- 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)- (T
_{02s}-T_{a})/(T_{02}-T_{a}) - (T
_{02s}+T_{a})/(T_{02}+T_{a}) - (P
_{02s}-P_{a})/(P_{02}-P_{a}) - (P
_{a}-P_{02s})/(P_{a}-P_{02})

Answer:- (T

_{02s}-T_{a})/(T_{02}-T_{a}) - (T
- Two position vectors are indicated by = and = . If
*a*, then the operation = amounts to obtaining vector from by^{2}+b^{2}=1- translation
- rotation
- magnification
- combination of translation, rotation and magnification

Answer:- rotation

a=cosθ and b=sinθ will rotate vector at θ angle counterclockwise. - 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:
- equal to 1.0
- greater than 1.0
- positive but less than 1.0
- dependent on the weight of the aircraft

Answer:- greater than 1.0

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

Answer:-

- The linear second order partial differential equation is
- Parabolic
- Hyperbolic
- Elliptic
- None of the above

Answer:- Elliptic

A=5, 2B=3, C=2

B^{2}-4AC = 2.25-40 = -37.75<0

If B^{2}-4AC = 0, parabolic

If B^{2}-4AC > 0, hyperbolic

If B^{2}-4AC < 0, elliptic

*Don’t compare this with quadratic equation* - All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:
- 15%
- 30%
- 70%
- 105%

Answer:- 70%

Approximately, Takeoff distance ∝ W^{2}

⇒ (s_{1}/s_{2}) = (W_{1}/W_{2})^{2}

⇒ s_{2}= 1.69s_{1}

⇒ takeoff distance increases by approximately 70% - 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
- Stress but no strain
- Strain but no stress
- Both stress and strain
- Neither stress nor strain

Answer:-

- 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:
- 28.3 m/s
- 40.0 m/s
- 56.6 m/s
- 80.0 m/s

Answer:- 56.6 m/s

v ∝ L^{0.5}

⇒ v_{2}/v_{1}= (L_{2}/L_{1})^{0.5}

v_{1}= 40, L_{1}= W

L_{2}= W/cos(bank angle) = 2W

⇒ v_{2}= (2W/W)^{0.5}v_{1}= 56.6 m/s - The eigen-values of a real symmetric matrix are always
- positive
- imaginary
- real
- complex conjugate pairs

Answer:- real

- 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)=x*. Given the e is the base of the natural logarithms, the concentration at_{0}*t=1/k*- falls to the value
*x*_{0} - rises to the value
*2x*_{0} - falls to the value
*x*_{0}/e - rises to the value
*ex*_{0}

Answer:- falls to the value

*x*_{0}/e

*⇒ ln x = -kt+c*, c=constant

*x(t=0)=x*_{0}⇒ ln x_{0}= c

*⇒ x/x*_{0}= e^{-kt}

At*t=1/k,***x=x**_{0}/e - falls to the value

# GATE 2010 AEROSPACE ENGINEERING (Q 1-10)

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