Aerospace Engineering GATE 2010 Questions with Answer

Ques 1 Aerodynamics

Isentropic efficiency η_d of a subsonic diffuser is defined as
(Note: 'a' represents the ambient, 2 represents the exit of the diffuser and 's' represents an
isentropic process)

Ques 2 Aerodynamics

Consider the flow of air (ρ=1.23 kg/m³) over a wing of chord length 0.5 m and span 3 m. Let the
free stream velocity be U=100 m/s and the average circulation around the wing be Γ=10 m²/s
per unit span. The lift force acting on the wing is

Ques 3 Aerodynamics

Consider a potential flow over a finite wing with the following circulation distribution
Γ(y)=100√1-(^2y/₄)²m²/s

Ques 4 Engineering Mathematics

Two position vectors are indicated by and If a²+b²=1, then the operationamounts to obtaining the position vector V₂ from V₁ by

Ques 5 Engineering Mathematics

The linear second order partial differential equation
5^∂2φ/_∂x²+3^∂2φ/_∂x∂y+2^∂2φ/_∂y²+9=0 is

Ques 6 Engineering Mathematics

The eigen-values of a real symmetric matrix are always

Ques 7 Engineering Mathematics

The concentration of a certain chemical species at time in a chemical reaction is described by the
differential equation
^dx_dt+kx=0, with x(t=0)=x_it Given that e is the base of the natural
logarithms, the concentration x at t=¹_k

Ques 8 Engineering Mathematics

The definite integral
∫¹_-1^dx_x²

Ques 9 Engineering Mathematics

Given that the Laplace transform of y(t)=e^-(2 cos 2t-sin 2t) is Y(s)=^2s/_(s+1)¹2+4
Laplace transform of y_t(t)=e(2 cos 2t-sin 2t) is

Ques 10 Engineering Mathematics

In a certain region a hill is described by the shape z(x,y)=¹/₅₀x⁴+y²-xy-3y
and y are in the horizontal plane and axis z points vertically upward. If î ĵ and &kcirc; unit vectors
along x, y and z, respectively, then at the point x=5, y=10 the unit vector in the direction of the
steepest slope of the hill will be:

Ques 11 Engineering Mathematics

The function
f(x,y)=x²+y²-xy-3y has an extremum at the point

Ques 12 Engineering Mathematics

In finding a root of the equation: x²-6x+5=0 the Newton-Raphson method achieves an order of
convergence equal to:

Ques 13 Engineering Mathematics

If e is the base of the natural logarithms then the equation of the tangent from the origin to the curve y=e^x is