JEE Advanced - Page 2 of 4 - Vidhyarthi Darpan

JEE Advanced 2015 Paper II Previous Year Paper

JEE Advanced 2015 Paper 2

Q. 1 A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M, the tension in the rod is zero for m = k(M/288). The value of k is

Q. 2 The energy of a system as a function of time t is given as E(t) = A²exp(-at), where a = 0.2 s⁻¹. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t=5 s is

Q. 3 The densities of two solid spheres A and B of the same radii R vary with radial distance r as Pₐ(r) = k(r/R) and Pᵦ(r) = k(r/R)⁵, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are Iₐ and Iᵦ, respectively. If Iᵦ/Iₐ = n/10, the value of n is

Q. 4 Four harmonic waves of equal frequencies and equal intensities I₀ have phase angles 0, π/3, 2π/3 and π. When they are superposed, the intensity of the resulting wave is nI₀. The value of n is

Q. 5 For a radioactive material, its activity A and rate of change of its activity R are defined as A = -dN/dt and R = -dA/dt, where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life l) and Q (mean life 2l) have the same activity at t = 0. Their rates of change of activities at t = 2l are Rₚ and Rᵩ, respectively. If Rₚ/Rᵩ = n/e, then the value of n is

Q. 6 A monochromatic beam of light is incident at 60⁰ on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle θ(n) with the normal (see the figure). For n = √3 the value of θ is 60⁰ and dθ/dn = m. The value of m is

Q. 7 In the following circuit, the current through the resistor R (= 2 Ω) is I Amperes. The value of I is

Q. 8 An electron in an excited state of Li²⁺ion has angular momentum 3h/2π. The de Broglie wavelength of the electron in this state is pπa₀ (where a₀ is the Bohr radius). The value of p is

Q. 9 Two spheres P and Q of equal radii have densities p₁ and p₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities d₁ and d₂ and viscosities n₁ and n₂, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure). If sphere P alone in L₂ has terminal velocity V of P and Q alone in L has terminal velocity V of Q, then

A. |V of P|/|V of Q| = n₁/n₂

B. |V of P|/|V of Q| = n₂/n₁

C. V of P. V of Q > 0

D. V of P. V of Q < 0

Q. 10 In terms of potential difference V, electric current I, permittivity E₀, permeability u₀ and speed of light c, the dimensionally correct equation(s) is (are)

A. μ₀I² = ε₀V²

B. cI = μ₀V

C. I =ε₀cV

D. μ₀cI = ε₀V

Q. 11 Consider a uniform spherical charge distribution of radius R₁ centred at the origin O. In this distribution, a spherical cavity of radius R₂, centred at P with distance OP = a = R₁ – R₂ (see figure) is made. If the electric field inside the cavity at position r is E(r), then the correct statement(s) is (are)

A. E is uniform, its magnitude is independent of R2 but its direction depends on r

B. E is uniform, its magnitude depends of R2 but its direction depends on r

C. E is uniform, its magnitude is independent of a but its direction depends on a

D. E is uniform and both its magnitude and direction depend on a

Q. 12 In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)

A. P has more tensile strength than Q

B. P is more ductile than Q

C. P is more brittle than Q

D. The Young’s modulus of P is more than that of Q

Q. 13 A spherical body f radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at s(r < R), then the correct option(s) is(are)

A. P(r = 0) = 0

B. P(r = 3R/4) / P(r = 2R/3) = 63/80

C. P(r = 3R/5) / P(r = 2R/5) = 16/21

D. P(r = R/2) / P(r = R/3) = 20/27

Q. 14 A parallel plate capacitor having plates of area S and plate separation d, has capacitance C₁ in air. When two dielectrics of different relative permittivities (E₁ = 2 and E₂ = 4) ar introduced between the two plates as shown in the figure, the capacitance becomes C₂. The ratio C₂/C₁ is

A. 6/5

B. 5/3

C. 7/5

D. 7/3

Q. 15 An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T₁, pressure P₁ and volume V₁ and the spring is in its relaxed state. The gas is then heated very slowly to temperature T₂, pressure P₂ and volume V₂. During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)

A. If V₂ = 2V₁ and T₂ = 3T₁, then the energy stored in the spring is 1/4 P₁V₁

B. If V₂ = 2V₁ and T₂ = 3T₁, then the change in internal energy is 3 P₁V₁

C. If V₂ = 3V₁ and T₂ = 4T₁, then the work done by the gas is 7/3 P₁V₁

D. If V₂ = 3V₁ and T₂ = 4T₁, then the heat supplied to the gas is 17/6 P₁V₁

Q. 16 A fission reaction is given, where x and y are two particles. Considering U to be at rest, the kinetic energies of the products are denoted by Kₓₑ, Kₛᵣ, Kₓ(2MeV) and Kᵧ(2MeV), respectively. Le the binding energies per nucleon of U, Xe and Sr be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s) is(are)

A. x = n, y = n, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

B. x = p, y = e⁻, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

C. x = p, y = n, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

D. x = n, y = n, Kₛᵣ = 86 MeV, Kₓₑ = 129 MeV

Questions: 17 – 18

In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are

I, w and d, respectively.

A uniform magnetic field B is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Q. 17 Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w₁ and w₂ and thicknesses are d₁ and d₂ respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V₁ and V₂ are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)

A. If w₁ = w₂ and d₁= 2d₂ , then V₂ = 2V₁

B. If w₁ = w₂ and d₁= 2d₂ , then V₂ =V₁

C. If w₁ = 2w₂ and d₁= d₂ , then V₂ = 2V₁

D. If w₁ = 2w₂ and d₁ =d₂ , then V₂ = V₁

Q. 18 Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n₁ and n₂, respectively. Strip 1 is placed in magnetic field B₁ and strip 2 is placed in magnetic field B₂, both along positive y-directions. Then V₁ and V₂ are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)

A. If B₁ = B₂ and n₁ = 2n₂ , then V₂ = 2V₁

B. If B₁ = B₂ and n₁ = 2n₂ , then V₂ =V₁

C. If B₁ = 2B₂ and n₁ = n₂ , then V₂ = 0.5V₁

D. If B₁ = 2B₂ and n₁ =n₂ , then V₂ = V₁

Questions: 19 – 20

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a particular value iₘ are confined in the medium of refractive index n₁. The numerical aperture (NA) of the structure is defined as sin iₘ.

Q. 19 For two structures namely S₁ with n₁ = √45/4 and n₂ = 3/2, and S₂ with n₁ = 8/5 and n₂ = 7/5 and taking the refractive index of water to be 4.3 and that of air to be I, the correct option(s) is (are)

A. NA of S₁ immersed in water is the same as that of S₂ immersed in a liquid of refractive index 16/3√15

B. NA of S₁ immersed in liquid of refractive index 6/√15 is the same as that of S₂ immersed in water

C. NA of S₁ placed in air is the same as that of S₂ immersed in liquid of refractive index 4/ √15

D. NA of S₁ placed in air is the same as that of S₂ placed in water

Q. 20 If two structures of same cross-sectional area, but different numerical apertures NA₁ and NA₂ (NA₂ < NA₁) are joined longitudinally, the numerical aperture of the combined structure is

A. NA₁NA₂/NA₁+NA₂

B. NA₁ + NA₂

C. NA₁

D. NA₂

Q. 21 The number of hydroxyl group(s) in Q is

Q. 22 Among the following the number of reaction(s) that produce(s) benzaldehyde is

Q. 23 In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe-C bond(s) is

Q. 24 Among the complex ions, [Co(NH₂-CH₂-CH₂-CH₂-NH₂)₂Cl₂]⁺, [CrCl₂(C₂O₄)₂]³⁻,

[Fe(H₂O)₄(OH)₂]⁺, [Fe(NH₃)₂(CN)₄]⁻, [Co(NH₂-CH₂-CH₂-NH₂)₂(NH₃)Cl]²⁺ and [Co(NH₃)₄(H₂O)Cl]²⁺, the number of complex ion(s) that show(s) cis-trans isomerism is

Q. 25 Three moles of B₂H₆ are completely reacted with methanol. Th number of moles of boroncontaining product formed is

Q. 26 The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of weal acid HY (0.10 M). If the given condition is satisfied, the difference in pKa values, ₚKₐ(HX) – ₚKₐ(HY), is (consider the degree of ionization of both acids to be <<1)

Q. 27 The closed vessel with rigid walls contains 1 mol of U and 1 mol of air at 298 K. Considering complete decay of U to Pb, the ratio of the final pressure to the initial pressure of the system of 298 K is

Q. 28 In dilute aqueous H₂SO₄, the complec diaquodioxalatoferrate(II) is oxidized by MnO₄⁻. For this reaction, the ratio of the rate of change of H⁺ to the rate of change of [MnO₄⁻] is

Q. 29 In the following reactions, the product S is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 30 The major product U in the following reactions is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 31 In the following reactions, the major product W is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 32 The correct statement(s) regarding, (i) HClO, (ii) HClO₂, (iii) HClO₃ and (iv) HClO₄, is (are)

A. The number of Cl=O bonds in (ii) and (iii) together is two

B. The number of lone pairs of electrons on Cl in (ii) and (iii) together is three

C. The hybridization of Cl in (iv) is sp³

D. Amongst (i) to (iv), the strongest acid is (i)

Q. 33 The pair(s) of ions where BOTH the ions are precipitated upon passing H₂S gas in presence of dilute HCl, is (are)

A. Ba²⁺, Zn²⁺

B. Bi³⁺, Fe³⁺

C. Cu²⁺, Pb²⁺

D. Hg²⁺, Bi³⁺

Q. 34 Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are

A. CH₃SiCl₃ and Si(CH₃)₄

B. (CH₃)₂SiCl₂ and (CH₃)₃SiCl

C. (CH₃)₂SiCl₂ and CH₃SiCl₃

D. SiCl₄ and (CH₃)₃SiCl

Q. 35 When O₂ is adsorbed on a metallic surface, electron transfer occurs from the metal to O₂. The TRUE statement(s) regarding this adsorption is(are)

A. O₂ is physisorbed

B. heat is released

C. occupancy of pi2p of O₂ is increased

D. bond length of π₂ₚ of O₂ is increased

Q. 36 One mole of a monoatomic real gas satisfies the equation p(V – b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

A. (A)

B. (B)

C. (C)

D. (D)

Question 37

In the given reactions

Q. 37 In the given reactions Compound X is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 38 The major compound Y is

A. (A)

B. (B)

C. (C)

D. (D)

Questions: 39 – 40

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7 degrees C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (-57.9 kJ mol⁻¹), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (Ka = 2.0 x 10⁻⁵) was mixed with 100 mL of 1.0 mL MaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6 degrees C was measured. (Consider heat capacity of all solutions as 4.2 J g⁻¹ K⁻¹ and density of all solutions as 1.0 g mL⁻¹)

Q. 39 Enthalpy of dissociation (in kJ mol⁻¹) of acetic acid obtained from the Expt. 2 is

A. 1.0

B. 10.0

C. 24.5

D. 51.4

Q. 40 The pH of the solution after Expt. 2 is

A. 2.8

B. 4.7

C. 5.0

D. 7.0

Q. 41 For any integer k, let aₖ = cos(kπ/7) + i sin(kπ/7), where i = √-1. The value of the given expression is

Q. 42 Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the firs eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

Q. 43 The coefficient of x⁹ in the (1+x)(1+x³)…(1+x¹⁰⁰) is

Q. 44 Suppose that the foci of the ellipse x²/9 + y²/5 = 1 are (f₁, 0) and (f₂, 0) where f₁>0 and f₂<0. Let P₁ and P₂ be two parabolas with a common vertex at (0, 0) and with foci at (f₁, 0) and (2f₂, 0), respectively. Let T₁ be a tangent to P₁ which passes through (2f₂, 0) and (T₂ be a tangent to P₂ which passes through (f₁, 0). If m1 is the slope of T₁ and m₂ is the slope of T₂, then the value of (1/m₁² + m₂²) is

Q. 45 Let m and n be two positive integers greater than 1, then the value of m/n is

Q. 46 Find the value:

=01(e9x+3tan-1x)12 + 9×21 + x2dx

where tan-1x takes only principal values, then the value of loge1 + -34is

Q. 47 Let R —> R be a continuous odd function, which vanishes exactly at one point and f(1) = 1/2. F(x) is given for all x is element of [-1, 2] and G(x) is given for all x is element of [-1,2]. Find the value of f(1/2) from the given data.

Q. 48 Suppose that p, q and r are three non-coplanar vectors in R³. Let the components of a vector s along p, q and r be 4, 3 and 5, respectively. If the components of this vector s along (-p+q+r), (p-q+r) and (-p-q+r) are x, y and z, respectively, then the value of 2x+y+z is

Q. 49 Let S be the set of all non-zero real numbers a such that the quadratic equation ax² – x + a = 0 has two distinct real roots x₁ and x₂ satisfying the inequality |x₁ – x₂| < 1. Which of the following intervals is (are) a subset(s) of S?

A. (-1/2, -1/√5)

B. (-1/√5, 0)

C. (0, 1/√5)

D. (1/√5 , 1/2)

Q. 50 If a = 3sin⁻¹(6/11) and b = 3cos⁻¹ (4/9), where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

A. cosβ > 0

B. sinβ < 0

C. cos(α +β) > 0

D. cosα < 0

Q. 51 Let E₁ and E₂ be two ellipses whose centres are at the origin. The major axes of E₁ and E₂ lie along the x-axis and the y-axis, respectively. Let S be the circle x² + (y-1)² = 2. The straight line x + y = 3 touches the curves S, E₁ and E₂ at P, Q and R, respectively. Suppose that PQ = PR = 2√2/3. If e₁ and e₂ are the eccentricities of E₁ and E₂, respectively, then the correct expression(s) is(are)

A. e₁² + e₂² = 43/40

B. e₁e₂ = √7/2√10

C. |e₁² – e₂²| = 5/8

D. e₁e₂ = √3/4

Q. 52 Consider the hyperbola H : x² – y² = 1 and a circle S with center N(x₂, 0). Suppose that H and S touch each other at a point P(x₁, y₁) with x₁>1 and y₁>0. The common tangent to H and S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle PMN, then the correct expression(s) is(are)

A. dl/d₁ = 1 – 1/3x₁² for x₁ > 1

B. dm/dx₁ = x₁/3√(x²-1) for x₁ > 1

C. dl/dx₁ = 1 + 1/3x₁² for x₁ > 1

D. dm/dy₁ = 1/3 for y₁ > 0

Q. 53 The option(s) with the values of a and L that satisfy the given equation is (are)

A. a = 2, L = [(e^4pi) – 1]/[(e^pi) – 1]

B. a = 2, L = [(e^4pi) + 1]/[(e^pi) + 1]

C. a = 4, L = [(e^4pi) – 1]/[(e^pi) – 1]

D. a = 4, L = [(e^4pi) + 1]/[(e^pi) + 1]

Q. 54 Let f, g : [-1, 2] —-> R be continuous functions which are twice differentiable on the interval (-1, 2). Let the values of f and g at the points -1, 0 and 2 be as given in the table. In each of the intervals (-1, 0) and (0, 2) the function (f – 3g)” never vanishes. Then the correct statement(s) is(are)

x=-1	x= 0	x=2
f(x)	3	6	0
g(x)	0	1	-1

A. f'(x) – 3g'(x) = 0 has exactly three solutions in (-1, 0)U(0, 2)

B. f'(x) – 3g'(x) = 0 has exactly one solution in (-1, 0)

C. f'(x) – 3g'(x) = 0 has exactly one solution in (0, 2)

D. f'(x) – 3g'(x) = 0 has exactly two solutions in (-1, 0) and exactly two solutions in (0,2)

Q. 55 Let f(x) = 7tan⁸x + 7tan⁶x – 3tan⁴x – 3tan²x for all x is element of (-π/2, π/2). Then the correct expression(s) is(are)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 56 Let f'(x) = 192x³/2+sin⁴πx for all x is a real number with f(1/2) = 0. If the given condition is satisfied, then the possible values of m and M are

m1/21f(x) dx M

A. m = 13, M = 24

B. m = 1/4, M = 1/2

C. m = -11, M = 0

D. m = 1, M = 12

Questions: 57 – 58

Let n₁ and n₂ be the number of red and black balls, respectively, in box I. Let n₃ and n₄ be the number of red and black balls, respectively, in box II.

Q. 57 One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is 1/3, then the correct option(s) with the possible values of n₁, n₂, n₃ and n₄ is (are)

A. n₁ = 3, n₂ = 3, n₃ = 5, n₄ = 15

B. n₁ = 3, n₂ = 6, n₃ = 10, n₄ = 50

C. n₁ = 8, n₂ = 6, n₃ = 5, n₄ = 20

D. n₁ = 6, n₂ = 12, n₃ = 5, n₄ = 20

Q. 58 A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer is 1/3, then the correct option(s) with the possible values of n₁ and n₂ is (are)

A. n₁ = 4 and n₂ = 6

B. n₁ = 2 and n₂ = 3

C. n₁ = 10 and n₂ = 20

D. n₁ = 3 and n₂ = 6

Q. 59 Let F: R —> R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x is element of (1/2, 3). Let f(x) = xF(x) for all x is element of R. The correct statement(s) is(are)

A. f'(1) < 0

B. f(2) < 0

C. f'(x) is not equal to 0 for any x is element of (1, 3)

D. f'(x) = 0 for some x is element of (1, 3)

Q. 60 Let F: R —> R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x is element of (1/2, 3). Let f(x) = xF(x) for all x is element of R. Using the given data, the correct expression(s) is (are)

A. 9f'(3) + f'(1) – 32 = 0

B. (B)

C. 9f'(3) – f'(1) + 32 = 0

D. (D)

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	7	4	6	3	2	2	1	2	AD	AC
Question	11	12	13	14	15	16	17	18	19	20
Answer	D	AB	BC	D	ABC	A	D	C	C	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	4	4	3	6	6	3	9	8	A	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	A	BC	CD	B	BCD	C	C	D	A	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	4	9	8	4	2	9	7	9	AD	BCD
Question	51	52	53	54	55	56	57	58	59	60
Answer	AB	ABD	AC	BC	AB	D	B	D	ABC	CD

JEE Advanced 2015 Paper I Previous Year Paper

JEE Advanced 2015 Paper 1

Q. 1 An infinitely long uniform line charge distribution of charge per unit length x lies parallel to the y-axis in the y-z plane at z = (root of 3/2)a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is xL/nE0 (E0 = permittivity of free space), then the value of n is

Q. 2 Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value on n is (hc = 1242 eV nm)

Q. 3 A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet’s gravity is 1/4th of its value at the surface of the planet. If the escape velocity from the planet is vesc = v(root of N), then the value of N is (ignore energy loss due to atmosphere)

Q. 4 Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds v₁ and v₂, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and v₁ = 3 m/s, then v₂ in m/s is (g = 10 m/s²)

Q. 5 Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted from B. The ratio (xA/xB) of their wavelengths xA and xB at which the peaks occur in their respective radiation curves is

Q. 6 A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is

Q. 7 A Young’s double slit interference arrangement with slits S₁ and S₂ is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by x² = p²m²λ² – d², where λ is the wavelength of light in air (refractive index = 1), 2d is the separation between the slits and m is an integer. The value of p is

Q. 8 Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification M₁. When the set-up is kept in a medium of refractive index 7/6, the magnification becomes M₂. The magnitude |M₂/M₁| is

Q. 9 Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one compete rotation of the circular scale moves it by two divisions on the linear scale. Then:

A. If the pitch of the screw gauge is twice the least count of the Vernier callipers, the

least count of the screw gauge is 0.01 mm.

B. If the pitch of the screw gauge is twice the least count of the screw gauge is 0.005 mm.

C. If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

D. If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge isi 0.005 mm.

Q. 10 Planck’s constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is (are)

A. M ∝ √c

B. M ∝ √G

C. L ∝ √h

D. L ∝ √G

Q. 11 Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies w₁ and w₂ and have total energies E₁ and E₂, respectively. The variations of their momenta p with positions x are shown in the figures. If a/b = n² and a/R = n, then the correct equation(s) is(are)

A. E₁w₁ = E₂w₂

B. w₂/w₁ = n²

C. w₁w₂ = n²

D. E₁/w₁ = E₂/w₂

Q. 12 A ring of mass M and radius R is rotating with angular speed w about a fixed vertical axis passing through its centre O with two point masses each of mass M/8 at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is 8w/9 and one of the masses is at a distance of 3R/5 from O. At this instant the distance of the other mass from O is

A. ⅔R

B. R/3

C. ⅗R

D. ⅘R

Q. 13 The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium then the correct statement(s) is(are)

A. Both charges execute simple harmonic motion.

B. Both charges will continue moving in the direction of their displacement.

C. Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement.

D. Charge -q executes simple harmonic motion while charge +q continues moving in the direction of its displacement.

Q. 14 Two identical glass rods S₁ and S₂ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S₁ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S₂. The distance d is

A. 60 cm

B. 70 cm

C. 80 cm

D. 90 cm

Q. 15 A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field B. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

A. If B is along z, F ∝ (L + R)

B. If B is along x, F = 0

C. If B is along y, F ∝ (L + R)

D. If B is along z, F = 0

Q. 16 A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are)

A. The average energy per mole of the gas mixture is 2RT.

B. The ratio of speed of sound in the gas mixture to that in helium gas is root of 6/5

C. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2

D. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/√2

Q. 17 In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure The electrical resistivities of Al and Fe are 2.7 x 10⁻⁸ ohm m and 1.0 x 10⁷ ohm m, respectively. The electrical resistance between the two faces P and Q of the composite bar is

A. 2475/64

B. 1875/64

C. 1875/49

D. 2475/132

Q. 18 For photo-electric effect with incident photon wavelength lambda, the stopping potential is V₀. Identify the correct variation(s) of V₀ with λ and 1/λ.

A. (A)

B. (B)

C. (C)

D. (D)

Q. 19 Match the nuclear processes given in column I with the appropriate option(s) in column II.

A. A – R,T ; B – P,S ; C – Q,T ; D – R

B. A – P,Q ; B – R,S ; C – T ; D – P

C. A – S ; B – P,T ; C – Q ; D – R

D. A – P ; B – R ; C – S,T ; D – P,Q

Q. 20 A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and U₀ are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

A. A – Q,S ; B – P,R ; C – P,T ; D – P

B. A – P,T ; B – R,S ; C – Q ; D – Q,R

C. A – P,Q,R,T ; B – Q,S ; C – P,Q,R,S ; D – P,R,T

D. A – P,T ; B – P,R ; C – S,Q ; D – T

Q. 21 The total number of sterioisomers that can exist for M is

Q. 22 The number of resonance structures for N is

Q. 23 The total number of lone pairs of electrons in N₂O₃ is

Q. 24 For the octahedral complexes of Fe³+ in SCN (thiocyanato-S) and in CN⁻ ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is

[Atomic number of Fe = 26]

Q. 25 Among the triatomic molecules/ions, BeCl₂, N₃⁻, N₂O, NO₂⁺, O₃, SCl₂, ICl₂⁻, I₃⁻ and XeF₂, the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the d-orbital(s) is

[Atomic number: S = 16, Cl = 17, I = 53 and Xe = 54]

Q. 26 Not considering the electronic spin, the degeneracy of the second excited state (n = 3) of H atom is 9, while the degeneracy of the second excited state of H⁻ is

Q. 27 All the energy released from the reaction X —-> Y, delta, G⁰ = -193 kJ mol⁻¹ is used for oxidizing M⁺ as M⁺ —-> M³⁺ + 2e⁻, E⁰ = -0.25 V. Under standard conditions, the number of moles of M⁺ oxidized when one mole of X is converted to Y is [F = 96500 C mol⁻²]

Q. 28 If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride-ammonia complex (which behaves as a strong electrolyte) is -0.0558 degrees C, the number of chloride(s) in the coordination sphere of the complex is

[Kf of water = 1.86 K kg mol⁻¹]

Q. 29 Compound(s) that on hydrogenation produce(s) optically inactive compound(s) is(are)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 30 The major product of the following reaction is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 31 In the following reaction the major product is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 32 The structure of D-(+)-glucose is given. The stricture of L-(-)-glucose is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 33 The major product of the reaction is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 34 The correct statement(s) about Cr²+ and Mn³+ is(are) [Atomic numbers of Cr = 24 and Mn = 25

A. Cr²+ is a reducing agent

B. Mn³⁺ is an oxidizing agent

C. Both Cr²+ and Mn³+ exhibit d⁴ electronic configuration

D. When Cr²+ is used as a reducing agent, the thromium ion attains d⁵ electronic

configuration

Q. 35 Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is(are)

A. Impure Cu strip is used as cathode

B. Acidified aqueous CuSO₄ is used as electrolyte

C. Pure Cu deposits at cathode

D. Impurities settle as anode-mud

Q. 36 Fe³⁺ is reduced to Fe²⁺ by using

A. H₂O₂ in presence of NaOH

B. Na₂O₂ in water

C. H₂O₂ in presence of H₂SO₄

D. Na₂O₂ in presence of H₂SO₄

Q. 37 The % yield of ammonia as a function of time in the reaction at (P, T₁) is given. If this reaction is conducted at (P, T₂) with T₂>T₁, the % yield of ammonia as a function of time is represented by

A. (A)

B. (B)

C. (C)

D. (D)

Q. 38 If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms wih m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

A. 1/2, 1/8

B. 1, 1/4

C. 1/2, 1/2

D. 1/4, 1/8

Q. 39 Match the anionic species given in Column I that are present in the ore(s) given in Column II.

Column – I Column – II

(A) Carbonate (P) Siderite

(B) Sulphide (Q) Malachite

(D) Oxide (S) Calamine (T) Argentite

A. A – P,T ; B – R ; C- T,S ; D – Q

B. A – P,Q,S ; B – T ; C – Q,R ; D – R

C. A – P,Q,S ; B – T ; C – P,R ; D – R

D. A – P,Q,S ; B – P,R ; C – S ; D – T,R

Q. 40 Match the thermodynamic processes given under column I with the expressions given under column II.

A. A – P,T ; B – Q,S ; C – S,T ; D – R

B. A – Q ; B – P,S ; C – R,T ; D – P,Q,S,T

C. A – R,T ; B – P,Q,S ; C – P,Q,S ; D – P,Q,S,T

D. A – P,S ; B-P,Q,S ; C- P,S ; D -P,Q

Q. 41 The number of distinct solutions of the equation 5/4 cos²(2x) + cos⁴x + sin⁴x + cos⁶x + sin⁶x = 2 in the interval [0, 2pi] is

Q. 42 Let the curve C be the mirror image of the parabola y² = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y = -5, then the distance between A and B is

Q. 43 The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96, is

Q. 44 Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

Q. 45 If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle (x-3)² + (y+2)² = r², then the value of r² is

Q. 46 Let f : R —> R be a function defined by

f(x) = [x], x <=2

f(x) = 0, x > 2

where [x] is the greatest integer less than or equal to x. The value of (4I – 1) is

Q. 47 A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm^3, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of V/250pi is

Q. 48 For a is an element of [0, 1/2], if F'(a) + 2 is the area of the region bounded by x = 0, y = 0, y = f(x) and x = a, then f(0) is

Q. 49 Let X and Y be two arbitrary, 3×3, non-zero, skew-symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

A. Y³Z⁴ – Z⁴Y³

B. X⁴⁴ + Y⁴⁴

C. X⁴Z³ – Z³X⁴

D. X²³ + Y²³

Q. 50 Which of the following values of a satisfy the equation

A. -4

B. 9

C. -9

D. 4

Q. 51 In R³, consider the planes P₁ : y = 0 and P₂ : x + z = 1. Let P₃ be a plane, different from P₁ and P₂, which passes through the intersection of P₁ and P₂. If the distance of the point (0, 1, 0) from P₃ is 1 and the distance of a point (a, b, c) from P₃ is 2, then which of the following relations is (are) true?

A. 2a + b + 2c + 2 = 0

B. 2a – b + 2c + 4 = 0

C. 2a + b – 2c – 10 = 0

D. 2a – b + 2c – 8 = 0

Q. 52 In R³, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P₁ : x + 2y – z + 1 = 0 and P₂ : 2x – y + z = 0. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P₁. Which of the following points lie(s) on M?

A. (0, -5/6, -2/3)

B. (-1/6, -1/3, 1/6)

C. (-5/6, 0, 1/6)

D. (-1/3, 0, 2/3)

Q. 53 Let P and Q be distinct points on the parabola y² = 2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle OPQ is 3√2, then which of the following is (are) the coordinates of P?

A. 4 , 2√2

B. 9 , 3√2

C. 1/4 , 1⁄√2

D. 1 , √2

Q. 54 Let y(x) be a solution of the differential equation (1 + eˣ)y’+ yeˣ = 1. If y(0) = 2, then which of the following statements is (are) true?

A. y(-4) = 0

B. y(-2) = 0

C. y(x) has a critical point in the interval (-1, 0)

D. y(x) has no critical point in the interval (-1, 0)

Q. 55 Consider the family of all circles whose centers lie on the straight line y = x. If this family of circles is represented by the differential equation Py” + Qy’ + 1 = 0, where P, Q are functions of x, y and y’ (here y’ = dy/dx, y” = d²y/dx²), then which of the following statements is (are) true?

A. P = y + x

B. P = y – x

C. P + Q = 1 – x + y + y’ + (y’)²

D. P – Q = x + y – y’ – (y’)²

Q. 56 Let g : R—>R be a differentiable function with g(0) = 0, g'(0) = 0 and g'(0) = 0 and g'(1) is not = 0. Let

f(x) = xg(x)/|x|, x is not = 0

f(x) = 0, x = 0

and h(x) = e^|x| for all x is element of R. Let (f . h)(x) denote f(h(x)) and (h . f)(x) denote h(f(x)). Then which of the following is (are) true?

A. f is differentiable at x = 0

B. h is differentiable at x = 0

C. f . h is differentiable at x = 0

D. h . f is differentiable at x = 0

Q. 57 Let f(x) = sin(pi/6 sin(pi/2 sinx)) for all x is element of R and g(x) = pi/2 sinx for all x element of R. Let (f . g)(x) denote f(g(x)) and (g . f)(x) denote g(f(x)). Then which of the following is (are) true?

A. Range of f is [-1/2, 1/2]

B. Range of f . g is [-1/2, 1/2]

C. lim(x—>0) f(x)/g(x) = pi/6

D. There is an x element of R such that (g . f)(x) = 1

Q. 58 Let PQR be a triangle. Let a = QR, b = RP and c = PQ. If |a| = 12, |b| = 4√3 and b.c = 24, then which of the following is (are) true?

A. |c|²/2 – |a| = 12

B. |c|²/2 + |a| = 30

C. |a x b + c x a| = 48√3

D. a.b = -72

Q. 59 Match the column

A. A – P,Q ; B – P,Q ; C – P,Q,S,T ; D – Q,T

B. A – P,S ; B – R,T ; C – S,T ; D – Q,T

C. A – R,T ; B – P,S ; C – S,T ; D – P,T

D. A – P,Q ; B – R,S ; C – S,T ; D – Q,S

Q. 60 Match the column

A. A – P,Q,T ; B – S,R ; C – P,T ; D – R

B. A – P,R,S ; B – P ; C – P,Q; D – S,T

C. A – P,T ; B – Q,R ; C – S,R ; D – R

D. A – Q,S ; B – S,T ; C – P,T D – S

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	6	2	2	7	2	3	3	7	BC	ACD
Question	11	12	13	14	15	16	17	18	19	20
Answer	BD	CD	C	B	ABC	ABD	B	AC	A	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	2	9	8	4	4	3	4	1	BD	A
Question	31	32	33	34	35	36	37	38	39	40
Answer	D	A	C	ABC	BCD	AB	B	A	B	C
Question	41	42	43	44	45	46	47	48	49	50
Answer	8	4	8	5	2	0	4	3	CD	BC
Question	51	52	53	54	55	56	57	58	59	60
Answer	BD	AB	AD	AC	BC	AD	ABC	ACD	A	B

JEE Advanced 2014 Paper II Previous Year Paper

JEE Advanced 2014 Paper 2

Q. 1 A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to scale.

A. A

B. B

C. C

D. D

Q. 2 A wire which passes through the hole in a small bead is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A. Always radially outwards

B. Always radially inwards

C. Radially outwards initially and radially inwards later

D. Radially inwards initially and radially outwards later

Q. 3 During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 Ω, as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is

A. 60 ± 0.15 Ω

B. 135 ± 0.56 Ω

C. 60 ± 0.25 Ω

D. 135 ± 0.23 Ω

Q. 4 Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively as shown in figure. If magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E₁, E₂ and E₃ respectively then

A. E₁>E₂>E₃

B. E₃>E₁>E₂

C. E₂>E₁>E₃

D. E₃>E₂>E₁

Q. 5 A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on top of the block. The refractive index of the liquid is

A. 1.21

B. 1.30

C. 1.36

D. 1.42

Q. 6 Parallel rays of light of intensity l = 912 Wm⁻² are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant σ = 5.7 x 10⁻⁸ Wm⁻² K⁻⁴ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

A. 330 K

B. 660 K

C. 990 K

D. 1550 K

Q. 7 A metal surface is illuminated by the light of two different wavelengths 248 nm and 310 nm. The maximum speed of the photoelectrons corresponding to these wavelengths is u₁ and u₂ respectively. If the ratio u₁:u₂ = 2:1 and hc = 1240 eV nm, the work function of the metal is nearly

A. 3.7 eB

B. 3.2 eV

C. 2.8 eV

D. 2.5 eV

Q. 8 If λ􀀁ᵤ is the wavelength of Kₐ X-ray line of copper (atomic number 29) and λₘₒ is the wavelength of the Kₐ X-ray line of molybdenum (atomic number 42), then the ratio λ􀀁ᵤ/λₘₒ is close to

A. 1.99

B. 2.14

C. 0.50

D. 0.48

Q. 9 A planet of radius R = 1/10 x (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $/5 on it and lower a wire of the same length and of linear mass density 10⁻³ kgm⁻¹ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 x 10⁶m and the acceleration to gravity on Earth is 10 ms⁻²)

A. 96 N

B. 108 N

C. 120 N

D. 150 N

Q. 10 A glass capillary tube is in the shape of a truncated cone with an apex angle α so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is p, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity)

A. (2S/bpg)cos (θ – α)

B. (2S/bpg)cos (θ + α)

C. (2S/bpg)cos (θ – α/2)

D. (2S/bpg)cos (θ + α/2)

Questions: 11 – 12

In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are Cᵥ – 3/2R, Cₚ = 5/2R and those for an ideal diatomic gas are Cᵥ = 5/2, Cₚ = 7/2R

Q. 11 Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

A. 550 K

B. 525 K

C. 513 K

D. 490 K

Q. 12 Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

A. 250 R

B. 200 R

C. 100 R

D. -100 R

Questions: 13 – 14

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.

Q. 13 If the piston is pushed at a speed of 5 mms⁻¹, the air comes out of the nozzle with a speed of

A. 0.1 ms⁻¹

B. 1 ms⁻¹

C. 2 ms⁻¹

D. 8 ms⁻¹

Q. 14 If the density of air is Pₐ and that of the liquid Pl, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A. √Pₐ/Pₗ

B. √PₐPₗ

C. √Pₗ/Pₐ

D. Pₗ

Questions: 15 – 16

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter-clockwise direction if seen from above.

Q. 15 When d ≈ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

A. Current in wire 1 and wire 2 is the direction PQ and RS respectively and h ≈ a

B. Current in wire 1 and wire 2 is the direction PQ and SR respectively and h ≈ a

C. Current in wire 1 and wire 2 is the direction PQ and SR respectively and h ≈ 1.2a

D. Current in wire 1 and wire 2 is the direction PQ and RS respectively and h ≈ 1.2a

Q. 16 Consider d>>a and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the current in the wires are in the opposite directions, the torque on the loop at its new positions will be (assume that the net field due to the wires is constant over the loop)

A. μ₀I²a²/d

B. μ₀I²a²/2d

C. √3 μ₀I²a²/d

D. √3 μ₀I²a²/2d

Q. 17 Four charges Q₁, Q₂, Q₃ and Q₄ of same magnitude are fixed along the x axis at x = -2a, -a, +a and +2a respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I and II and select the correct answer.

A. P-3, Q-1, R-4, S-2

B. P-4, Q-2, R-3, S-1

C. P-3, Q-1, R-2, S-4

D. P-4, Q-2, R-1, S-3

Q. 18 Four combinations of two thin lenses are given in list I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer.

A. P-1, Q-2, R-3, S-4

B. P-2, Q-4, R-3, S-1

C. P-4, Q-1, R-2, S-3

D. P-2, Q-1, R-3, S-4

Q. 19 A block of mass m₁ = 1 kg another mass m₂ = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination θ. Various values of θ are given in List I. The coefficient of friction between the block m₁ and the plane is always zero. The coefficient of static and dynamic friction between the blocks m₂ are given. Match the correct expression of the friction in List II and the angles given in List I, and choose the correction. The acceleration due to gravity is denoted by g. [Useful information: tan(5.5°) ≈ 0.1; tan(11.5°) ≈ 0.2; tan(16.5°) ≈ 0.3]

A. P-1, Q-1, R-1, S-3

B. P-2, Q-2, R-2, S-3

C. P-2, Q-2, R-2, S-4

D. P-2, Q-2, R-3, S-3

Q. 20 A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer.

A. P-2, Q-3, R-2, S-4

B. P-2, Q-3, R-1, S-4

C. P-1, Q-1, R-1, S-4

D. P-2, Q-3, R-1, S-1

Q. 21 The acidic hydrolysis of ether (X) shown below is fastest when

A. One phenyl group is replaced by a methyl group

B. One phenyl group is replaced by a para-methoxyphenyl group

C. Two phenyl groups are replaced by two para-methoxyphenyl groups

D. No structural change is made to X.

Q. 22 Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure. the correct order of their boiling point is

A. I >II>III

B. III >II>I

C. II >III>I

D. III >I>II

Q. 23 The major product in the following reaction is

A. A

B. B

C. C

D. D

Q. 24 Hydrogen peroxide in its reaction with KIO₄ and NH₂OH respectively, is acting as a

A. Reducing agent, oxidising agent

B. Reducing agent, reducing agent

C. Oxidising agent, oxidising agent

D. Oxidising agent, reducing agent

Q. 25 The product formed in the reaction SOCl₂ with white phosphorus is

A. PCl₃

B. SO₂Cl₂

C. SCl₃

D. POCl₃

Q. 26 Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is

A. 0

B. 1

C. 2

D. 3

Q. 27 For the identification of β – naphthol using dye test, it is necessary to use

A. Dichloromethane solution of β-naphthol

B. Acidic solution of β-naphthol

C. Neutral solution of β-naphthol

D. Alkaline solution of β-naphthol

Q. 28 For the elementary reaction M → N, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M I s

A. 4

B. 3

C. 2

D. 1

Q. 29 For the process H₂O (l) → H₂O (g) at T = 100°C and 1 atmosphere pressure, the correct choice is

A. ΔS.system > 0 and ΔS.surroundings > 0

B. ΔS.system > 0 and ΔS.surroundings < 0

C. ΔS.system < 0 and ΔS.surroundings > 0

D. ΔS.system < 0 and ΔS.surroundings < 0

Q. 30 Assuming 2s – 2p mixing is NOT operative, the paramagnetic species among the following is

A. Be₂

B. B₂

C. C₂

D. N₂

Questions: 31 – 32

Schemes 1 and 2 describe sequential transformation of alkynes M and N.

consider only the major products formed in each step for both the schemes.

Q. 31 The product X is

A. A

B. B

C. C

D. D

Q. 32 The correct statement with respect to product Y is

A. It gives positive Tollens test and is a functional isomer of X

B. It gives positive Tollens test and is a geometrical isomer of X

C. It gives a positive iodoform test and is a functional isomer of X

D. It gives a positive iodoform test and is a geometrical isomer of X

Questions: 33 – 34

An aqueous solution of metal ion M1 reacts separately with reagents Q and R in excess to give tetrahedral and square planar complexes, respectively. And aqueous solution of another metal ion M2 always reforms tetrahedral complexes with these reagents. Aqueous solution of M2 on reaction with reagent S gives white precipitate which dissolves in excess of S. The reactions are summarized in the figure given below.

Q. 33 M1, Q and R respectively are

A. Zn²⁺, KCN and HCl

B. Ni²⁺, HCl and KCN

C. Cd²⁺, KCN and HCl

D. Co²⁺, HCL and KCN

Q. 34 Reagent S is

A. K₄[Fe(CN)₆]

B. Na₂HPO₄

C. K₂CrO₄

D. KOH

Questions: 35 – 36

X and Y are two volatile liquids with molar weights of 10 g mol⁻¹ and 40 g mol⁻¹ respectively. two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of a tube of length L = 24 cm, as shown in the figure. The tube is filled with an inert gas at 1 atmosphere pressure and a temperature of 300 K. Vapours of X and Y react to form a product which is first observed at a distance d cm from the plug soaked in X. take X and Y to have equal molecular diameters and assume ideal behaviour of the inert gas and the two vapours.

Q. 35 The value of d in cm (shown in figures) as estimated from Graham’s law is

A. 8

B. 12

C. 16

D. 20

Q. 36 The experimental value of d is found to be smaller than the estimate obtained using Graham’s law. This is due to

A. Larger mean free path for X as compared to that of Y

B. Larger mean free path for Y as compared to that of X

C. Increased collision frequency of Y with the inert gas as compared to that of X with the inert gas

D. Increased collision frequency of X with the inert gas as compared to that of Y with the inert gas

Q. 37 Different possible thermal decomposition pathways for peroxy esters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer.

A. P-1, Q-3, R-4, S-2

B. P-2, Q-4, R-3, S-1

C. P-4, Q-1, R-2, S-3

D. P-3, Q-2, R-1, S-4

Q. 38 Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer.

A. P-1, Q-4, R-2, S-3

B. P-3, Q-1, R-4, S-2

C. P-3, Q-4, R-2, S-1

D. P-4, Q-1, R-3, S-2

Q. 39 Match each coordination compound in List I with an appropriate pair of characteristics from List __ and select the correct answer. {en = H₂NCH₂CH₂NH₂; atomic numbers: Ti = 22;

Cr = 24; Co = 27; Pt = 78}

A. P-4, Q-2, R-3, S-1

B. P-3, Q-1, R-4, S-2

C. P-2, Q-1, R-3, S-4

D. P-1, Q-3, R-4, S-2

Q. 40 Match the orbital overlap figures shown in List I with the description given in List Ii and select the correct answer.

A. P-2, Q-1, R-3, S-4

B. P-4, Q-3, R-1, S-2

C. P-2, Q-3, R-1, S-4

D. P-4, Q-1, R-3, S-2

Q. 41 The function y = f(x) is the solution of the differential equation in the image in (-1, 1) satisfying f(0) = 0. Then the value of the integral in the image is

A. π/3 – √3/2

B. π/3 – √3/4

C. π/6 – √3/4

D. π/6 – √3/2

Q. 42 The value of the integral in the image is equal to

A. A

B. B

C. C

D. D

Q. 43 Coefficient of x¹¹ in the expansion of (1 + x²)⁴(1 + x³)⁷(1 + x⁴)¹² is

A. 1051

B. 1106

C. 1113

D. 1120

Q. 44 Let f:[0, 2] → R be function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let the integral in the image, for x ϵ [0, 2]. If F’(x) = f’(x) for all x ϵ (0, 2), then F(2) equals

A. e² – 1

B. e⁴ – 1

C. e – 1

D. e⁴

Q. 45 The common tangents to the circle x² + y² = 2 and the parabola y² = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is

A. 3

B. 6

C. 9

D. 15

Q. 46 For x ϵ (0, π) the equation sin x + 2 sin 2x – sin 3x = 3 has

A. Infinitely many solutions

B. Three solutions

C. One solution

D. No solution

Q. 47 In a triangle the sum of two sides is x and the product of the same two sides is y. I f x² – c² = y, where c is the third side of the triangle, then the ratio of the in-radius to the circumradius of the triangle is

A. 3y/2x(x+c)

B. 3y/2c(x+c)

C. 3y/4x(x+c)

D. 3y/4c(x+c)

Q. 48 Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

A. 264

B. 265

C. 53

D. 67

Q. 49 Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her is

A. 1/2

B. 1/3

C. 2/3

D. 3/4

Q. 50 The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

A. Only purely imaginary roots

B. All real roots

C. Two real and two purely imaginary roots

D. Neither real nor purely imaginary roots

Questions: 51 – 52

Let a, r, s, t be nonzero real numbers. Let P(at², 2at), Q, R(ar², 2ar) and S(as², 2as) be distinct points on the parabola y² = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0).

Q. 51 The value of r is

A. -1/t

B. (t²+1)/t

C. 1/t

D. (t²-1)/t

Q. 52 If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

A. (t²+1)²/2t³

B. a(t²+1)²/2t³

C. a(t²+1)²/t³

D. a(t²+2)²/t³

Questions: 53 – 54

Given that for each a ϵ (0, 1), the equation in the image exists. Let the limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).

Q. 53 The value of g(1/2) is

A. π

B. 2π

C. π/2

D. π/4

Q. 54 The value of g’(1/2) is

A. π/2

B. π

C. -π/2

D. 0

Questions: 55 – 56

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xᵢ be the number on the card drawn from the i^th box, I = 1, 2, 3.

Q. 55 The probability that x₁ + x₂ + x₃ is odd, is

A. 29/105

B. 53/105

C. 57/105

D. 1/2

Q. 56 The probability that x₁, x₂, x₃ are in an arithmetic progression is

A. 9/105

B. 10/105

C. 11/105

D. 7/105

Q. 57 Match the elements of List I and List II.

A. P-1, Q-2, R-4, S-3

B. P-2, Q-1, R-3, S-4

C. P-1, Q-2, R-3, S-4

D. P-2, Q-1, R-4, S-3

Q. 58 P-3, Q-2, R-4, S-1

A. P-3, Q-2, R-4, S-1

B. P-2, Q-3, R-4, S-1

C. P-3, Q-2, R-1, S-4

D. P-2, Q-3, R-1, S-4

Q. 59 Match the elements of List I and List II.

A. P-4, Q-3, R-2, S-1

B. P-2, Q-4, R-3, S-1

C. P-4, Q-3, R-1, S-2

D. P-2, Q-4, R-1, S-3

Q. 60 Let f₁:R → R, f₂:[0, ∞) → R, f₃:R → R and f₄:R → [0, ∞) be defined by equations in the image. Match the elements of List I and List II.

A. P-3, Q-1, R-4, S-2

B. P-1, Q-3, R-4, S-2

C. P-3, Q-1, R-2, S-4

D. P-1, Q-3, R-2, S-4

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	D	C	C	C	A	A	B	B	D
Question	11	12	13	14	15	16	17	18	19	20
Answer	D	D	C	A	C	B	A	B	D	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	C	B	D	A	A	C	D	B	B	C
Question	31	32	33	34	35	36	37	38	39	40
Answer	A	C	B	D	C	D	A	C	B	C
Question	41	42	43	44	45	46	47	48	49	50
Answer	B	A	C	B	D	D	B	C	A	D
Question	51	52	53	54	55	56	57	58	59	60
Answer	D	B	A	D	B	C	C	D	A	D

JEE Advanced 2014 Paper I Previous Year Paper

JEE Advanced 2014 Paper 1

Q. 1 At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I₀cos(wt), with I₀ = 1A and w = 500 rad s⁻¹ starts flowing in it with the initial direction shown in the figure. At t = 7π/6w, the key is switched from B to D. Now

onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20μF, R = 10 Ω and the battery is ideal with emf of 50V, identify the correct statement(s).

A. Magnitude of the maximum charge on the capacitor before t = 7π/6w is 1×10⁻³ C.

B. The current in the left part of the circuit just before t = 7π/6w is clockwise.

C. Immediately after A is connected to D, the current in R is 10A.

D. Q = 2×10⁻³ C.

Q. 2 A light source, which emits two wavelengths λ₁ = 400 nm and λ₂ = 600 nm, is used in a Young’s double slit experiment. If recorded fringe widths for λ₁ and λ₂ are β₁ and β₂, number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then

A. β₁ > β₂

B. m₁ > m₂

C. From the central maximum, 3rd maximum of λ₂ overlaps with 5th minimum of λ₁

D. The angular separation of fringes of λ₁ is greater than λ₂

Q. 3 One end of a taut string of length 3m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms⁻¹. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

A. y(t) = A sin πx/6 cot 50πt/3

B. y(t) = A sin πx/3 cos 100πt/3

C. y(t) = A sin 5πx/6 cos 250πt/3

D. y(t) = A sin 5πx/2 cos 250πt

Q. 4 A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with di-electric in between is C₁. When the capacitor is charged, the plate area covered by the dielectric gets charge Q₁ and the rest of the area gets charge Q₂. The electric field in the dielectric is E₁ and that in the other portion is E₂. Choose the correct option(s), ignoring edge effects.

A. E₁/E₂ = 1

B. E₁/E₂ = 1/K

C. Q₁/Q₂ = 3/K

D. C₁/C₂ = 2+K/K

Q. 5 Let E₁(r), E₂(r) and E₃(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density x, and an infinite plane with uniform surface charge density d. If E₁(r₀) = E₂(r₀) = E₃(r₀) at a given distance r₀, then

A. Q = 4σπ(r₀)²

B. r₀ = x/2πσ

C. E₁(r₀/2) = 2E₂(r₀/2)

D. E₂(r₀/2) = 4E₃(r₀/2)

Q. 6 A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s⁻¹. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 + or 0.005)m, the gas in the tube is (Useful information: Root of 167RT = 640 J¹/² mole⁻¹/², √140RT = 590 J¹/² mole⁻¹/². The molar masses M in grams are given in the options. Take the values of root of 10/M for each gas as given there.)

A. Neon (M = 20, √(10/20) = 7/10)

B. Nitrogen (M = 28, √(10/28) = 3/5)

C. Oxygen (M = 32, √(10/32) = 9/16)

D. Argon (M = 36, √(10/36) = 17/32)

Q. 7 Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kg water by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40K?

A. 4 if wires are in parallel

B. 2 if wires are in series

C. 1 if wires are in series

D. 0.5 if wires are in parallel

Q. 8 In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ₁ and that between the floor and the ladder is μ₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then

A. μ₁ = 0, μ₂ ≠ 0 and N₂ tanθ = mg/2

B. μ₁ ≠ 0, μ₂ = 0 and N₁ tanθ = mg/2

C. μ₁ ≠ 0, μ₂ ≠ 0 and N₂ = mg/(1+μ₁μ₂)

D. μ₁ = 0, μ₂ ≠ 0 and N₁ tanθ = mg/2

Q. 9 A transparent thin film of uniform thickness and refractive index n₁ = 1/4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n₂ = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

A. |f₁| = 3R

B. |f₁| = 2.8R

C. |f₂| = 2R

D. |f₂| = 1.4R

Q. 10 Two ideal batteries of emf V₁ and V₂ and three resistances R₁, R₂ and R₃ are connected as shown in the figure. The current in resistance R₂ would be zero if

A. V₁ = V₂ and R₁ = R₂ = R₃

B. V₁ = V₂ and R₁ = 2R₂ = R₃

C. V₁ = 2V₂ and 2R₁ =2 R₂ = R₃

D. 2V₁ = V₂ and 2R₁ = R₂ = R₃

Q. 11 Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 degrees and 60 degrees with respect to the horizontal respectively as shown in the figure. The speed of A is 100√3 m/2. At time t = 0 s, an observer in A finds B at a distance of 500m. This observer sees B moving with a constant velocity perpendicular to the line of motion of

A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is

Q. 12 During Searle’s experiment, zero of the Vernier scale lies between 3.20 x 10⁻² m and 3.25 x 10⁻² m of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 x 10⁻² m and 3.25 x 10⁻² m of the main scale but now the 45th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 x 10⁻⁷ m². The least count of the Vernier scale is 1.0 x 10⁻⁵ m. The maximum percentage error in the Young’s modulus of the wire is

Q. 13 A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s⁻¹ is

Q. 14 Two parallel wires in the plane of the paper are distance X₀ apart. A point charge is moving with speed u between the wires at a distance X₁ from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R₁. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R₂. If X₀/X₁ = 3, the value of R₁/R₂ is

Q. 15 To find the distance d over which a signal can be seen clearly in foggy conditions, a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density p of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S¹/ⁿ. The value of n is

Q. 16 A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 ohm resistance, it can be converted into a voltmeter of range 0 – 30 V. If connected to a 2n/249 ohm resistance, it becomes an ammeter of range 0 – 1.5 A. The value of n is

Q. 17 Consider an elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ = 4m. A block of mass 1kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n x 10) Joules. The value of n is (take acceleration due to gravity = 10 m/s⁻²)

Q. 18 A rocket is moving in a gravity free space with a constant acceleration of 2 m/s² along +x direction (see figure). The length of a chamber inside the rocket is 4m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.2 m/s from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Q. 19 A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 m/s with respect to the ground. The rotational speed of the platform in rad/s after the balls leave the platform is

Q. 20 A thermodynamic system is taken from an initial state i with internal energy Uᵢ = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Wₐ􀀁 = 200 J, Wᵢᵦ= 50 J and Wᵦ􀀁 = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qᵢₐ􀀁, Qᵢᵦ and Qᵦ􀀁 respectively. If the internal energy of the system in the state b is Uᵦ = 200 J and Qᵢₐ􀀁 = 500 J, the ratio Qᵦ􀀁/Qᵢᵦ is

Q. 21 The correct combination of names for isomeric alcohols with molecular formula C₄H₁₀O is/are

A. tert-butanol and 2-methylpropan-2-ol

B. tert-butanol and 1, 1=dimethylethan-1-ol

C. n-butanol and butan-1-ol

D. isobutyl alcohol and 2-methylpropan-1-ol

Q. 22 The reactivity of compound Z with different halogens under appropriate conditions is given. The observed pattern of electrophilic substitution can be explained by

A. the steric effect of the halogen

B. the steric effect of the tert-butyl group

C. the electronic effect of the phenolic group

D. the electronic effect of the tert-butyl group

Q. 23 In the reaction shown, the major product(s) formed is/are

A. (A)

B. (B)

C. (C)

D. (D)

Q. 24 An ideal gas in a thermally insulated vessel at internal pressure = P₁, volume – V₁ and absolute temperature = T₁ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P₂, V₂ and T₂, respectively. For this expansion,

A. q = 0

B. T₂ = T₁

C. P₂V₂ = P₁V₁

D. P₂V₂ʸ = P₁V₁ʸ

Q. 25 Hydrogen bonding plays a central role in the following phenomena:

A. Ice floats in water

B. Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions

C. Formic acid is more acidic than acetic acid

D. Dimerisation of acetic acid in benzene

Q. 26 In a galvanic cell, the salt bridge

A. does not participate chemically in the cell reaction.

B. stops the diffusion of ions from one electrode to another.

C. is necessary for the occurrence of the cell reaction.

D. ensures mixing of the two electrolytic solutions.

Q. 27 Upon heating with Cu₂S, the reagent(s) that give copper metal is/are

A. CuFeS₂

B. CuO

C. Cu₂O

D. CuSO₄

Q. 28 The correct statement(s) for orthoboric acid is/are

A. It behaves as a weak acid in water due to self ionization.

B. Acidity of its aqueous solution increases upon addition of ethylene glycol.

C. It has a three dimensional structure due to hydrogen bonding.

D. It is a weak electrolyte in water.

Q. 29 For the reaction:

I⁻ + ClO₃⁻ + H₂SO₄ —–> Cl⁻ + H₂SO₄⁻ + I₂

The correct statement(s) in the balanced equation is/are:

A. Stoichiometric coefficient of HSO₄⁻ is 6.

B. Iodide is oxidized.

C. Sulphur is reduced.

D. H₂O is one of the products.

Q. 30 The pair(s) of reagents that yield paramagnetic species is/are

A. Na and excess of NH₃

B. K and excess of O₂

C. Cu and dilute HNO₃

D. O₂ and 2-ethylanthraquinol

Q. 31 Consider all possible isometric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are

Q. 32 A list of species having the formula XZ₄ is given below.

XeF₄, SF₄, SiF₄, BF₄⁻, BrF₄⁻, [Cu(NH₃)₄]²⁺, [FeCl₄]²⁻, [CoCl₄]²⁻ and [PtCl4]²⁻ Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is

Q. 33 Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi₂S₃ and SnS₂, the total number of BLACK coloured sulfides is

Q. 34 The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are)

Q. 35 Consider the following list of reagents:

Acidified K₂Cr₂O₇, alkaline KMnO₄, CuSO₄, H₂O₂, Cl₂, O₃, FeCl₃, HNO₃ and Na₂S₂O₃. The total number of reagents that can oxidise aqueous iodide to iodine is

Q. 36 The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown is

Q. 37 In an atom, the total number of electrons having quantum numbers n = 4, |mₗ| = 1 and mₛ = -1/2 is

Q. 38 If the value of Avogadro number is 6.023 x 10²³ mol⁻¹ and the value of Boltzmann constant is 1.380 x 10⁻²³ J/K, then the number of significant digits in the calculated value of the universal gas constant is

Q. 39 A compound H₂X with molar weight of 80 g is dissolved in a solvent having density of 0.4 g ml⁻¹. Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

Q. 40 MX₂ dissociates into M²⁺ and X⁻ ions in an aqueous solution, with a degree of dissociation (alpha) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is

Q. 41 Let M and N be two 3×3 matrices such that MN = NM. Further, if M ≠ N² and M² = N⁴, then

A. determinant of (M² + MN²) is 0

B. there is a 3×3 non-zero matrix U such that (M² + MN²)U is the zero matrix

C. determinant of (M² + MN²) ≥ 1

D. for a 3×3 matrix U, if (M² + MN²) U equals the zero matrix then U is the zero matrix

Q. 42 For every pair of continuous functions f, g:[0, 1] —> ℝ such that max {f(x): x ∈ [0, 1]} = max{g(x):x is ∈ [0, 1]}, the correct statement(s) is (are):

A. (f(c))² + 3f(c) = (g(c))² + 3g(c) for some c ∈ [0, 1]

B. (f(c))² + f(c) = (g(c))² + 3g(c) for some c ∈ [0, 1]

C. (f(c))² + 3f(c) = (g(c))² + g(c) for some c ∈ [0, 1]

D. (f(c))² = (g(c))² for some c ∈ [0, 1]

Q. 43 f:(0, infinity) —-> ℝ is given. Then

A. f(x) is monotonically increasing on [1, ∞ )

B. f(x) is monotonically decreasing on (0, 1)

C. f(x) + f(1/x) = 0, for all x ∈ (0, ∞)

D. f(2ˣ) is an odd function of x on ℝ

Q. 44 Let a is an element of ℝ and let f: ℝ —-> ℝ be given by f(x) = x⁵ – 5x + a. Then

A. f(x) has three real roots if a > 4

B. f(x) has only one real root if a > 4

C. f(x) has three real roots if a < -4

D. f(x) has three real roots is -4 < a < 4

Q. 45 Let f:[a, b] —> [1, infinity) be a continuous function and let g : ℝ—> ℝbe defined as Then

A. g(x) is continuous but not differentiable at a

B. g(x) is differentiable on ℝ

C. g(x) is continuous but not differentiable at b

D. g(x) is continuous and differentiable at either a or b but not both

Q. 46 Let f:(-π/2, π/2) —-> ℝ be given by f(x) = (log(secx + tanx))³ Then

A. f(x) is an odd function

B. f(x) is a one-one function

C. f(x) is an onto function

D. f(x) is an even function

Q. 47 From a point P(λ, λ, λ) perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that angle QPR is a right angle, then the possible value(s) of λ is (are)

A. √2

B. 1

C. -1

D. – √ 2

Q. 48 Let x, y and z be three vectors each of magnitude √2 and the angle between each pair of them is π⁄ 3. If a is a nonzero vector perpendicular to x and yxz and b is a nonzero vector perpendicular to y and z × x, then

A. b = (b.z)(z-x)

B. a = (a.y)(y-z)

C. a.b = -(a.y)(b.z)

D. a = (a.y)(z-y)

Q. 49 A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)² + y² = 16 and x² + y² = 1. Then

A. radius of S is 8

B. radius of S is 7

C. centre of S is (-7, 1)

D. centre of S is (-8, 1)

Q. 50 Let M be a 2×2 symmetric matrix with integer entries. Then M is invertible is

A. the first column of M is the transpose of the second row of M

B. the second row of M is the transpose of the first column of M

C. M is a diagonal matrix with nonzero entries in the main diagonal

D. the product of entries in the main diagonal of M is not the square of an integer

Q. 51 Let a, b, c be positive integers such that b/a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b+2, then the value of a² + a – 14/a+1 is

Q. 52 Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is

Q. 53 Let n₁ < n₂ < n₃ < n₄ < n₅ be positive integers such that n₁ + n₂ + n₃ + n₄ + n₅ = 20. Then the number of such distinct arrangements (n₁, n₂, n₃, n₄, n₅) is

Q. 54 Let f : ℝ—> ℝ and g : ℝ—> ℝ be respectively given by f(x) = |x| + 1 and g(x) = x² + 1. Define h :

ℝ—> ℝ by

h(x) = max{f(x), g(x)} if x <= 0,

h(x) = min{f(x), g(x)} if x > 0.

The number of points at which h(x) is not differentiable is

Q. 55 The value of the given integral is

014x3d2dx2(1-x2)5dx

Q. 56 The slope of the tangent to the curve (y-x⁵)² = x(1+x²)² at the point (1, 3) is

Q. 57 The largest value of the nonnegative integer a for which the given condition applies is

Q. 58 Let f:[0, 4π] —> [0, π] be defined by f(x) = cos⁻¹(cosx). The number of points x ∈ [0, 4π] satisfying the equation f(x) = 10-x/10 is

Q. 59 For a point P in the plane, let d₁(P) and d₂(P) be the distances of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d₁(P) + d₂(P) ≤ 4, is

Q. 60 Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If axb + bxc = pa + qb + rc, where p, q and r are scalars, then the value of (p² + 2q² + r²)/q² is

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	CD	ABC	ACD	AD	C	D	BD	CD	AC	ABD
Question	11	12	13	14	15	16	17	18	19	20
Answer	5	4	2	3	3	5	4	2 OR8	4	2
Question	21	22	23	24	25	26	27	28	29	30
Answer	ACD	ABC	A	ABC	ABD	AC	BCD	BD	ABD	ABC
Question	31	32	33	34	35	36	37	38	39	40
Answer	5	4	6 OR 7	3	7	1	6	4	8	2
Question	41	42	43	44	45	46	47	48	49	50
Answer	AB	AD	ACD	BD	AC	ABC	C	ABC	BC	CD
Question	51	52	53	54	55	56	57	58	59	60
Answer	4	5	7	3	2	8	0	3	6	4

JEE Advanced 2013 Paper II Previous Year Paper

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
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

JEE Advanced 2013 Paper I Previous Year Paper

JEE Advanced 2013 Paper 1

Q. 1 The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A. 5.112 cm

B. 5.124 cm

C. 5.136 cm

D. 5.148 cm

Q. 2 A ray of light travelling in the direction (1/2)(î + √3ĵ) is incident on a plane mirror. After reflection, it travels along the direction (1/2)(î – √3ĵ). The angle of incidence is

A. 30°

B. 45°

C. 60°

D. 75°

Q. 3 In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

A. A

B. B

C. C

D. D

Q. 4 Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

A. 1 : 4

B. 1 : 2

C. 6 : 9

D. 8 : 9

Q. 5 Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity K and the other 2K. The temperature difference between the ends along the xaxis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

A. 2.0 s

B. 3.0 s

C. 4.5 s

D. 6.0 s

Q. 6 A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 x 10⁸ m/s. The final momentum of the object is

A. 0.3 x 10⁻¹⁷ kg m/s

B. 1.0 x 10⁻¹⁷ kg m/s

C. 3.0 x 10⁻¹⁷ kg m/s

D. 9.0 x 10⁻¹⁷ kg m/s

Q. 7 A particle of mass m is projected from the ground with an initial speed uo at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed uo. The angle that the composite system makes with the horizontal immediately after the collision is

A. π/4

B. π/4 + α

C. π/2 – α

D. π/2

Q. 8 The work done on a particle of mass m by a force (given in the image, K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is

A. 2Kπ/a

B. Kπ/a

C. Kπ/2a

D. 0

Q. 9 One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

A. 0.25

B. 0.50

C. 2.00

D. 4.00

Q. 10 The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is ⅔ times the wavelength in free space. The radius of the curved surface

A. 1 m

B. 2 m

C. 3 m

D. 6 m

Q. 11 A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m⁻¹) x] cos [(628 s⁻¹) t]. Assuming π= 3.14, the correct statement(s) is (are)

A. The number of nodes is 5.

B. The length of the string is 0.25 m.

C. The maximum displacement of the midpoint of the string, from its equilibrium

position is 0.01 m.

D. The fundamental frequency is 100 Hz.

Q. 12 A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)

A. A

B. B

C. C

D. D

Q. 13 A particle of mass M and positive charge Q, moving with a constant velocity u̅1 = 4î m/s enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity u̅2 = 2(√3î + ĵ) m/s. The correct statement(s) is (are)

A. The direction of the magnetic field is -z direction.

B. The direction of the magnetic field is +z direction.

C. The magnitude of the magnetic field is 50πM/3Q units

D. The magnitude of the magnetic field is 100πM/3Q units

Q. 14 Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ₁ and ρ₂ respectively, touch each other. The net electric field at a distance 2R from the center of the smaller sphere, along with the line joining the centers of the spheres, is zero. The ratio ρ₁/ρ₂ can be

A. -4

B. -32/25

C. 32/25

D. 4

Q. 15 In the circuit shown in the figure, there are two parallel plate capacitors each of

capacitance C. The switch S₁ is pressed first to fully charge the capacitor C₁ and then released. The switch S₂ is then pressed to charge the capacitor C₂. After some time, S₂ is released and then S₃ is pressed. After some time,

A. the charge on the upper plate of C₁ is 2CV0.

B. the charge on the upper plate of C₁ is CV0.

C. the charge on the upper plate of C₂ is 0.

D. the charge on the upper plate of C₂ is -CV0.

Q. 16 The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is

Q. 17 A freshly prepared sample of a radioisotope of half-life 1386 s has activity 10³ disintegrations per second. Given that In 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after

preparation of the sample is

Q. 18 A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms-1) of the particle is zero, the speed (in m/s) after 5 s is

Q. 19 A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-I about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad/s) of the system is

Q. 20 A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is

Q. 21 The compound that does NOT liberate CO₂, on treatment with aqueous sodium

bicarbonate solution, is

A. Benzoic acid

B. Benzenesulphonic acid

C. Salicylic acid

D. Carbolic acid (Phenol)

Q. 22 Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

A. NO

B. NO₂

C. N₂O

D. N₂O₄

Q. 23 Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 °C. For this process, the correct statement is

A. The adsorption requires activation at 25 °C.

B. The adsorption is accompanied by a decrease in enthalpy.

C. The adsorption increases with increase of temperature.

D. The adsorption is irreversible.

Q. 24 Sulfide ores are common for the metals

A. Ag, Cu and Pb

B. Ag, Cu and Sn

C. Ag, Mg and Pb

D. Al, Cu and Pb

Q. 25 The arrangement of X- ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X- is 250 pm, the radius of A⁺ is

A. 104 pm

B. 125 pm

C. 183 pm

D. 57 pm

Q. 26 Upon treatment with ammoniacal H₂S, the metal ion that precipitates as a sulfide is

A. Fe(III)

B. Al(III)

C. Mg(II)

D. Zn(II)

Q. 27 The standard enthalpies of formation of CO₂(g), H₂0(l) and glucose(s) at 25 °C are -400 kJ/mol, -300 kJ/mol and -1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25 °C is

A. + 2900 kJ

B. – 2900 kJ

C. – 16.11 kJ

D. + 16.11 kJ

Q. 28 Consider the following complex ions, P, Q and R.

The correct order of the complex ions, according to their spin-only magnetic moment

values (in B.M.) is

A. R<Q<P

B. Q<R<P

C. R<P<Q

D. Q<P<R

Q. 29 In the reaction,

P + Q → R + S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The

concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

A. 2

B. 0

C. 3

D. 1

Q. 30 KI in acetone, undergoes SN₂ reaction with each of P, Q, R and S. The rates of the reaction vary as

A. P>Q>R>S

B. S>P>R>Q

C. P>R>Q>S

D. R>P>S>Q

Q. 31 The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

A. A

B. B

C. C

D. D

Q. 32 Among P, Q, R and S, the aromatic compound(s) is/are

A. P

B. Q

C. R

D. S

Q. 33 The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

A. A

B. B

C. C

D. D

Q. 34 Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are)

A. A

B. B

C. C

D. D

Q. 35 The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100 th of that of a strong acid (HX, 1M), at 25 °C. The kₐ of HA is

A. 1 x 10⁻⁴

B. 1 x 10⁻⁵

C. 1 x 10⁻⁶

D. 1 x 10⁻³

Q. 36 The total number of carboxylic acid groups in the product P is

Q. 37 A tetrapeptide has —COON group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with —NH₂ group attached to a chiral center is

Q. 38 EDTA⁴⁻ is ethylenediaminetetraacetate ion. The total number of N-Co-O bond angles in [Co(EDTA)]¹⁻ complex ion is

Q. 39 The total number of lone-pairs of electrons in melamine is

Q. 40 The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at -73 °C is “M” times that of the de Broglie wavelength of Ne at 727 °C. M is

Q. 41 Pick the correct option:

A. 1/√2

B. 1/2

C. 1/√7

D. 1/3

Q. 42 Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then the probability that the problem is solved correctly by at least one of them is

A. 235/236

B. 21/256

C. 3/256

D. 253/256

Q. 43 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 44 The number of points in (-∞, ∞), for which x² – x sinx – cosx = 0, is

A. 6

B. 4

C. 2

D. 0

Q. 45 The area enclosed by the curves y = sin x + cos x and y = |cos x – sin x| over the interval [0 , π/2] is

A. 4(√2 – 1)

B. 2√2 (√2 – 1)

C. 2(√2 + 1)

D. 2√2 (√2 + 1)

Q. 46 A curve passes through the point (1, π/6). Let the slope of the curve at each point (x, y) be y/x + sec(y/x), x > 0. Then the equation of the curve is

A. A

B. B

C. C

D. D

Q. 47 Choose the correct option:

A. 23/25

B. 25/23

C. 23/24

D. 24/23

Q. 48 For a> b> c> 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2√2 . Then

A. a + b – c > 0

B. a – b + c < 0

C. a – b + c > 0

D. a + b – c < 0

Q. 49 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 50 Let P̅R̅ = 3î + ĵ -2k̂ and S̅Q̅ = î – 3ĵ -4k̂ determine diagonals of a parallelogram PQRS and P̅T̅ = î + 2ĵ + 3k̂ be another vector. Then the volume of the parallelepiped determined by the vectors PT , PQ and PS is

A. 5

B. 20

C. 10

D. 30

Q. 51 Choose the correct option:

A. 1056

B. 1088

C. 1120

D. 1332

Q. 52 For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?

A. A

B. B

C. C

D. D

Q. 53 Let f (x) = x sin πx, x > 0 . Then for all natural numbers n, f'(x) vanishes at

A. a unique point in the interval (n, n + 1/2)

B. a unique point in the interval (n + 1/2, n + 1)

C. a unique point in the interval (n, n + 1)

D. two points in the interval (n, n + 1)

Q. 54 A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

A. 24

B. 32

C. 45

D. 60

Q. 55 A line l passing through the origin is perpendicular to the lines Then, the coordinate(s) of the point(s) on l2, at a distance of √17 from the point of intersection of l and l₁ is (are)

A. (7/3, 7/3, 5/3)

B. (-1, -1, 0)

C. (1, 1, 1)

D. (7/9, 7/9, 8/9)

Q. 56 The coefficients of three consecutive terms of (1+x)ⁿ⁺⁵ are in the ratio 5: 10: 14. Then n =

Q. 57 A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k – 20 =

Q. 58 Of the three independent events E₁, E₂, and E₃, the probability that only E₁ occurs is α, only E₂ occurs is β and only E₃ occurs is γ. Let the probability p that none of the events E₁, E₂ or E₃ occurs to satisfy the equations (α – 2β)p = αβ and (β – 3γ)p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

Q. 59 A vertical line passing through the point (h, 0) intersects the ellipse x²/4 + y²/3 = 1 at the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R.

Q. 60 Consider the set of eight vectors (given in the image). Three non-coplanar vectors can be chosen from V in 2ᵖ ways. Then p is

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	A	B	D	A	B	A	D	C	C
Question	11	12	13	14	15	16	17	18	19	20
Answer	BC	AD	AC	BD	BD	1	4	5	8	5
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	B	B	A	A	D	C	B	D	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	BD	ABCD	A	BCD	A	2	4	8	6	5
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	A	D	C	B	A	B	AC	D	C
Question	51	52	53	54	55	56	57	58	59	60
Answer	AD	CD	BC	AC	BD	6	5	6	9	5