Aerospace Engineering Gate Yearwise 


Aerospace Engineering Gate 2010 Questions with Answer

Ques 1 GATE 2010

Isentropic efficiency ηd 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)

A

Toz,-Tα/Toz-Tα

B

To2x+Ta/To2+Tox

C

P02-Pa/P02-Pa

D

Pa-P0γ2/Pa-P02


(c) is the correct answer.

Ques 2 GATE 2010

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

A

615 N

B

1845 N

C

3690 N

D

4920 N


(c) is the correct answer.

Ques 3 GATE 2010

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

If the free stream velocity is 100 m/s, the induced angle of attack is

A

0.125 radians

B

-0.125 radians

C

0.125√1-(y/2)2 radians

D

-0.125√1-(y/2)2radians


(b) is the correct answer.

Ques 4 GATE 2010

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

A

translation

B

rotation

C

magnification

D

combination of translation, rotation, and magnification.


(b) is the correct answer.

Ques 5 GATE 2010

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

A

Parabolic

B

Hyperbolic

C

Elliptic

D

None of the above


(c) is the correct answer.

Ques 6 GATE 2010

The eigen-values of a real symmetric matrix are always

A

positive

B

imaginary

C

real

D

complex conjugate pairs


(c) is the correct answer.

Ques 7 GATE 2010

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

A

falls to the value 0.5x0

B

rises to the value 2x0

C

falls to the value x0e

D

rises to the value ex0


(c) is the correct answer.

Ques 8 GATE 2010

The definite integral
∫1-1dxx2

A

does not exist

B

is equal to 2

C

is equal to 0

D

is equal to -2


(a) is the correct answer.

Ques 9 GATE 2010

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 yt(t)=e(2 cos 2t-sin 2t) is

A

2(s-2)/(s-1)2+4

B

2(s+2)/(s+3)2+4

C

2(s+2)/(s+1)2+4

D

2(s-1)/(s-1)2+4


(d) is the correct answer.

Ques 10 GATE 2010

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:

A

î

B

ĵ

C

&kcirc;

D

î+ĵ+&kcirc;


(a) is the correct answer.

Ques 11 GATE 2010

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

A

(1,2)

B

(3,0)

C

(2.2)

D

(1.1)


(a) is the correct answer.

Ques 12 GATE 2010

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

A

1.0

B

1.67

C

2.0

D

2.5


(c) is the correct answer.

Ques 13 GATE 2010

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

A

y=x

B

y=πx

C

y=x/e

D

y=ex


(d) is the correct answer.

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