Aerospace Engineering GATE 2011 Questions with Answer

Ques 1 Aerodynamics

It is seen that the drag polar of a certain aerofoil is symmetric about the C_d axis. This drag polar
could refer to

Ques 2 Aerodynamics

The aerodynamic centre of a supersonic aerofoil, with chord c, is located at

Ques 3 Aerodynamics

Winglets are used on wings to minimize

Ques 4 Aerodynamics

In the context of Prandtl's lifting line theory for a finite wing, which of the following combinations
of statements is TRUE?
P: The bound vortex is responsible for the lift force
Q: The trailing vortices are responsible for the induced drag
R: The bound vortex is responsible for the induced drag
S: The trailing vortices are responsible for the lift force

Ques 5 Aerodynamics

Consider flow over a thin aerofoil at Mach number, M_x=0.5 at an angle of attack, a. Using the Prandtl-Glauert rule for compressibility correction, the formula for lift coefficient, c_b can be written as

Ques 6 Aerodynamics

Prandtl’s lifting line equation for a general wing is given by where U_∞ is the free-stream velocity, α is the angle of attack, y₀ is the spanwise location, α_L=0(y₀) gives the spanwise variation of zero-lift angle, c is the chord, b is the span, and Γ(y₀) gives the spanwise variation of circulation.
The rate of change of circulation with angle of attack Γ_α=^∂Γ/_∂α is

Ques 7 Aerodynamics

Prandtl’s lifting line equation for a general wing is given by where U_∞ is the free-stream velocity, α is the angle of attack, y₀ is the spanwise location, α_L=0(y₀) gives the spanwise variation of zero-lift angle, c is the chord, b is the span, and Γ(y₀) gives the spanwise variation of circulation.
Given that , the corresponding lift curve-slope is
^∂C_L/_∂α is

Ques 8 Engineering Mathematics

Consider x, y, z to be right-handed Cartesian coordinates. A vector function is defined in this
coordinate system as v=3xi+3xyj-yz²k, where i, j and k are the unit vectors along x, y and
z axes, respectively. The curl of v is given by

Ques 9 Engineering Mathematics

Which of the following functions is periodic?

Ques 10 Engineering Mathematics

The function
f(x₁,x₂,x₃)=x₁²+x₂²+x₃²-2x₁-4x₂-6x₃+14 has its minimum value at

Ques 11 Engineering Mathematics

Consider the function f(x₁,x₂)=x₁²+2x₂²+e^-x₁-x₂ The vector pointing in the direction of
maximum increase of the function at the point (1, -1) is

Ques 12 Engineering Mathematics

Two simultaneous equations given by y=π+x and y=x-π have

Ques 13 Engineering Mathematics

Consider the function f(x)=x-sin(x). The Newton-Raphson iteration formula to find the root of
the function starting from an initial guess x⁽⁰⁾ at iteration k is