GATE 2010 AEROSPACE ENGINEERING (Q 1-10)

  1. Isentropic efficiency of a subsonic diffuser id defined as
    (Note: ‘a’ represents the ambient, ‘2’ represents the exit of the diffuser and ‘s’ represents an isentropic process) 

    1. (T02s-Ta)/(T02-Ta)
    2. (T02s+Ta)/(T02+Ta)
    3. (P02s-Pa)/(P02-Pa)
    4. (Pa-P02s)/(Pa-P02)

    Answer:- (T02s-Ta)/(T02-Ta)

  2. Two position vectors are indicated by = and = . If a2+b2=1, then the operation = amounts to obtaining vector from by
    1. translation
    2. rotation
    3. magnification
    4. combination of translation, rotation and magnification

    Answer:- rotation
    a=cosθ and b=sinθ will rotate vector at θ angle counterclockwise.

  3. An aircraft is climbing at a constant speed in a straight line at a steep angle of climb. The load factor it sustains during the climb is:
    1. equal to 1.0
    2. greater than 1.0
    3. positive but less than 1.0
    4. dependent on the weight of the aircraft

    Answer:- greater than 1.0

  4. In a general case of homogeneous material under thermo mechanical loading the number of distinct components of the state of stress is
    1. 3
    2. 4
    3. 5
    4. 6

    Answer:-

  5. The linear second order partial differential equation is
    1. Parabolic
    2. Hyperbolic
    3. Elliptic
    4. None of the above

    Answer:- Elliptic
    A=5, 2B=3, C=2
    B2-4AC = 2.25-40 = -37.75<0
    If B2-4AC = 0, parabolic
    If B2-4AC > 0, hyperbolic
    If B2-4AC < 0, elliptic
    Don’t compare this with quadratic equation

  6. All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:
    1. 15%
    2. 30%
    3. 70%
    4. 105%

    Answer:- 70%
    Approximately, Takeoff distance ∝ W2
    ⇒ (s1/s2) = (W1/W2)2
    ⇒ s2 = 1.69s1
    ⇒ takeoff distance increases by approximately 70%

  7. A vertical slender rod is suspended by a hinge at the top and hangs freely. It is heated until it attains a uniform temperature T. Neglecting the effect of gravity, the rod has
    1. Stress but no strain
    2. Strain but no stress
    3. Both stress and strain
    4. Neither stress nor strain

    Answer:-

  8. An aircraft stalls at speed of 40 m/s in straight and level flight. The slowest speed at which this aircraft can execute a level turn at a bank angle of 60 degrees is:
    1. 28.3 m/s
    2. 40.0 m/s
    3. 56.6 m/s
    4. 80.0 m/s

    Answer:- 56.6 m/s
    v ∝ L0.5
    ⇒ v2/v1 = (L2/L1)0.5
    v1 = 40, L1 = W
    L2 = W/cos(bank angle) = 2W
    ⇒ v2 = (2W/W)0.5v1 = 56.6 m/s

  9. The eigen-values of a real symmetric matrix are always
    1. positive
    2. imaginary
    3. real
    4. complex conjugate pairs

    Answer:- real

  10. The concentration x of a certain chemical species at time t in a chemical reaction is described by the differential equation , with x(t=0)=x0. Given the e is the base of the natural logarithms, the concentration at t=1/k
    1. falls to the value x0
    2. rises to the value 2x0
    3. falls to the value x0 /e
    4. rises to the value ex0

    Answer:- falls to the value x0 /e



    ⇒ ln x = -kt+c, c=constant
    x(t=0)=x0 ⇒ ln x0 = c
    ⇒ x/x0 = e-kt
    At t=1/k, x=x0 /e

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s