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GATE 2017-2018 :: GATE Production

  1. Let X be a normal random variable with mean 1 and variance 4. The probability P{X<0} is
  2. A.
    0.5
    B.
    greater than zero and less than 0.5
    C.
    greater than 0.5 and less than 1.0
    D.
    1.0

  3. Choose the CORRECT set of functions, which are linearly dependent.
  4. A.
    sin x , sin2 x and cos2 x
    B.
    cos x , sin x and tan x
    C.
    cos 2x , sin2 x and cos2 x
    D.
    cos 2x , sin x and cos x

  5. The eigenvalues of a symmetric matrix are all
  6. A.
    complex with non-zero positive imaginary part
    B.
    complex with non-zero negative imaginary part
    C.
    real
    D.
    pure imaginary

  7. The partial differential equation  is a
  8. A.
    linear equation of order 2
    B.
    non-linear equation of order 1
    C.
    linear equation of order 1
    D.
    non-linear equation of order 2

  9. Match the CORRECT pairs.

  10. A.
    P-2, Q-1, R-3
    B.
    P-3, Q-2, R-1
    C.
    P-1, Q-2, R-3
    D.
    P-3, Q-1, R-2

  11. A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young's modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the section-SS is

  12. A.
    P/A
    B.
    P(E1 - E2)/A(E1 + E2)
    C.
    PE2/AE1
    D.
    PE1/AE2

  13. For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop ∆p over a length L and the wall shear stress tw are related by
  14. A.
    tw = ∆pD/4L
    B.
    tw = ∆pD2/4L2
    C.
    tw = ∆pD/2L
    D.
    tw = 4∆pL/D

  15. For a ductile material, toughness is a measure of
  16. A.
    resistance to scratching
    B.
    ability to absorb energy upto fracture
    C.
    ability to absorb energy till elastic limit
    D.
    resistance to indentation

  17. A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm3/s is
  18. A.
    160
    B.
    167.6
    C.
    1600
    D.
    1675.5

  19. In the 3-2-1 principle of fixture design, 3 refers to the number of
  20. A.
    clamps required
    B.
    locators on the primary datum face
    C.
    degrees of freedom of the workpiece
    D.
    operations carried out on the primary datum face