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GATE 2017-2018 :: GATE Production

  1. A process needs to be standardized for method and time. Which one of the following represents the sequence of work study experiments?
  2. A.
    Time study followed by method study
    B.
    Only time study
    C.
    Time study and method study simultaneously
    D.
    Method study followed by time study

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  3. Reduction in the variability of manufactured product characteristics will definitely result in observations close to
  4. A.
    the upper control limit in X chart.
    B.
    the lower control limit in X chart.
    C.
    the lower control limit in R chart.
    D.
    the center line in R chart.

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  5. x + 2y + z = 4 
    2x + y + 2z = 5 
    x - y + z = 1 
    The system of algebraic equations given above has
  6. A.
    a unique solution of x = 1, y = 1 and z = 1.
    B.
    only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0).
    C.
    infinite number of solutions.
    D.
    no feasible solution.

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  7. For the matrix A = , ONE of the normalized eigen vectors is given as
  8. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  9. Consider the differential equation x2 d2y/dx2 + x dy/dx - 4y = 0 with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
  10. A.
    x2
    B.
    sin(Ï€x/2)
    C.
    ex sin(Ï€x/2)
    D.
    e-x sin(Ï€x/2)

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  11. The inverse Laplace transform of the function F(s) = 1/s(s + 1) is given by
  12. A.
    f (t) = sint
    B.
    f (t) = e-t sint
    C.
    f (t) = e-t
    D.
    f (t) = 1 - e-t

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  13. A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
  14. A.
    1/20
    B.
    1/12
    C.
    3/10
    D.
    1/2

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  15. The state of stress at a point under plane stress condition is 
    σxx = 40 MPa, σyy = 100 MPa and txy = 40 MPa 
    The radius of the Mohr's circle representing the given state of stress in MPa is
  16. A.
    40
    B.
    50
    C.
    60
    D.
    100

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  17. A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in N.m is

  18. A.
    100.6
    B.
    54.4
    C.
    22.1
    D.
    15.7

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  19. Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is
  20. A.
    40
    B.
    20
    C.
    10
    D.
    5

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