MEGHALAYA CIVIL SERVICE JUNIOR GRADE [PART B MAINS] (FEB 2022 AND JULY 2023)NO.MPSC/ADVT-54/1/2020-2021/53 — question paper

CHEMISTRY-I, Paper-VI, Optional. 250 marks; 3 hours. Answer any five questions. Q7 and Q8 each carry 50 marks. This batch covers Q7(a,c,d,e,f) and Q8(b,c,d,f), nine lettered responses totalling 69 marks; other lettered parts are not included. A candidate selects whole parent questions, not independent subquestions. The figures in the margin indicate full marks. No word limit is printed.

What are trans-uranium elements? Why are they so called? Give the method of preparation of neptunium and comment on the stability of the element.

CHEMISTRY-I, Paper-VI, Optional. 250 marks; 3 hours. Answer any five questions. Q7 and Q8 each carry 50 marks. This batch covers Q7(a,c,d,e,f) and Q8(b,c,d,f), nine lettered responses totalling 69 marks; other lettered parts are not included. A candidate selects whole parent questions, not independent subquestions. The figures in the margin indicate full marks. No word limit is printed.

What are actinides? Why are they so called?

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Verify Cayley-Hamilton theorem for the matrix A = [[0, 0, 1], [3, 1, 0], [-2, 1, 4]]. Hence find A⁻¹.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Solve: d²y/dx² − 2dy/dx + 5y = 10 sin x.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

How are the three vectors a⃗ × b⃗, b⃗ × c⃗ and c⃗ × a⃗ related when it is known that a⃗ + b⃗ + c⃗ = 0⃗?

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

A function f(x) is defined as follows: f(x) = x sin(1/x), x ≠ 0; f(x) = 0, x = 0. Show that f(x) is continuous at x = 0.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Reduce the equation 2x² + 3y² − 4x + 5y + 4 = 0 to the standard form and find its foci and eccentricity.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Find the nature of the quadratic surface given by the equation 2x² + 5y² + 3z² − 4x + 20y − 6z − 5 = 0.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Find the eigenvector of the matrix A = [[1, 1, 0], [0, 2, 2], [0, 0, 3]].
(b)(i) Show that a set of vectors which contains the zero vector is necessarily linearly dependent.
(b)(ii) In V = R³, where R is the set of real numbers, examine each of the following sets of vectors for linear dependence: S = {(2, 1, 2), (8, 4, 8)}; S = {(1, 2, 0), (0, 3, 1), (−1, 0, 1)}.
(c) State whether the following is True or False with justification: There exists a 3 × 3 real matrix C such that C⁻¹ [[1, 1, 1], [0, 1, 1], [0, 0, 0]] C = [[1, 4, 6], [0, 2, 5], [0, 0, 3]].
(d) Let f be the bilinear form on R³ defined by f{(x₁,x₂,x₃),(y₁,y₂,y₃)} = 3x₁y₁ − 2x₁y₂ + 5x₂y₁ + 7x₂y₂ − 8x₂y₃ + 4x₃y₂ − x₃y₃. Find the matrix of f relative to the basis {e₁ = (1,0,0), e₂ = (0,1,0), e₃ = (0,0,1)}.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) If f(x) = (x − a)^m (x − b)^n, where m and n are positive integers, show that c in Rolle’s theorem divides the segment a ≤ x ≤ b in the ratio m : n.
(b) Show that the maximum rectangle with a given perimeter is a square.
(c) Show that the function f(x) = xy/√(x² + y²), if x² + y² ≠ 0; 0, if x = y = 0, is continuous, possesses partial derivative but is not differentiable at the origin.
(d) What is the area of the entire surface formed when the cardioid r = a(1 + cos θ) is revolved about the initial line? Find it in the case of cardioid r = a(1 − cos θ).

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Let V be a finite dimensional vector space. Then show that (i) for the identity linear map I : V → V, Rank I = dim V and Nullity I = 0 and (ii) for the zero linear map O : V → V, Rank O = 0 and Nullity O = 0.
(b) A conical tent of a given capacity has to be constructed. Find the ratio of the height to the radius of the base for the minimum amount of canvas required for the tent.
(c) Evaluate ∬ √(a²b² − b²x² − a²y²)/√(a²b² + b²x² + a²y²) dx dy where the field of integration being the positive quadrant of the ellipse x²/a² + y²/b² = 1.
(d) Examine f(x,y,z) = 2xyz − 4zx − 2yz + x² + y² + z² − 2x − 4y + 4z for extreme values.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Find the equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y − z + 4 = 0 which is parallel to the x-axis.
(b) Find the equation of the sphere through the circle x² + y² = a², z = 0 and through the centre of the sphere (x − α)² + (y − β)² + (z − γ)² = r².
(c) Prove that the enveloping cylinder of the ellipsoid x²/a² + y²/b² + z²/c² = 1 whose generators are parallel to the line x/0 = y/(±√(a² − b²)) = z/c meet the plane z = 0 in circles.
(d) Prove that the straight lines represented by the equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 will be equidistant from the origin if f⁴ − g⁴ = c(bf² − ag²).

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Show that the equation (x³ − 3x²y + 2xy²)dx − (x³ − 2x²y + y³)dy = 0 is exact and find the solution if y = 1 when x = 1.
(b) Solve: p³ − p(x² + xy + y²) + xy(x + y) = 0, p = dy/dx.
(c) By using variation of parameter method, solve d²y/dx² + y = sec x.
(d) Reduce to Clairaut’s form by putting x² = u and y² = v, solve the equation (px − y)(x − py) = 2p.

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) A uniform ladder is in equilibrium with one end resting on the ground and the other against a vertical wall; if the ground and the wall be both rough, the coefficients of friction be μ and μ′ respectively; and if the ladder be on the point of slipping at both ends, show that the inclination of the ladder to the horizon is given by tan θ = (1 − μμ′)/(2μ).
(b) A cannon ball has a range R on the horizontal plane. If h and h′ are the greatest heights in the two paths for which this is possible, prove that R = 4√(hh′).
(c) Show that the depth of the centre of pressure of a rhombus totally immersed with one diagonal vertical and its centre at a depth h is (h² + a²/(2h))/h where a is the length of the vertical diagonal.
(d) Two smooth spheres of masses m₁ and m₂ moving with velocities u₁ and u₂ along the line of centres. Find the velocity after impact and show that loss of kinetic energy is ½[m₁m₂/(m₁ + m₂)](u₁ − u₂)²(1 − e²).

MATHEMATICS-I, Paper-VI, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Prove that a proper vector u⃗ always remains parallel to a fixed line if and only if u⃗ × du⃗/dt = 0⃗.
(b) Prove that if F⃗ is a vector point function ∇ × (∇ × F⃗) = ∇(∇ · F⃗) − ∇²F⃗ where ∇ = î ∂/∂x + ĵ ∂/∂y + k̂ ∂/∂z.
(c) Evaluate ∮Γ (eˣ dx + 2y dy − dz) by using Stokes’ theorem where Γ is the curve x² + y² = 4, z = 2.
(d) Verify Green’s theorem in the plane for ∮Γ (x² dx + xy dy) where Γ is a square in the xy-plane given by x = 0, y = 0, x = a, y = a (a > 0) described in the anti-clockwise sense.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Prove that any two right (left) cosets of a subgroup H of a group G are either disjoint or identical.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Prove that every convergent sequence in R is a Cauchy sequence.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Form a partial differential equation by eliminating a, b and c from x²/a² + y²/b² + z²/c² = 1.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Find all basic solutions of the following system: x + 2y + z = 4; 2x + y + 5z = 5.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Question 1: answer any five of seven alternatives, 10 marks each. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. All seven alternatives are offered for study.

Convert the following number systems to another:
(i) 11001₂ to decimal number system
(ii) 47068₈ to decimal number system
(iii) 1AC₁₆ to decimal number system
(iv) 428₁₀ to hexadecimal number system
(v) 42₁₀ to binary number system

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Using simplex method, solve the following: Z = 5x₁ + 3x₂ subject to the constraints x₁ + x₂ ≤ 2; 5x₁ + 2x₂ ≤ 10; 3x₁ + 8x₂ ≤ 12; x₁, x₂ ≥ 0.
(b) Find the dual of the following problem: Minimize Z = 2y + 5z subject to the constraints x + y ≥ 2; 2x + y + 6z ≤ 6; x − y + 3z = 4; x, y, z ≥ 0.
(c) An agriculturist has a farm with 125 acres. He produces radish, mutter and potato. Whatever he raises is fully sold in the market. He gets ₹5 for radish per kg, ₹4 for mutter per kg and ₹5 for potato per kg. The average yield is 1500 kg of radish per acre, 1800 kg of mutter per acre and 1200 kg of potato per acre. To produce each 100 kg of radish and mutter, and to produce each 80 kg of potato, a sum of ₹12·50 has to be used for manure. Labour for each acre to raise the crop is 6 man-days for radish and potato each and 5 man-days for mutter. A total of 500 man-days labour at the rate of ₹40 per man-day is available. Formulate this as a linear programming problem to maximize the agriculturist’s total profit.

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Apply Charpit’s method to solve (p² + q²)y = qz.
(b) By using the method of separation of variables, solve two-dimensional Laplace’s equation ∂²u/∂x² + ∂²u/∂y² = 0.
(c) Solve: (z² − 2yz − y²)p + (xy + zx)q = xy − zx.
(d) Form a partial differential equation by eliminating the function f from z = y² + 2f(1/x + log y).

MATHEMATICS-II, Paper-VII, Optional. 250 marks; 3 hours. Answer Question No. 1 which is compulsory and four remaining questions, selecting two from each Section. Each of Questions 2–8 carries 50 marks; all printed subparts are included in each integrated response. Assume suitable data if considered necessary and indicate the same clearly. No word limit is printed. Section A contains Questions 2–5 and Section B contains Questions 6–8.

(a) Calculate by Simpson’s one-third rule an approximate value of ∫₋₃³ x⁴ dx by taking seven equidistant ordinates. Compare it with the exact value and the value obtained by using the trapezoidal rule.
(b) Use Newton’s backward interpolation formula to find f(7·5), given x: 1, 2, 3, 4, 5, 6, 7, 8; f(x): 1, 8, 27, 64, 125, 216, 343, 512.
(c) What do you mean by logic gates? Describe OR, AND and NOT gates.
(d) Let (B, +, ·, ′) be a Boolean algebra. Show that a′ + b = 1 if and only if a + b = b, ∀a,b∈B. Also show that if for a,b,c∈B, a + b = a + c and a·b = a·c, then b = c.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

At a point above the surface of the earth, the gravitational potential is −5.12×10^7 J kg^−1 and the acceleration due to gravity is 6.4 m s^−2. Assuming the mean radius of the earth to be 6.4×10^6 m, calculate the height of the point above the earth’s surface.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

A particle is dropped from a height of 200 m above the earth surface. Calculate the eastward deflection of the particle due to Coriolis force when it hits the ground if the particle is dropped at (i) 30° N, (ii) 45° N and (iii) at the north pole.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

A particle is moving with simple harmonic motion along a straight line. Its velocities when passing through the points 3 cm and 4 cm from the centre of its path are 16 cm/s and 12 cm/s respectively. Find the amplitude, period of motion and maximum velocity of the particle.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

Two particles of mass 2 kg each are moving with velocities 3î + 4ĵ m/s and 5î + 6ĵ m/s. Find the kinetic energy of the system relative to the centre of mass.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

In a Newton’s ring setup placed in air, the diameters of 5th and 10th dark rings are found to be 0.336 cm and 0.590 cm respectively. When a small quantity of liquid is added between the glass plate and the lens, the diameters of 5th and 10th dark rings are found to be 0.218 cm and 0.451 cm respectively. Calculate the refractive index of the liquid.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

Assuming the sun to be a blackbody at a temperature of 5800 K, use Stefan’s law to show that the total radiant energy emitted by the sun per second is 3.95×10^26 joules. Given, radius of the sun is 7×10^8 m.

PHYSICS-I, Paper-VI, Optional. 250 marks; 3 hours. Q1 is compulsory and asks for any five of seven lettered alternatives, each carrying10marks. A candidate then answers four whole parent questions from the rest, selecting at least one from each section. The figures in the margin indicate full marks. No word limit is printed. Suitable data may be assumed if stated clearly.

Calculate the change of entropy when 10 g of ice at −10 °C is converted into steam at 100 °C. Given, specific heat of ice is 0.5 cal/g/°C, latent heat of fusion is 80 cal/g and latent heat of vaporization is 540 cal/g.

PHYSICS-I, Paper-VI, Optional. Exact printed occurrence PHYS1-VI-Q5(a), page 142, 20 marks. Diagram artwork is an explanatory study schematic and not to scale.

Describe the construction and working principle of Michelson’s interferometer with a neat diagram. How is it used to measure the wavelength of monochromatic light?

PHYSICS-I, Paper-VI, Optional. Exact printed occurrence PHYS1-VI-Q8(a), page 143, 15 marks.

Define critical constants for van der Waals’ equation of state and obtain expressions for the critical temperature, pressure, and volume in terms of the constants of van der Waals’ equation.

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, with printed alternatives A or B, and a candidate answers three other parent questions with at least one from each section. This batch preserves both alternatives to Questions 1 and 5 plus Questions 2, 3, 6 and 7 as eight separate study models. No word limit is printed for these positions.

Write a critical note on the importance of archaeological sources for the history of ancient India.

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, with printed alternatives A or B, and a candidate answers three other parent questions with at least one from each section. This batch preserves both alternatives to Questions 1 and 5 plus Questions 2, 3, 6 and 7 as eight separate study models. No word limit is printed for these positions.

Discuss the distinctive features of the Harappan Civilization. Give reasons for its decline.

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, with printed alternatives A or B, and a candidate answers three other parent questions with at least one from each section. This batch preserves both alternatives to Questions 1 and 5 plus Questions 2, 3, 6 and 7 as eight separate study models. No word limit is printed for these positions.

Give an account of the life and conditions of the Rigvedic people. Is it correct to call them ‘an agricultural people’? Give reasons for your answer.

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, with printed alternatives A or B, and a candidate answers three other parent questions with at least one from each section. This batch preserves both alternatives to Questions 1 and 5 plus Questions 2, 3, 6 and 7 as eight separate study models. No word limit is printed for these positions.

Examine the position of women in peninsular India during ancient period.

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, and a candidate answers three other parent questions with at least one from each section. Question 4 directs candidates to write notes on any four topics, in not more than 150 words each. This batch preserves all eight printed Q4 choices as separate study models.

Teachings of Gautama Buddha

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, and a candidate answers three other parent questions with at least one from each section. Question 4 directs candidates to write notes on any four topics, in not more than 150 words each. This batch preserves all eight printed Q4 choices as separate study models.

Mahajanapadas

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, and a candidate answers three other parent questions with at least one from each section. Question 4 directs candidates to write notes on any four topics, in not more than 150 words each. This batch preserves all eight printed Q4 choices as separate study models.

Positions of the Brahmins in peninsular India during the post-Vedic period

HISTORY-I, Paper-VI, Optional. 250 marks; 3 hours. Questions 1 and 5 are compulsory, and a candidate answers three other parent questions with at least one from each section. Question 4 directs candidates to write notes on any four topics, in not more than 150 words each. This batch preserves all eight printed Q4 choices as separate study models.

Nature of the Mauryan administration