GATE 2007 AEROSPACE ENGINEERING (Q 1-10)

  1. Which one of the following engines should be used by a subsonic passenger transport airplane for minimum specific fuel consumption?
    1. Turbojet engine with after burner
    2. Turbofan engine
    3. Ramjet engine
    4. Scramjet engine

    Answer:- Turbofan engine
    SFC in increasing order:- (1)Turbofan (2)Turbojet with after burner (3)Ramjet (4)Scramjet

  2. A spring-mass-damper system with a mass of 1 kg is found to have a damping ratio of 0.2 and a natural frequency of 5 rad/s. The damping of the system is given by
    1. 2 Ns/m
    2. 2 N/s
    3. 0.2 kg/s
    4. 0.2 N/s

    Answer:- 2 Ns/m
    m = 1 kg
    ζ = 0.2
    ω0 = 5 rad/s
    ω0 = (k/m)1/2 ⇒ k = mω02 ⇒ k = 25 kg/s2
    ζ = c/{2(mk)1/2} ⇒ c = 2ζ(mk)1/2 ⇒ c = 2 kg/s = 2 Ns/m

  3. If f(θ) =, then f(α)f(β) =
    1. f(α/β)
    2. f(α+β)
    3. f(α-β)
    4. 2 x 2 zero matrix

    Answer:- f(α+β)
    f(α)f(β) =

    =

    =

    = f(α+β)

  4. An artificial satellite remains in orbit and does not fall to the earth because
    1. the centrifugal force acting on it balances the gravitational attraction
    2. the on-board rocket motors provide continuous boost to keep it in orbit
    3. its transverse velocity keeps it from hitting the earth although it falls continuously
    4. due to its high speed it derives sufficient lift from the rarefied atmosphere

    Answer:- its transverse velocity keeps it from hitting the earth although it falls continuously

  5. The Euler iteration formula for numerically integrating a first order nonlinear differential equation of the form = f(x), with a constant step size of Δt is
    1. xk+1 = xk−Δt*f(xk)
    2. xk+1 = xk+(Δt2/2)*f(xk)
    3. xk+1 = xk−(1/Δt)*f(xk)
    4. xk+1 = xk+Δt*f(xk)

    Answer:- xk+1 = xk+Δt*f(xk)

  6. The number of natural frequencies of an elastic beam with cantilever boundary conditions is
    1. 1
    2. 3
    3. 1000
    4. Infinite

    Answer:-

  7. For maximum range of a glider, which one of the following conditions is true?
    1. lift to drag ratio is maximum
    2. rate of descent is minimum
    3. descent angle is maximum
    4. lift to weight ratio is maximum

    Answer:- lift to drag ratio is maximum

    • Maximum endurance for a reciprocating engine, propeller driven airplane requires lowest SFC and maximum CL3/2/CD
    • Maximum range for a reciprocating engine, propeller driven airplane requires lowest possible SFC and maximum CL/CD
    • Maximum endurance for a jet airplane requires minimum TSFC and maximum CL/CD
    • Maximum range for a jet airplane requires minimum TSFC and maximum CL1/2/CD
  8. An airplane with a larger wing as compared to a smaller wing will necessarily have
    1. more longitudinal static stability
    2. less longitudinal static stability
    3. same longitudinal static stability
    4. more longitudinal static stability for an aft tail airplane if aerodynamic center of the larger wing is behind the center of gravity of the airplane

    Answer:-

  9. The minimum value of J(x) = x2−7x+30 occurs at
    1. x = 7/2
    2. x = 7/30
    3. x = 30/7
    4. x = 30

    Answer:- x = 7/2
    J(x) = x2−7x+30
    J'(x) = 2x−7
    J”(x) = 2
    ⇒ minimum value occurs when J'(x) = 2x−7 = 0x = 7/2

  10. Two airplanes are identical except for the location of the wing. The longitudinal static stability of the airplane with low wing configuration will be
    1. more than the airplane with high wing configuration
    2. less than the airplane with high wing configuration
    3. same as the airplane with high wing configuration
    4. more if elevator is deflected

    Answer:-

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