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GATE 2017-2018 :: GATE Instrumentation

  1. The open loop transfer function of a unity gain negative feedback control system is given by G(s) = (s2 + 4s + 8)/[s(s + 2)(s + 8)]. The angle θ , at which the root locus approaches the zeros of the system, satisfies
  2. A.
    |θ| = π - tan-1 (1/4)
    B.
    |θ| = 3π/4 - tan-1 (1/3)
    C.
    |θ| = π/2 - tan-1 (1/4)
    D.
    |θ| = π/4 - tan-1 (1/3)

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  3. With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: 
    (i) 1 Ω connected at port B draws a current of 3 A 
    (ii) 2.5 Ω connected at port B draws a current of 2 A

    With 10 V dc connected at port A, the current drawn by 7  connected at port B is
  4. A.
    3/7 A
    B.
    5/7 A
    C.
    1 A
    D.
    9/7 A

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  5. With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: 
    (i) 1 Ω connected at port B draws a current of 3 A 
    (ii) 2.5 Ω connected at port B draws a current of 2 A

    For the same network, with 6 V dc connected at port A, 1 Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is
  6. A.
    6 V
    B.
    7 V
    C.
    8 V
    D.
    9 V

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  7. The deflection profile y (x) of a cantilever beam due to application of a point force F (in Newton), as a function of distance x from its base, is given by y(x) = 0.001F x2(1 - x/3)m. The angular deformation θ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.

    The translation S of the spot of laser light on the photo detector when a force of F = 1 N is applied to the cantilever is
  8. A.
    1 mm
    B.
    3 mm
    C.
    6 mm
    D.
    12 mm

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  9. The deflection profile y (x) of a cantilever beam due to application of a point force F (in Newton), as a function of distance x from its base, is given by y(x) = 0.001F x2(1 - x/3)m. The angular deformation θ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.

    If linear variable differential transformers (LVDTs) are mounted at x = 1/2 m and x = 1/4 m on the cantilever to measure the effect of time varying forces, the ratio of their outputs is
  10. A.
    12/7
    B.
    40/11
    C.
    176/23
    D.
    112/15

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  11. The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). 
    Gc (s) is a lead compensator if
  12. A.
    a =1, b = 2
    B.
    a = 3, b = 2
    C.
    a = "“3, b = "“1
    D.
    a = 3, b = 1

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  13. The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). 
    The phase of the above lead compensator is maximum at
  14. A.
    √2 rad/s
    B.
    √3 rad/s
    C.
    √6 rad/s
    D.
    1/√3 rad/s

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  15. In the circuit shown, the three voltmeter readings are V1 = 220 V, V2 = 122 V, V3 = 136 V.

    The power factor of the load is
  16. A.
    0.45
    B.
    0.50
    C.
    0.55
    D.
    0.60

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  17. In the circuit shown, the three voltmeter readings are V1 = 220 V, V2 = 122 V, V3 = 136 V.

    If RL = 5 Ω, the approximate power consumption in the load is
  18. A.
    700 W
    B.
    750 W
    C.
    800 W
    D.
    850 W

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  19. Choose the most appropriate alternative from the options given below to complete the following sentence: 
    If the tired soldier wanted to lie down, he ___ the mattress out on the balcony.
  20. A.
    should take
    B.
    shall take
    C.
    should have taken
    D.
    will have taken

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