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Meghalaya Police Service Preliminary Examination 2022 - Multiple Subjects — question paper

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Meghalaya Police Service Preliminary Examination 2022 - Multiple Subjects

Paper #3169 · 17-12-2022 · Multiple subjects · 514 reviewed questions · Showing 321–360 of 514

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Accuracy note: This is a reviewed structured rendering of an official previous-year paper and may cover only part of it. Where available, explanatory notes describe unresolved source or answer issues without supplying a scoring answer. Official examination authority notices remain final.

  1. In simple harmonic motion, the maximum magnitudes of acceleration and velocity are 6 ft/s² and 3 ft/s, respectively. What is the period of the motion?
    1. π sec
    2. 2 sec
    3. 1/2 sec
    4. 1/4 sec
  2. In ideal projectile motion with no air resistance and constant gravitational acceleration g, a particle is projected at speed u at an angle α above the horizontal. Its maximum height above the launch point is:
    1. u² sin²(α)/(2g)
    2. 2u sin(α)/g
    3. u² sin(2α)/g
    4. u sin(2α)/g
  3. A particle in simple harmonic motion has period 1 s and amplitude 2 m. What is its speed (the magnitude of its velocity) when its displacement from the mean position is 1 m?
    1. 4π² m/sec
    2. 2π√3 m/sec
    3. 2√3 m/sec
    4. None of these
  4. For ideal projectile motion with no air resistance, when a projectile lands at its launch height, at what angle to the horizontal is its range greatest for a fixed launch speed?
    1. 90 degrees
    2. 60 degrees
    3. 45 degrees
    4. 30 degrees
  5. In simple harmonic motion with amplitude A, at what distance from the mean position is the particle’s speed equal to half its maximum speed?
    1. (√3/2) x amplitude
    2. (1/2) x amplitude
    3. amplitude
    4. None of these
  6. A particle starts from rest at x=c (c>0) on a straight line from fixed point O and moves away from O under acceleration a=μ/x², where μ>0. What is its speed when x=2c?
    1. √(μ/c)
    2. √(c/μ)
    3. √(2c/μ)
    4. √(c/(2μ))
  7. The trigonometric (polar) form of the complex number z = 1 + i is:
    1. cos(π/4)+i sin(π/4)
    2. √2[cos(π/4)+i sin(π/4)]
    3. cos 0+i sin 0
    4. cos(π/2)+i sin(π/2)
  8. For matrices A and B, both the sum A + B and the product AB are defined when:
    1. A and B are of the same order
    2. A and B are square matrices of the same order
    3. Number of columns of A = Number of rows of B
    4. None of these
  9. A coplanar system of forces in the xy-plane has zero algebraic moment about each of the points O(0,0), A(1,0) and B(0,2). What can be concluded about the system?
    1. Reduces to a single resultant
    2. Reduces to a couple
    3. Is in equilibrium
    4. None of these
  10. For a uniform triangular lamina in a uniform gravitational field, its centre of gravity lies at the:
    1. Centroid of the triangle
    2. Orthocentre of the triangle
    3. In-centre of the triangle
    4. None of these
  11. A 4 lb body is in limiting equilibrium on a rough plane inclined at 30° to the horizontal. What is the coefficient of friction between the body and the plane?
    1. 1/√2
    2. 1/√3
    3. 1/√6
    4. 1
  12. How many distinct elements generate an infinite cyclic group G?
    1. 1
    2. 2
    3. Infinite
    4. None of these
  13. For x ≠ 0 and y ≠ 0, the differential equation x²(dy/dx) + y² = 0 has general integral:
    1. x+y=k
    2. xy=k
    3. 1/x+1/y=k
    4. x³+y³=k
  14. The polynomial 2x³−15x²+46x−42 has the root 3+i√5. Which description is correct for its other two roots?
    1. One real root and one non-real complex root
    2. Two non-real complex roots
    3. Two real roots
    4. None of these
  15. The straight line through P=(−2,3,−1) and Q=(−3,4,5), extended beyond segment PQ if necessary, meets the plane 3x+y+z=8 at:
    1. (-2,3,-1)
    2. (-3,4,5)
    3. (-5,6,17)
    4. (8,9,0)
  16. For real p, the p-series ∑ₙ₌₁^∞ 1/nᵖ converges when:
    1. p > 1
    2. p < 1
    3. p = 1
    4. None of these
  17. For the parabola y²=8x, find the area of the finite region enclosed by the curve and its latus rectum.
    1. 32/3 square units
    2. 64/3 square units
    3. 16/3 square units
    4. None of these
  18. For real n ≠ −1 and x > 0, an antiderivative of x^n with respect to x is:
    1. n x^(n−1) + C
    2. x^(n+1)/(n+1) + C
    3. x^n/n + C
    4. x^(n−1)/(n−1) + C
  19. The asymptotes of the hyperbola x² − y² = 16 are:
    1. x + y = 0
    2. x − y = 0
    3. y = ±x
    4. y = ±4x
  20. For n = 1, 2, 3, …, the sequence aₙ = (n + 1)/n is:
    1. Monotonic increasing
    2. Monotonic decreasing
    3. Not bounded
    4. Oscillatory
  21. The radius of the sphere x²+y²+z²=25 is
    1. 5
    2. 25
    3. √5
    4. 10
  22. The Cartesian coordinates of the point with polar coordinates (r, θ) = (2, π/2), where θ is in radians, are:
    1. (0,2)
    2. (2,0)
    3. (1,2)
    4. (2,1)
  23. For the matrix A = [[1, 2, 3], [2, 4, 6]], its order (number of rows × number of columns) is:
    1. 2×2
    2. 2×3
    3. 3×2
    4. 3×3
  24. The value of [[1,-1],[0,2]] + [[0,1],[0,-2]] is (each inner bracket denotes one matrix row)
    1. [[1,0],[0,0]]
    2. [[0,0],[0,0]]
    3. [[0,1],[1,0]]
    4. [[1,-1],[0,1]]
  25. Using ordinary matrix multiplication, compute [[1, 0], [0, 1]] × [[1, 0], [0, 1]]. Each inner bracket denotes one row.
    1. [[1,0],[0,1]]
    2. [[0,1],[0,1]]
    3. [[0,1],[1,0]]
    4. [[0,0],[1,0]]
  26. Evaluate limₓ→₀ sin(3x)/x, with x measured in radians.
    1. 1
    2. 0
    3. 3
    4. 1/3
  27. Let f(x) = x² for x ≠ 1 and f(1) = 0. Which statement about f at x = 1 is correct?
    1. Continuous at x=1
    2. Discontinuous at x=1
    3. Not defined at x=1
    4. None of these
  28. If x changes from 1 to 1.5, then the increment of x is
    1. 0.5
    2. 2
    3. -0.5
    4. -2
  29. For x ≠ 0, if f(x) = 1/x, then f′(x) is:
    1. 1/x²
    2. −1/x
    3. −1/x²
    4. x²
  30. For x > 0, if f(x) = √x, then f′(x) is:
    1. 1/√x
    2. 1/(2√x)
    3. 1/x
    4. 1/x²
  31. For y = x², what is the slope of the tangent at the point (−1, 1)?
    1. 1
    2. -1
    3. 2
    4. -2
  32. A particle moves along a straight line with position s(t) = 6t + (1/2)t² − (1/3)t³, where s is in metres and t is in seconds. What is its velocity at t = 1 second?
    1. 6 units/second
    2. 37/6 units/second
    3. 3 units/second
    4. 6 units/second²
  33. Differentiate f(x) = 3x² + 2x with respect to x.
    1. 6x+2
    2. 6x
    3. x³+x²
    4. 6x³+2x²
  34. For the circle x² + y² = a² (a > 0), at a point where y ≠ 0, the derivative dy/dx is:
    1. x/y
    2. y/x
    3. -x/y
    4. -y/x
  35. With x measured in radians, the derivative d(cos x)/dx is:
    1. -sin x
    2. sin x
    3. sec x
    4. -sec x
  36. The volume V of a right circular cone with base radius r and perpendicular height h is:
    1. (1/3)πr²h
    2. (4/3)πr²h
    3. πr²h
    4. 2πr²h
  37. The value of ξ in Lagrange's Mean Value Theorem for the function f(x)=x² between 0 and 2 is
    1. 0
    2. 2
    3. 1
    4. -1
  38. Evaluate limₓ→₀ (tan x)/x, with x measured in radians.
    1. 0
    2. 1
    3. π/2
    4. Does not exist
  39. Evaluate limₓ→₀ (eˣ − 1)/x.
    1. 1
    2. 0
    3. Undefined
    4. -1
  40. If f(x)=3x-2, then f(-1) is
    1. -2
    2. -5
    3. 1
    4. 5

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