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GATE 2017-2018 :: GATE Mechanical

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

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  3. The inverse Laplace transform of the function F(s) = 1/s(s + 1) is given by
  4. 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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  5. For the matrix A =  , ONE of the normalized eigen vectors is given as
  6. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  7. Calculate the punch size in mm, for a circular blanking operation for which details are given below.
    Size of the blank    25 mm
    Thickness of the sheet  2 mm
    Radial clearance between punch and die 0.06 mm
    Die allowance     0.05 mm
  8. A.
    24.83
    B.
    24.89
    C.
    25.01
    D.
    25.17

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  9. In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is
  10. A.
    0.006
    B.
    0.031
    C.
    0.062
    D.
    0.600

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  11. In a DC arc welding operation, the voltage-arc length characteristic was obtained as Varc = 20 + 5l where the arc length l was varied between 5 mm and 7 mm. Here Varc denotes the arc voltage in Volts. The arc current was varied from 400 A to 500 A. Assuming linear power source characteristic, the open circuit voltage and the short circuit current for the welding operation are
  12. A.
    45 V, 450 A
    B.
    75 V, 750 A
    C.
    95 V, 950 A
    D.
    150 V, 1500 A

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  13. A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

  14. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  15. Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counter flow 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
  16. A.
    40
    B.
    20
    C.
    10
    D.
    5

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  17. A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ∆T. If the thermal coefficient of the material is α, Young's modulus is E and the Poisson's ratio is υ , the thermal stress developed in the cube due to heating is
  18. A.
    -[α(∆T)E]/(1 - 2υ)
    B.
    -[2α(∆T)E]/(1 - 2υ)
    C.
    -[3α(∆T)E]/(1 - 2υ)
    D.
    -[α(∆T)E]/3(1 - 2υ)

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  19. A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is
  20. A.
    8
    B.
    16
    C.
    24
    D.
    32

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