JEE Advanced 2010 Paper 1
Q. 1 The correct structure of ethylenediaminetetraacetic acid (EDTA) among the structures (A), (B), (C), (D) is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 2 The ionization isomer of [Cr(H₂O)₄Cl(NO₂)]Cl is
A. [Cr(H₂O)₄(O₂N)]Cl₂
B. [Cr(H₂O)₄Cl₂](NO₂)
C. [Cr(H₂O)₄Cl(ONO)]Cl
D. [Cr(H2O)4Cl2(NO2)] . H2O
Q. 3 The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are
A. BrCH₂CH₂CH₂CH₂CH₃ and CH₃CH₃C ≡ CH
B. BrCH₂CH₂CH₃ and CH₃CH₂CH₂C ≡ CH
C. BrCH₂CH₂CH₂CH₂CH₃ and CH₃C ≡ CH
D. BrCH₂CH₂CH₂CH₃ and CH₃CH₂C ≡ CH
Q. 4 The correct statement about the disaccharide shown in figure (1) is
A. Ring (a) is pyranose with α – glycosidic link
B. Ring (a) is furanose with α – glycosidic link
C. Ring (b) is furanose with α – glycosidic link
D. Ring (b) is pyranose with β- glycosidic link
Q. 5 In the reaction given in figure (1) , the products among (A), (B), (C), (D) are
A. (A)
B. (B)
C. (C)
D. (D)
Q. 6 Plots showing the variation of the rate constant (k) with temperature (T) are given in (A), (B), (C), (D). The plot that follows Arrhenius equation is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 7 The species which by definition has ZERO standard molar enthalpy of formation at 298 K is
A. Br₂ (g)
B. Cl₂ (g)
C. H₂O (g)
D. CH₄ (g)
Q. 8 The bond energy (in kcal mol⁻¹) of a C-C single bond is approximately
A. 1
B. 10
C. 100
D. 1000
Q. 9 The reagent(s) used for softening the temporary hardness of water is(are)
A. Ca₃(PO₄)₂
B. Ca(OH)₂
C. Na₂CO₃
D. NaOCl
Q. 10 In the reaction given in figure (1), the intermediate(s) among (A), (B), (C), (D) is(are)
A. (A)
B. (B)
C. (C)
D. (D)
Q. 11 In the Newman projection for 2, 2-dimethybutane given in figure (1), X and Y can respectively be
A. H and H
B. H and C₂H₅
C. C₂H₅ and H
D. CH₃ and CH₃
Q. 12 Among the following, the intensive property is (properties are)
A. molar conductivity
B. electromotive force
C. resistance
D. heat capacity
Q. 13 Aqueous solutions of HNO₃, KOH, CH₃COOH, and CH₃COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)
A. HNO₃ and CH₃COOH
B. KOH and CH₃COONa
C. HNO₃ and CH₃COONa
D. CH₃COOH and CH₃COONa
Questions: 14 – 16
Copper is the most noble of the first row transition metals and occur in small deposits in several countries. Ores of copper include chalcanthite (CuSO₄ . 5H₂O), atacamite (Cu₂Cl(OH)₃), Cuprite (Cu₂O), copper glance (Cu₂S) and malachite (Cu₂(OH)₂CO₃). However, 80% of the world copper production comes from the ore chalcopyrite (CuFeS₂). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.
Q. 14 Partial roasting of chalcopyrite produces
A. Cu₂S and FeO
B. Cu₂O and FeO
C. CuS and Fe₂O₃
D. Cu₂O and Fe₂O3₃
Q. 15 Iron is removed from chalcopyrite is
A. FeO
B. FeS
C. Fe₂O₃
D. FeSiO₃
Q. 16 In self-reduction, the reducing species is
A. S
B. O²⁻
C. S²⁻
D. SO₂
Questions: 17 – 18
The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in higher processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:
M(s) | M⁺(aq; 0.05 molar) || M⁺(aq; 1 molar) | M(s) For the above electrolytic cell the magnitude of the cell potential |E Cell| = 70 mV
Q. 17 For the above cell
A. E cell < 0; ΔG > 0
B. E cell > 0; ΔG < 0
C. E cell < 0; ΔG⁰ > 0
D. E cell > 0; ΔG⁰ < 0
Q. 18 If the 0.05 molar solution of M⁺ is replaced by a 0.0025 molar M⁺ solution, then the magnitude of the cell potential would be
A. 35 mV
B. 70 mV
C. 140 mV
D. 700 mV
Q. 19 The total number of basic groups in the following form of lysine given in figure is
Q. 20 The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C₄H₆ is
Q. 21 In the figure given , the total number of intramolecular aldol condensation products formed from ‘Y’ is
Q. 22 Amongst the following compounds given in figure (1), the total number of compounds soluble in aqueous NaOH is
Q. 23 Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is
KCN, K₂SO₄, (NH₄)2C₂O₄, NaCl, Zn(NO₃)₂, FeCl₃, K₂CO₃, NH₄NO₃, LiCN
Q. 24 Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF₅ is
Q. 25 The value of n in the molecular formula BenAl₂Si₆O₁₈ is
Q. 26 A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL and 25.0 mL. The number of significant figures in the average titre value is
Q. 27 The concentration of R in the reaction R → P was measured as a function of time and the following data is obtained given in figure . The order of the reaction is
Q. 28 The number of neutrons emitted when ²³⁵₉₂U undergoes controlled nuclear fission to ¹⁴²₅₄Xe and ⁹⁰₃₈Sr is
Q. 29 If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression a/c sin2C + c/a sin 2A is
A. 1/2
B. √3/2
C. 1
D. √3
Q. 30 Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is
A. x + 2y – 2z = 0
B. 3x + 2y – 2z = 0
C. x – 2y + z = 0
D. 5x + 2y – 4z = 0
Q. 31 Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that ωʳ₁ + ωʳ₂ + ωʳ₃ = 0 is
A. 1/18
B. 1/9
C. 2/9
D. 1/36
Q. 32 Let P, Q, R and S be the points on the plane with position vectors -2î – ĵ, 4î, 3î + 3ĵ and -3î + 2ĵ respectively. The quadrilateral PQRS must be a
A. parallelogram, which is neither a rhombus nor a rectangle
B. square
C. rectangle, but not a square
D. rhombus, but not a square
Q. 33 The number of 3 x 3 matrices A (given in figure ), whose entries are either 0 and 1 and for which the system A has exactly two distinct solutions, is
A. 0
B. 2⁹ – 1
C. 168
D. 2
Q. 34 Find the value of the equation given in figure (1).
A. 0
B. 1/12
C. 1/24
D. 1/64
Q. 35 Let p and q be real numbers such that p ≠ 0, p³ ≠ q and p³ ≠ -q. If α and β are nonzero complex numbers satisfying α + β = -p and α³ + β³ = q, then a quadratic equation having α/β and β/α as its roots is
A. (p³ + q)x² – (p³ + 2q)x + (p³ + q) = 0
B. (p³ + q)x² – (p³ – 2q)x + (p³ + q) = 0
C. (p³ – q)x² – (5p³ – 2q)x + (p³ – q) = 0
D. (p³ – q)x² – (5p³ + 2q)x + (p³ – q) = 0
Q. 36 Let f, g and h be real – valued functions defined on the interval [0, 1] by f(x) = e^x^2 + e^-x^2, g(x) = xe^x^2 + e^-x^2 and h(x) = x^2e^-x^2 + e^-x^2. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then
A. a = b and c ≠ b
B. a = c and a ≠ b
C. a ≠ b and c ≠ b
D. a = b = c
Q. 37 Let A and B be two distinct points on the parabola y² = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be
A. -1/r
B. 1/r
C. 2/r
D. -2/r
Q. 38 Let ABC be a triangle such that ∠ACB = π/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x² + x + 1, b = x² – 1 and c = 2x + 1 is (are)
A. -(2 + √3)
B. 1 + √3
C. 2 + √3
D. 4√3
Q. 39 Let z₁ and z₂ be two distinct complex numbers and let z = (1 – t)z₁ + tz₂ for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then which is the correct option among (A), (B), (C), (D)
A. (A)
B. (B)
C. (C)
D. (D)
Q. 40 Let f be a real-valued function defined on the interval (0, ∞) by f(x) given in figure (1). Then which of the following statement(s) is (are) true?
A. f”(x) exists for all x ∈ (0, ∞)
B. f'(x) exists for all x ∈ (0, ∞) and f’ is continuous on (0, ∞), but not differentiable on (0, ∞)
C. there exists α > 1 such that |f'(x)| < |f(x)| for all x ∈ (0, ∞)
D. there exists β > 1 such that |f(x)| + |f'(x)| ≤ β for all x ∈ (0, ∞)
Q. 41 Find the value(s) of the equation given in figure (1):
A. 22/7 – π
B. 2/105
C. 0
D. 71/15 – 3π/2
Questions: 42 – 44
Let p be an odd prime number and Tp be the following set of 2 x 2 matrices (given in figure (1):
Q. 42 The number of A in Tp such that A is either symmetric or skew – symmetric or both, and det (A) divisible by p is
A. (p – 1)²
B. 2 (p – 1)
C. (p-1)² + 1
D. 2p – 1
Q. 43 The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is
[NOTE: The trace of a matrix is the sum of its diagonal entries.]
A. (p – 1)(p² – p + 1)
B. p³ – (p – 1)²
C. (p – 1)²
D. (p – 1)(p² – 2)
Q. 44 The number of A in Tp such that det (A) is not divisible by p is
A. 2p³
B. p³ – 5p
C. p³ – 3p
D. p³ – p²
Questions: 45 – 46
The circle x² + y² – 8x = 0 and hyperbola x²/⁹ – y²/⁴ = 1 intersect at the points A and B.
Q. 45 Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
A. 2x – √5y – 20 = 0
B. 2x – √5y + 4 = 0
C. 3x – 4y + 8 = 0
D. 4x – 3y + 4 = 0
Q. 46 Equation of the circle with AB as its diameter is
A. x² + y² – 12x + 24 = 0
B. x² + y² + 12x + 24 = 0
C. x² + y² + 24x – 12 = 0
D. x² + y² – 12x – 24 = 0
Q. 47 The number of values of θ in the interval (-π/2, π/2) such that θ ≠ nπ/5 for n = 0, ±1, ±2 and tanθ = cot5θ as well as sin 2θ = cos 4θ is
Q. 48 The maximum value of the expression 1 / (sin²θ + 3sinθcosθ + 5cos²θ) is
Q. 49 If a⃗ and b⃗ are vectors in space given by a⃗ = î – 2ĵ/√5 and b⃗ = 2î + ĵ + 3k̂/√14, then the value of (2a⃗ + b⃗) . [(a⃗ x b⃗) x (a⃗ – 2b⃗)] is
Q. 50 The line 2x + y = 1 is tangent to the hyperbola x²/a² – y²/b² = 1. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is
Q. 51 If the distance between the plane Ax – 2y + z = d and the plane containing the lines x-1/2 = y- 2/3 = z-3/4 and x-2/3 = y-3/4 = z-4/5 is √6, then |d| is
Q. 52 For any real number x, let |x| denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x – [x], if [x] is odd, 1 + [x] – x, if [x] is even. Then the value of the equation given in figure (1)
Q. 53 Let ω be the complex number cos 2π/3 + i sin 2π/3. Then the number of distinct complex numbers z satisfying the determinant given in figure (1), is equal to
Q. 54 Let Sk, k = 1, 2, …….., 100, denote the sum of the infinite geometric series whose first term is k-1/k! and the common ratio is 1/k. Then find the value of the equation given in figure (1)
Q. 55 The number of all possible values of θ, where 0 < θ < π, for which the system of equations (y + z) cos 3θ = (xyz) sin 3θ
x sin 3θ = 2 cos 3θ/y + 2 sin 3θ/z
(xyz) sin 3θ = (y + 2z) cos 3θ + y sin 3θ
have a solution (xo, yo, zo) with yo zo ≠ 0, is
Q. 56 Let f be a real – valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to
Q. 57 Consider a thin square sheet of side L and thickness t, made of a material of resistivity ρ. The resistance between two opposite faces, shown by the shaded areas in the figure (1) is
A. directly proportional to L
B. directly proportional to t
C. independent of L
D. independent of t
Q. 58 A real gas behaves like an ideal gas if its
A. pressure and temperature are both high
B. pressure and temperature are both low
C. pressure is high and temperature is low
D. pressure is low and temperature is high
Q. 59 Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100W, 60W and 40W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀, respectively, the relation between these resistances is
A. 1/R₁₀₀ = 1/R₄₀ + 1/R₆₀
B. R₁₀₀ = R₄₀ = R₆₀
C. R₁₀₀ > R₆₀ > R₄₀
D. 1/R₁₀₀ > 1/R₆₀ > 1/R₄₀
Q. 60 To verify Ohm’s law, a student is provided with a test resistor RT, a high resistance R₁, a small resistance R₂, two identical galvanometers G₁ and G₂, and a variable voltage source V. The correct circuit to carry out the experiment among figure (A), (B), (C), (D) is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 61 An AC voltage source of variable angular frequency ω and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased
A. the bulb glows dimmer
B. the bulb glows brighter
C. total impedance of the circuit is unchanged
D. total impedance of the circuit increases
Q. 62 A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of circle. The tension in the wire is
A. IBL
B. IBL/π
C. IBL/2π
D. IBL/4π
Q. 63 A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg(sinθ – μ cosθ) to P₂ = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like
A. (A)
B. (B)
C. (C)
D. (D)
Q. 64 A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
A. 2GM/7R (4√2 – 5)
B. -2GM/7R (4√2 – 5)
C. GM/4R
D. 2GM/5R (√2-1)
Q. 65 A few electric field lines for a system of two charges Q₁ and Q₂ fixed at two different points on the x-axis are shown in the figure . These lines suggest
A. |Q₁| > |Q₂|
B. |Q₁| < |Q₂|
C. at a finite distance to the left of Q1 the electric field is zero
D. at a finite distance to the right of Q2 the electric field is zero
Q. 66 A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stopwatch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?
A. Error Δt in measuring T, the time period, is 0.05 seconds
B. Error ΔT in measuring T, the time period , is 1 second
C. Percentage error in the determination of g is 5%
D. Percentage error in the determination of g is 2.5%
Q. 67 A point mass of 1 kg collides elastically with a stationary point mass of 5kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are) correct for the system of theses two masses?
A. Total momentum of the system is 3 kg ms⁻¹
B. Momentum of 5 kg mass after collision is 4 kg ms⁻¹
C. Kinetic energy of the centre of mass is 0.75 J
D. Total kinetic energy of the system is 4J
Q. 68 A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure (1)). If the refractive index of the material of the prism is √3, which of the following is (are) correct?
A. The ray gets totally internally reflected at face CD
B. The ray comes out through face AD
C. The angle between the incident ray and the emergent ray is 90°
D. The angle between the incident ray and the emergent ray is 120°
Q. 69 One mole of an ideal gas in initial stage A undergoes a cyclic process ABCD, as shown in the figure (1). Its pressure at A is P₀. Choose the correct option(s) from the following
A. Internal energies at A and B are the same
B. \Work done by the gas in process AB is P₀V₀ ln 4
C. Pressure at C is P₀/4
D. Temperature at C is T₀/4
Questions: 70 – 72
When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx², it performs simple harmonic motion. The corresponding time period is proportional to √m/k, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to Vo for |x| ≥ X₀. (See figure (1)).
Q. 70 If the total energy of the particle is E, it will perform periodic motion only if
A. E < 0
B. E > 0
C. V₀ > E > 0
D. E > V₀
Q. 71 For periodic motion of small amplitude A, the time period T of this particle is proportional to
A. A√m/α
B. 1/A√m/α
C. A√α/m
D. 1/A√α/m
Q. 72 The acceleration of this particle for |x| > X₀ is
A. proportional to V₀
B. proportional to V₀/mX₀
C. proportional to √V₀/mX₀
D. Zero
Questions: 73 – 74
Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0) if they are placed in a magnetic field, i.e., the critical temperature Tc(B) is a function of the magnetic field strength B. The dependence of Tc(B) on B is shown in the figure (1).
Q. 73 In the graphs (A), (B), (C), (D), the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B₂ (dashed line). If B2 is larger than B₁, which of the following graphs shows the correct variation of R with T in these fields?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 74 A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when
A. B = 5 Tesla, Tc (B) = 80 K
B. B = 5 Tesla, 75 K < Tc (B) < 100 K
C. B = 10 Tesla, 75 K < Tc (B) < 100 K
D. B = 10 Tesla, Tc (B) = 70 K
Q. 75 The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m₂₅ to m₅₀. The ratio m₂₅/m₅₀ is
Q. 76 An α-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are λα and λp respectively. The ratio λα/λp, to the nearest integer, is
Q. 77 When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂ then the value of R in Ω is
Q. 78 Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T₁ and T₂, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?
Q. 79 When two progressive waves y₁ = 4sin(2x – 6t) and y₂ = 3sin(2x – 6t – π/2) are superimposed, the amplitude of the resultant wave is
Q. 80 A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 x 10⁻⁷ m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young’s modulus of the material of the wire is n x 10⁹ Nm⁻², the value of n is
Q. 81 A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by the distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is
Q. 82 Gravitational acceleration on the surface of a planet is √6/11 g, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is ⅔ times that of the earth. If the escape speed on the surface of the earth is taken to be 11kms⁻¹, the escape speed on the surface of the planet in kms⁻¹ will be
Q. 83 A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = 3.36 x 10⁵ J kg⁻¹) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
Q. 84 A stationary source is emitting sound at a fixed frequency fo, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of fo. What is the difference in the speeds of the cars (in km per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is ms⁻¹
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | C | B | D | A | D | A | B | C | B | AC |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | BD | AB | CD | A | D | C | B | C | 2 | 5 |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | 1 | 4 | 3 | 0 OR 8 | 3 | 3 | 0 | 4 | D | C |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | C | A | A | B | B | D | CD | B | ACD | BC |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | A | D | C | D | B | A | 3 | 2 | 5 | 2 |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | 6 | 4 | 1 | 3 | 3 | 9 | C | D | D | C |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| Answer | B | C | A | A | AD | AC | AC | ABC | ABCD | C |
| Question | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| Answer | B | D | A | B | 6 | 3 | 4 | 9 | 5 | 4 |
| Question | 81 | 82 | 83 | 84 | ||||||
| Answer | 6 | 3 | 8 | 7 |