, then x =
A. 2 log₃2 / 2 log₃2 – 1
B. 2 / 2 – log₂3
C. 1 / 1 – log₄3
D. 2 log₂3 / 2 log₂3 – 1
Q. 43 Let ω be a complex cube root of unity with ω ≠ 1 and P = [Pᵢⱼ] be a n x n matrix with Pᵢⱼ = ωᶦ⁺ʲ. Then P² ≠ 0, when n =
A. 57
B. 55
C. 58
D. 56
Q. 44 The function f(x) = 2 |x| + |x + 2| – ||x + 2| – 2 |x|| has a local minimum or a local maximum at x =
A. -2
B. -2 / 3
C. 2
D. 2 / 3
Q. 45 For a ∈ R (the set of all real numbers), a ≠ -1, in the equation given in figure (1), then a =
A. 5
B. 7
C. -15 / 2
D. -17 / 2
Q. 46 Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2√7 on y-axis is (are):
A. x² + y² – 6x + 8y + 9 = 0
B. x² + y² – 6x + 7y + 9 = 0
C. x² + y² – 6x – 8y + 9 = 0
D. x² + y² – 6x – 7y + 9 = 0
Q. 47 Two lines L1 : x = 5, y / 3 – α = z / -2 and L2 : α, y / -1 = z / 2 – α are coplanar. Then α can take value(s):
A. 1
B. 2
C. 3
D. 4
Q. 48 In a triangle PQR, P is the largest angle and cos P = 1 / 3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle
is (are)
A. 16
B. 18
C. 24
D. 22
Questions: 49 – 50
Let S = S₁ ∩ S₂ ∩ S₃, where
S₁ = {z ∈ C : |z| < 4}
S₂ = {z ∈ C : lm [(z – 1 + √3i) / (1 – √3i)] > 0}
S₃ = {z ∈ C : Re z > 0}
Q. 49 Area of S:
A. 10π / 3
B. 20π / 3
C. 16π / 3
D. 32π / 3
Q. 50 Find the value of the question given in figure (1):
A. 2-√3 / 2
B. 2+√3 / 2
C. 3-√3 / 2
D. 3+√3 / 2
Questions: 51 – 52
A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, 3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls.
Q. 51 If 1 ball is drawn from each of the boxes B₁, B₂ and B₃, the probability that all 3 drawn balls are of the same colour is:
A. 82 / 648
B. 90 / 648
C. 558 / 648
D. 566 / 648
Q. 52 If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B₂ is:
A. 116 / 181
B. 126 / 181
C. 65 / 181
D. 55 / 181
Questions: 53 – 54
Let f: [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) and satisfies f”(x) – 2f'(x) + f(x) ≥ eˣ, x ∈ [0, 1].
Q. 53 Which of the following is true for 0 < x < 1?
A. 0 < f(x) < ∞
B. -1/2 < f(x) < 1/2
C. -1/4 < f(x) < 1
D. -∞ < f(x) < 0
Q. 54 If the function eˣ f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true?
A. f'(x) < f(x), 1/4 < x < 3/4
B. f'(x) > f(x), 0 < x < 1/4
C. f'(x) < f(x), 0 < x < 1/4
D. f'(x) < f(x), 3/4 < x < 1
Questions: 55 – 56
Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0
Q. 55 Length of chord PQ is
A. 7a
B. 5a
C. 2a
D. 3a
Q. 56 If chord PQ subtends an angle θ at the vertex of y² = 4ax, then tan θ =
A. 2/3√7
B. -2/3√7
C. 2/3√5
D. -2/3√5
Q. 57 A line L : y = mx + 3 meets y-axis at E(0, 3) and the arc of the parabola y² = 16x, 0 ≤ y ≤ 6 at the point F(x₀, y₀). The tangent to the parabola at F(x₀, y₀) intersects the y-axis at G(0, y₁). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum. Match List I with List II (given in figure (1)) and select the correct answer using the code given below:
A. P4, Q1, R2, S3
B. P3, Q4, R1, S2
C. P1, Q3, R2, S4
D. P1, Q3, R4, S2
Q. 58 Match List I with List II (given in figure (1)) and select the correct answer using the code given below:
A. P4, Q3, R1, S2
B. P4, Q3, R2, S1
C. P3, Q4, R2, S1
D. P3, Q4, R1, S2
Q. 59 Consider the lines L1 : x – 1 /2 = y / -1 = z + 3 / 1, L2 : x – 4 / 1 = y + 3 / 1 = z + 3 / 2 and the planes P1 : 7x + y + 2z = 3, P2 : 3x + 5y – 6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L1 and L2, and perpendicular to planes P₁ and P₂. Match List – I with List -II (given in figure (1)) and select the correct answer using the code given below:
A. P3, Q2, R4, S1
B. P1, Q3, R4, R2
C. P3, Q2, R1, S4
D. P2, Q4, R1, S3
Q. 60 Match List – I with List – II (given in figure (1)) and select the correct answer using the code given below:
A. P4, Q2, R3, S1
B. P2, Q3, R1, S4
C. P3, Q4, R1, S2
D. P1, Q4, R3, S2
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | D | CD | ABCD | AC | BD | AD | AD | AB | B | B |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | C | A | B | A | B | A | C | D | C | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | ACD | AB | CD | ABD | B | BD | B | C | C | B |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | A | A | A | D | B | A | A | D | D | A |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | CD | ABC | BCD | AB | B | AC | AD | BD | B | C |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | A | D | D | C | B | D | A | B | A | C |