Download Graduate Aptitude Test in Engineering (GATE) 2015 AE Aerospace Engineering Question Paper
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
GATE 2015 AEROSPACE ? AE
AE 4/8
Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, ???? = 8 ???????? from the sea
level. The nozzle operates in
(A) under-expanded condition for ???? > 8 ????????
(B) under-expanded condition for ???? < 8 ????????
(C) sonic exit condition for ???? > 8 ????????
(D) unchoked condition for ???? < 8 ????????
Q. 26 ? Q. 55 carry two marks each.
Q.26
In the solution of 0 2
2
2
= + ? y
dx
dy
dx
y d
, if the values of the integration constants are identical and
one of the initial conditions is specified as 1 ) 0 ( = y , the other initial condition = ? ) 0 ( y _____.
Q.27
For ???? > 0, the general solution of the differential equation y
dx
dy
2 1 ? = asymptotically
approaches _______.
Q.28
For a parabola defined by
2
, 0, y ax bx c a = ++ ? the coordinates (, ) xy of the extremum are
(A)
?
?
?
?
?
?
?
?
?
+
?
0 ,
2
4
2
2
a
ac b
a
b
(B)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
2
4
,
2
2
(C)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
4
4
,
2
2
(D) ( ) c , 0
Q.29
The 2-D stress state at a point P in the x-y coordinate system is ?
60 50
50 ?40
? ???????????? . The magnitude
of the tangential stress (in ???????????? ) on a surface normal to the x-axis at P is _____.
Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of
100 ???? /mm
2
. Under this load, the volume of the cube shrinks by 0.05%. The Young's modulus of
the material, ???? = 300 ???????????? . The Poisson's ratio of the material is _____.
Q.31 A massless cantilever beam PQ has a solid square cross section (10 ???????? ? 10 ???????? ). This beam is
subjected to a load ???? through a rigid massless link at the point Q, as shown below (figure not to
scale). If the Young's modulus of the material ???? = 200 ???????????? , the deflection (in ???????? ) at point Q
is _____.
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
GATE 2015 AEROSPACE ? AE
AE 4/8
Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, ???? = 8 ???????? from the sea
level. The nozzle operates in
(A) under-expanded condition for ???? > 8 ????????
(B) under-expanded condition for ???? < 8 ????????
(C) sonic exit condition for ???? > 8 ????????
(D) unchoked condition for ???? < 8 ????????
Q. 26 ? Q. 55 carry two marks each.
Q.26
In the solution of 0 2
2
2
= + ? y
dx
dy
dx
y d
, if the values of the integration constants are identical and
one of the initial conditions is specified as 1 ) 0 ( = y , the other initial condition = ? ) 0 ( y _____.
Q.27
For ???? > 0, the general solution of the differential equation y
dx
dy
2 1 ? = asymptotically
approaches _______.
Q.28
For a parabola defined by
2
, 0, y ax bx c a = ++ ? the coordinates (, ) xy of the extremum are
(A)
?
?
?
?
?
?
?
?
?
+
?
0 ,
2
4
2
2
a
ac b
a
b
(B)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
2
4
,
2
2
(C)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
4
4
,
2
2
(D) ( ) c , 0
Q.29
The 2-D stress state at a point P in the x-y coordinate system is ?
60 50
50 ?40
? ???????????? . The magnitude
of the tangential stress (in ???????????? ) on a surface normal to the x-axis at P is _____.
Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of
100 ???? /mm
2
. Under this load, the volume of the cube shrinks by 0.05%. The Young's modulus of
the material, ???? = 300 ???????????? . The Poisson's ratio of the material is _____.
Q.31 A massless cantilever beam PQ has a solid square cross section (10 ???????? ? 10 ???????? ). This beam is
subjected to a load ???? through a rigid massless link at the point Q, as shown below (figure not to
scale). If the Young's modulus of the material ???? = 200 ???????????? , the deflection (in ???????? ) at point Q
is _____.
GATE 2015 AEROSPACE ? AE
AE 5/8
Q.32
An aircraft, with a wing loading
???? ???? = 500 ???? / ???? 2
, is gliding at ?
???? ???? ?
???????????? = 10 and ???? ???? = 0.69.
Considering the free stream density ???? ?
= 0.9 ???????? / ???? 3
, the equilibrium glide speed (in ???? / ???? )
is _____.
Q.33 For a thin flat plate at 2 degrees angle of attack, the pitching moment coefficient about the trailing
edge is _____.
Q.34 A satellite is to be transferred from its geostationary orbit to a circular polar orbit of the same radius
through a single impulse out-of-plane maneuver. The magnitude of the change in velocity required
is __________ times the magnitude of the escape velocity.
Q.35 A planetary probe is launched at a speed of 200 ???????? / ???? and at a distance of 71,400 ???????? from the
mass center of its nearest planet of mass 1.9 ? 10
28
???????? . The universal gravitational constant,
???? = 6.67 ? 10
?11
???? 3
???????? ???? 2
. The ensuing path of the probe would be
(A) elliptic (B) hyperbolic (C) parabolic (D) circular
Q.36 The velocity profile of an incompressible laminar boundary layer over a flat plate developing under
constant pressure is given by
( )
3
2
1
2
3
?
?
?
?
?
?
? =
?
? ?
y y
U
y u
. The freestream velocity s m U / 10 =
?
and
the dynamic viscosity of the fluid
s m
kg
5
10 8 . 1
?
? = ? . At a streamwise station where the boundary
layer thickness mm 5 = ? , the wall shear stress is _________ Pa
3
10
?
? .
Q.37
The Pitot tube of an aircraft registers a pressure
2
0
/ 54051 m N p = . The static pressure, density
and the ratio of specific heats of the freestream are
2
/ 45565 m N p =
?
,
3
/ 6417 . 0 m kg =
?
? and
???? = 1.4, respectively. The indicated airspeed (in s m / ) is
(A) 6 . 157 (B) 6 . 162 (C) 0 . 172 (D) 3 . 182
Q.38
Consider a NACA 0012 aerofoil of chord c in a freestream with velocity
?
V at a non-zero positive
angle of attack ? . The average time-of-flight for a particle to move from the leading edge to the
trailing edge on the suction and pressure sides are
1
t and
2
t , respectively. Thin aerofoil theory
yields the velocity perturbation to the freestream as
(1 cos )
sin
V
? ?
?
?
+
on the suction side and as
(1 cos )
sin
V
? ?
?
?
+
? on the pressure side, where ? corresponds to the chordwise position,
( ) ? cos 1
2
? =
c
x . Then
21
tt ? is
(A)
( )
22
8
4
c
V
??
??
?
?
?
(B) 0
(C)
( )
2 2
4
4
? ?
??
?
?
V
c
(D)
( )
2 2
4
8
? ?
??
?
?
V
c
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
GATE 2015 AEROSPACE ? AE
AE 4/8
Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, ???? = 8 ???????? from the sea
level. The nozzle operates in
(A) under-expanded condition for ???? > 8 ????????
(B) under-expanded condition for ???? < 8 ????????
(C) sonic exit condition for ???? > 8 ????????
(D) unchoked condition for ???? < 8 ????????
Q. 26 ? Q. 55 carry two marks each.
Q.26
In the solution of 0 2
2
2
= + ? y
dx
dy
dx
y d
, if the values of the integration constants are identical and
one of the initial conditions is specified as 1 ) 0 ( = y , the other initial condition = ? ) 0 ( y _____.
Q.27
For ???? > 0, the general solution of the differential equation y
dx
dy
2 1 ? = asymptotically
approaches _______.
Q.28
For a parabola defined by
2
, 0, y ax bx c a = ++ ? the coordinates (, ) xy of the extremum are
(A)
?
?
?
?
?
?
?
?
?
+
?
0 ,
2
4
2
2
a
ac b
a
b
(B)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
2
4
,
2
2
(C)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
4
4
,
2
2
(D) ( ) c , 0
Q.29
The 2-D stress state at a point P in the x-y coordinate system is ?
60 50
50 ?40
? ???????????? . The magnitude
of the tangential stress (in ???????????? ) on a surface normal to the x-axis at P is _____.
Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of
100 ???? /mm
2
. Under this load, the volume of the cube shrinks by 0.05%. The Young's modulus of
the material, ???? = 300 ???????????? . The Poisson's ratio of the material is _____.
Q.31 A massless cantilever beam PQ has a solid square cross section (10 ???????? ? 10 ???????? ). This beam is
subjected to a load ???? through a rigid massless link at the point Q, as shown below (figure not to
scale). If the Young's modulus of the material ???? = 200 ???????????? , the deflection (in ???????? ) at point Q
is _____.
GATE 2015 AEROSPACE ? AE
AE 5/8
Q.32
An aircraft, with a wing loading
???? ???? = 500 ???? / ???? 2
, is gliding at ?
???? ???? ?
???????????? = 10 and ???? ???? = 0.69.
Considering the free stream density ???? ?
= 0.9 ???????? / ???? 3
, the equilibrium glide speed (in ???? / ???? )
is _____.
Q.33 For a thin flat plate at 2 degrees angle of attack, the pitching moment coefficient about the trailing
edge is _____.
Q.34 A satellite is to be transferred from its geostationary orbit to a circular polar orbit of the same radius
through a single impulse out-of-plane maneuver. The magnitude of the change in velocity required
is __________ times the magnitude of the escape velocity.
Q.35 A planetary probe is launched at a speed of 200 ???????? / ???? and at a distance of 71,400 ???????? from the
mass center of its nearest planet of mass 1.9 ? 10
28
???????? . The universal gravitational constant,
???? = 6.67 ? 10
?11
???? 3
???????? ???? 2
. The ensuing path of the probe would be
(A) elliptic (B) hyperbolic (C) parabolic (D) circular
Q.36 The velocity profile of an incompressible laminar boundary layer over a flat plate developing under
constant pressure is given by
( )
3
2
1
2
3
?
?
?
?
?
?
? =
?
? ?
y y
U
y u
. The freestream velocity s m U / 10 =
?
and
the dynamic viscosity of the fluid
s m
kg
5
10 8 . 1
?
? = ? . At a streamwise station where the boundary
layer thickness mm 5 = ? , the wall shear stress is _________ Pa
3
10
?
? .
Q.37
The Pitot tube of an aircraft registers a pressure
2
0
/ 54051 m N p = . The static pressure, density
and the ratio of specific heats of the freestream are
2
/ 45565 m N p =
?
,
3
/ 6417 . 0 m kg =
?
? and
???? = 1.4, respectively. The indicated airspeed (in s m / ) is
(A) 6 . 157 (B) 6 . 162 (C) 0 . 172 (D) 3 . 182
Q.38
Consider a NACA 0012 aerofoil of chord c in a freestream with velocity
?
V at a non-zero positive
angle of attack ? . The average time-of-flight for a particle to move from the leading edge to the
trailing edge on the suction and pressure sides are
1
t and
2
t , respectively. Thin aerofoil theory
yields the velocity perturbation to the freestream as
(1 cos )
sin
V
? ?
?
?
+
on the suction side and as
(1 cos )
sin
V
? ?
?
?
+
? on the pressure side, where ? corresponds to the chordwise position,
( ) ? cos 1
2
? =
c
x . Then
21
tt ? is
(A)
( )
22
8
4
c
V
??
??
?
?
?
(B) 0
(C)
( )
2 2
4
4
? ?
??
?
?
V
c
(D)
( )
2 2
4
8
? ?
??
?
?
V
c
GATE 2015 AEROSPACE ? AE
AE 6/8
Q.39 Air enters an aircraft engine at a velocity of 180 ???? / ???? with a flow rate of 94 ???????? / ???? . The engine
combustor requires 9.2 ???????? / ???? of air to burn 1 ???????? / ???? of fuel. The velocity of gas exiting from the
engine is 640 ???? / ???? . The momentum thrust (in ???? ) developed by the engine is
(A) 43241 (B) 45594 (C) 47940 (D) 49779
Q.40 A solid rocket motor is designed with a cylindrical end-burning propellant grain of length 1 ???? and
diameter 32 ???????? . The density of the propellant grain is 1750 ???????? / ???? 3
. The specific impulse of the
motor is 190 ???? and the acceleration due to gravity is 9.8 ???? / ???? 2
. If the propellant burns for a period
of 150 ???? , then the thrust (in ???? ) produced by the rocket motor is ________.
Q.41 A liquid propellant rocket has the following component masses:
Mass of payload kg 180 =
Mass of fuel kg 470 =
Mass of oxidizer kg 1170 =
Mass of structures kg 150 =
Mass of guidance systems kg 20 =
The effective exhaust velocity is 3136 ???? / ???? . The velocity increment (in ???????? / ???? ) of the rocket at
burnout, while operating in outer space, is ________.
Q.42 If all the eigenvalues of a matrix are real and equal, then
(A) the matrix is diagonalizable
(B) its eigenvectors are not necessarily linearly independent
(C) its eigenvectors are linearly independent
(D) its determinant is necessarily zero
Q.43
The value of the integral ( )dx x x x
?
+ + +
2
1
2 3
1 2 3 4 evaluated numerically using Simpson's rule with
one step is
(A) 26.5 (B) 26 (C) 25.5 (D) 25.3
Q.44 The following data is for a single degree of freedom system with viscous damping:
mass, ???? = 10 ???????? ; spring stiffness, ???? = 2.25 ???? / ???????? ;
damping coefficient, ???? = 0.0125 ???? ???? / ???????? .
The ratio of any two successive amplitudes is _____.
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
GATE 2015 AEROSPACE ? AE
AE 4/8
Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, ???? = 8 ???????? from the sea
level. The nozzle operates in
(A) under-expanded condition for ???? > 8 ????????
(B) under-expanded condition for ???? < 8 ????????
(C) sonic exit condition for ???? > 8 ????????
(D) unchoked condition for ???? < 8 ????????
Q. 26 ? Q. 55 carry two marks each.
Q.26
In the solution of 0 2
2
2
= + ? y
dx
dy
dx
y d
, if the values of the integration constants are identical and
one of the initial conditions is specified as 1 ) 0 ( = y , the other initial condition = ? ) 0 ( y _____.
Q.27
For ???? > 0, the general solution of the differential equation y
dx
dy
2 1 ? = asymptotically
approaches _______.
Q.28
For a parabola defined by
2
, 0, y ax bx c a = ++ ? the coordinates (, ) xy of the extremum are
(A)
?
?
?
?
?
?
?
?
?
+
?
0 ,
2
4
2
2
a
ac b
a
b
(B)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
2
4
,
2
2
(C)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
4
4
,
2
2
(D) ( ) c , 0
Q.29
The 2-D stress state at a point P in the x-y coordinate system is ?
60 50
50 ?40
? ???????????? . The magnitude
of the tangential stress (in ???????????? ) on a surface normal to the x-axis at P is _____.
Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of
100 ???? /mm
2
. Under this load, the volume of the cube shrinks by 0.05%. The Young's modulus of
the material, ???? = 300 ???????????? . The Poisson's ratio of the material is _____.
Q.31 A massless cantilever beam PQ has a solid square cross section (10 ???????? ? 10 ???????? ). This beam is
subjected to a load ???? through a rigid massless link at the point Q, as shown below (figure not to
scale). If the Young's modulus of the material ???? = 200 ???????????? , the deflection (in ???????? ) at point Q
is _____.
GATE 2015 AEROSPACE ? AE
AE 5/8
Q.32
An aircraft, with a wing loading
???? ???? = 500 ???? / ???? 2
, is gliding at ?
???? ???? ?
???????????? = 10 and ???? ???? = 0.69.
Considering the free stream density ???? ?
= 0.9 ???????? / ???? 3
, the equilibrium glide speed (in ???? / ???? )
is _____.
Q.33 For a thin flat plate at 2 degrees angle of attack, the pitching moment coefficient about the trailing
edge is _____.
Q.34 A satellite is to be transferred from its geostationary orbit to a circular polar orbit of the same radius
through a single impulse out-of-plane maneuver. The magnitude of the change in velocity required
is __________ times the magnitude of the escape velocity.
Q.35 A planetary probe is launched at a speed of 200 ???????? / ???? and at a distance of 71,400 ???????? from the
mass center of its nearest planet of mass 1.9 ? 10
28
???????? . The universal gravitational constant,
???? = 6.67 ? 10
?11
???? 3
???????? ???? 2
. The ensuing path of the probe would be
(A) elliptic (B) hyperbolic (C) parabolic (D) circular
Q.36 The velocity profile of an incompressible laminar boundary layer over a flat plate developing under
constant pressure is given by
( )
3
2
1
2
3
?
?
?
?
?
?
? =
?
? ?
y y
U
y u
. The freestream velocity s m U / 10 =
?
and
the dynamic viscosity of the fluid
s m
kg
5
10 8 . 1
?
? = ? . At a streamwise station where the boundary
layer thickness mm 5 = ? , the wall shear stress is _________ Pa
3
10
?
? .
Q.37
The Pitot tube of an aircraft registers a pressure
2
0
/ 54051 m N p = . The static pressure, density
and the ratio of specific heats of the freestream are
2
/ 45565 m N p =
?
,
3
/ 6417 . 0 m kg =
?
? and
???? = 1.4, respectively. The indicated airspeed (in s m / ) is
(A) 6 . 157 (B) 6 . 162 (C) 0 . 172 (D) 3 . 182
Q.38
Consider a NACA 0012 aerofoil of chord c in a freestream with velocity
?
V at a non-zero positive
angle of attack ? . The average time-of-flight for a particle to move from the leading edge to the
trailing edge on the suction and pressure sides are
1
t and
2
t , respectively. Thin aerofoil theory
yields the velocity perturbation to the freestream as
(1 cos )
sin
V
? ?
?
?
+
on the suction side and as
(1 cos )
sin
V
? ?
?
?
+
? on the pressure side, where ? corresponds to the chordwise position,
( ) ? cos 1
2
? =
c
x . Then
21
tt ? is
(A)
( )
22
8
4
c
V
??
??
?
?
?
(B) 0
(C)
( )
2 2
4
4
? ?
??
?
?
V
c
(D)
( )
2 2
4
8
? ?
??
?
?
V
c
GATE 2015 AEROSPACE ? AE
AE 6/8
Q.39 Air enters an aircraft engine at a velocity of 180 ???? / ???? with a flow rate of 94 ???????? / ???? . The engine
combustor requires 9.2 ???????? / ???? of air to burn 1 ???????? / ???? of fuel. The velocity of gas exiting from the
engine is 640 ???? / ???? . The momentum thrust (in ???? ) developed by the engine is
(A) 43241 (B) 45594 (C) 47940 (D) 49779
Q.40 A solid rocket motor is designed with a cylindrical end-burning propellant grain of length 1 ???? and
diameter 32 ???????? . The density of the propellant grain is 1750 ???????? / ???? 3
. The specific impulse of the
motor is 190 ???? and the acceleration due to gravity is 9.8 ???? / ???? 2
. If the propellant burns for a period
of 150 ???? , then the thrust (in ???? ) produced by the rocket motor is ________.
Q.41 A liquid propellant rocket has the following component masses:
Mass of payload kg 180 =
Mass of fuel kg 470 =
Mass of oxidizer kg 1170 =
Mass of structures kg 150 =
Mass of guidance systems kg 20 =
The effective exhaust velocity is 3136 ???? / ???? . The velocity increment (in ???????? / ???? ) of the rocket at
burnout, while operating in outer space, is ________.
Q.42 If all the eigenvalues of a matrix are real and equal, then
(A) the matrix is diagonalizable
(B) its eigenvectors are not necessarily linearly independent
(C) its eigenvectors are linearly independent
(D) its determinant is necessarily zero
Q.43
The value of the integral ( )dx x x x
?
+ + +
2
1
2 3
1 2 3 4 evaluated numerically using Simpson's rule with
one step is
(A) 26.5 (B) 26 (C) 25.5 (D) 25.3
Q.44 The following data is for a single degree of freedom system with viscous damping:
mass, ???? = 10 ???????? ; spring stiffness, ???? = 2.25 ???? / ???????? ;
damping coefficient, ???? = 0.0125 ???? ???? / ???????? .
The ratio of any two successive amplitudes is _____.
GATE 2015 AEROSPACE ? AE
AE 7/8
Q.45 Determine the correctness or otherwise of the following assertion [a] and reason [r]:
Assertion [a]: Aircraft directional static stability can be improved by moving the vertical tail
rearward.
Reason [r]: Moving the vertical tail rearward increases the moment arm from the tail aerodynamic
center to the aircraft center of gravity.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true and [r] is false
Q.46 Consider a 2-D blunt body in an incompressible fluid stream. The flow is irrotational and can be
modeled as a linear combination of a uniform flow and a line source (Rankine half body) as shown
below. Let s
be the distance of the line source from the front stagnation point. Let d be the
upstream distance from the stagnation point to the streamwise location (labeled below as P) where
the oncoming stream reaches 90% of its undisturbed velocity. Then = s d / _____.
Q.47 Following are the operational parameters of an axial compressor stage:
Air mass flow rate = 24 ???????? / ????
Static temperature of air at the rotor inlet = 278 ????
Velocity of air at the rotor inlet (zero whirl velocity) = 140 ???? / ????
Work done on the compressor rotor = 734 ????????
Isentropic efficiency of the compressor stage = 0.86
Ratio of specific heats = 1.4
Specific heat at constant pressure = 1.005 ???????? / ????????????
The stagnation pressure ratio across the axial compressor stage is ________.
Q.48 The thin rectangular tube shown below is made of a material with shear modulus, ???? = 80 ???????????? .
The shear flow is calculated based on the mid-thickness dimensions. If the free end is allowed to
twist no more than 0.0727 ???????????? , then the maximum torque (in ???????? ) which the tube can be subjected
to at its free end is _______.
s
d
uniform flow
line source
Rankine half body
P
FirstRanker.com - FirstRanker's Choice
GATE 2015 AEROSPACE ? AE
AE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1
The partial differential equation
2
2
0
u
u
tx
??
?
??
?
??
+ =
??
is
(A) linear and first order (B) linear and second order
(C) non-linear and first order (D) non-linear and second order
Q.2 The system of equations for the variables x and y
f y d x c
e y b x a
= +
= +
has a unique solution only if
(A) 0 ? ? c b d a (B) 0 ? ? d b c a
(C) d b c a + ? +
(D) d b c a ? ? ?
Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes
(A) non-oscillatory motion (B) random motion
(C) oscillatory and periodic motion (D) oscillatory and non-periodic motion
Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center.
The cantilever undergoes
(A) bending without twisting (B) bending and twisting
(C) neither bending nor twisting (D) twisting without bending
Q.5 The two non-zero principal stresses at a point in a thin plate are ???? 1
= 25 ???????????? and
???? 2
= ?25 ???????????? . The maximum shear stress (in ???????????? ) at this point is _____.
Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be
???? 1
and ?
1
, respectively. The density variation with altitude ( ???? versus h) in that layer is governed by
( ???? : specific gas constant, ???? : temperature, ???? ???? : acceleration due to gravity at sea level)
(A)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ? ? ?
1
)
(B)
???? ???? 1
= ???? ? ?
???? ???? ???????? ?( ?
1
? ?)
(C)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ? ? ?
1
)
(D)
???? ???? 1
= ???? ? ?
???????? ???? ???? ?( ?
1
? ?)
Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing,
with thin cambered airfoil section at small angles of attack, leads to
(A) a shift of the aerodynamic center and no shift of the center of pressure
(B) a shift of the center of pressure and no shift of the aerodynamic center
(C) shift of both the aerodynamic center and the center of pressure
(D) no shift either of the aerodynamic center or of the center of pressure
Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?
(A) Short period (B) Phugoid
(C) Dutch roll (D) Spiral
Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?
(A) NACA 0012 (B) NACA 2312 (C) NACA 23012 (D) Clarke Y profile
GATE 2015 AEROSPACE ? AE
AE 2/8
Q.10 The primary purpose of a trailing edge flap is to
(A) avoid flow separation
(B) increase
max , l
C
(C) reduce wave drag (D) reduce induced drag
Q.11 Which one of the following aero engines has the highest propulsive efficiency?
(A) Turbojet engine without afterburner (B) Turbojet engine with afterburner
(C) Turbofan engine (D) Ramjet engine
Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:
(A) increases linearly (B) decreases linearly
(C) is independent (D) increases nonlinearly
Q.13 A rocket engine produces a total impulse of 112 ???????? . ???? in a burn time period of 3.5 minutes with a
propellant mass flow rate of 0.25 ???????? / ???? . The effective exhaust velocity (in ???? / ???? ) of gas ejecting
from the engine is _____.
Q.14
The function x x y ? =
3
has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points
Q.15 A 0.5 ???????? mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness
of 5 ???? / ???????? . The static displacement (in ???????? ) of the mass is _____.
Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below
(Figures not to scale). Which pair of cases results in identical stress distribution at section S ? S
located far away from both ends?
[I]
[II]
[III]
[IV]
(A) I and II (B) II and III (C) III and IV (D) IV and I
GATE 2015 AEROSPACE ? AE
AE 3/8
Q.17 An aircraft in level and unaccelerated flight with a velocity of ???? ?
= 300 ???? / ???? requires a power of
9 ? 10
6
???? . If the aircraft weighs 1.5 ? 10
5
???? , the lift-to-drag ratio
???? ???? is _____.
Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _____.
Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and
incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the
biplane experiences
(A) a higher lift and a higher drag (B) a higher lift and a lower drag
(C) a lower lift and a lower drag (D) a lower lift and a higher drag
Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily.
As a result, the center of pressure of the aircraft
(A) shifts forward (B) shifts rearward
(C) does not shift (D) coincides with the neutral point
Q.21 Consider a wing of elliptic planform, with its aspect ratio ? ? AR . Its lift-curve slope,
=
? d
dC
L
_____.
Q.22
An ideal gas in a reservoir has a specific stagnation enthalpy of
0
h . The gas is isentropically
expanded to a new specific stagnation enthalpy of
0
2
h
and velocity u. The flow is one-dimensional
and steady. Then
2
0
u
h
= _____.
Q.23
The Reynolds number, Re is defined as
?
L U
?
where L is the length scale for a flow,
?
U is its
reference velocity and ? is the coefficient of kinematic viscosity. In the laminar boundary layer
approximation, comparison of the dimensions of the convection term
x
u
u
?
?
and the viscous term
2
2
x
u
?
?
? leads to the following relation between the boundary layer thickness ? and Re :
(A) Re ? ? (B) Re 1 ? ? (C) Re ? ?
(D) Re 1 ? ?
Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by
i
? ,
c
? ,
t
? and
n
? ,
respectively. Which one of the following is correct?
(A)
n t c i
? ? ? ? < < <
(B)
n c i t
? ? ? ? < < <
(C)
n i t c
? ? ? ? < < <
(D)
n t i c
? ? ? ? < < <
GATE 2015 AEROSPACE ? AE
AE 4/8
Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, ???? = 8 ???????? from the sea
level. The nozzle operates in
(A) under-expanded condition for ???? > 8 ????????
(B) under-expanded condition for ???? < 8 ????????
(C) sonic exit condition for ???? > 8 ????????
(D) unchoked condition for ???? < 8 ????????
Q. 26 ? Q. 55 carry two marks each.
Q.26
In the solution of 0 2
2
2
= + ? y
dx
dy
dx
y d
, if the values of the integration constants are identical and
one of the initial conditions is specified as 1 ) 0 ( = y , the other initial condition = ? ) 0 ( y _____.
Q.27
For ???? > 0, the general solution of the differential equation y
dx
dy
2 1 ? = asymptotically
approaches _______.
Q.28
For a parabola defined by
2
, 0, y ax bx c a = ++ ? the coordinates (, ) xy of the extremum are
(A)
?
?
?
?
?
?
?
?
?
+
?
0 ,
2
4
2
2
a
ac b
a
b
(B)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
2
4
,
2
2
(C)
?
?
?
?
?
?
?
? + ? ?
a
ac b
a
b
4
4
,
2
2
(D) ( ) c , 0
Q.29
The 2-D stress state at a point P in the x-y coordinate system is ?
60 50
50 ?40
? ???????????? . The magnitude
of the tangential stress (in ???????????? ) on a surface normal to the x-axis at P is _____.
Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of
100 ???? /mm
2
. Under this load, the volume of the cube shrinks by 0.05%. The Young's modulus of
the material, ???? = 300 ???????????? . The Poisson's ratio of the material is _____.
Q.31 A massless cantilever beam PQ has a solid square cross section (10 ???????? ? 10 ???????? ). This beam is
subjected to a load ???? through a rigid massless link at the point Q, as shown below (figure not to
scale). If the Young's modulus of the material ???? = 200 ???????????? , the deflection (in ???????? ) at point Q
is _____.
GATE 2015 AEROSPACE ? AE
AE 5/8
Q.32
An aircraft, with a wing loading
???? ???? = 500 ???? / ???? 2
, is gliding at ?
???? ???? ?
???????????? = 10 and ???? ???? = 0.69.
Considering the free stream density ???? ?
= 0.9 ???????? / ???? 3
, the equilibrium glide speed (in ???? / ???? )
is _____.
Q.33 For a thin flat plate at 2 degrees angle of attack, the pitching moment coefficient about the trailing
edge is _____.
Q.34 A satellite is to be transferred from its geostationary orbit to a circular polar orbit of the same radius
through a single impulse out-of-plane maneuver. The magnitude of the change in velocity required
is __________ times the magnitude of the escape velocity.
Q.35 A planetary probe is launched at a speed of 200 ???????? / ???? and at a distance of 71,400 ???????? from the
mass center of its nearest planet of mass 1.9 ? 10
28
???????? . The universal gravitational constant,
???? = 6.67 ? 10
?11
???? 3
???????? ???? 2
. The ensuing path of the probe would be
(A) elliptic (B) hyperbolic (C) parabolic (D) circular
Q.36 The velocity profile of an incompressible laminar boundary layer over a flat plate developing under
constant pressure is given by
( )
3
2
1
2
3
?
?
?
?
?
?
? =
?
? ?
y y
U
y u
. The freestream velocity s m U / 10 =
?
and
the dynamic viscosity of the fluid
s m
kg
5
10 8 . 1
?
? = ? . At a streamwise station where the boundary
layer thickness mm 5 = ? , the wall shear stress is _________ Pa
3
10
?
? .
Q.37
The Pitot tube of an aircraft registers a pressure
2
0
/ 54051 m N p = . The static pressure, density
and the ratio of specific heats of the freestream are
2
/ 45565 m N p =
?
,
3
/ 6417 . 0 m kg =
?
? and
???? = 1.4, respectively. The indicated airspeed (in s m / ) is
(A) 6 . 157 (B) 6 . 162 (C) 0 . 172 (D) 3 . 182
Q.38
Consider a NACA 0012 aerofoil of chord c in a freestream with velocity
?
V at a non-zero positive
angle of attack ? . The average time-of-flight for a particle to move from the leading edge to the
trailing edge on the suction and pressure sides are
1
t and
2
t , respectively. Thin aerofoil theory
yields the velocity perturbation to the freestream as
(1 cos )
sin
V
? ?
?
?
+
on the suction side and as
(1 cos )
sin
V
? ?
?
?
+
? on the pressure side, where ? corresponds to the chordwise position,
( ) ? cos 1
2
? =
c
x . Then
21
tt ? is
(A)
( )
22
8
4
c
V
??
??
?
?
?
(B) 0
(C)
( )
2 2
4
4
? ?
??
?
?
V
c
(D)
( )
2 2
4
8
? ?
??
?
?
V
c
GATE 2015 AEROSPACE ? AE
AE 6/8
Q.39 Air enters an aircraft engine at a velocity of 180 ???? / ???? with a flow rate of 94 ???????? / ???? . The engine
combustor requires 9.2 ???????? / ???? of air to burn 1 ???????? / ???? of fuel. The velocity of gas exiting from the
engine is 640 ???? / ???? . The momentum thrust (in ???? ) developed by the engine is
(A) 43241 (B) 45594 (C) 47940 (D) 49779
Q.40 A solid rocket motor is designed with a cylindrical end-burning propellant grain of length 1 ???? and
diameter 32 ???????? . The density of the propellant grain is 1750 ???????? / ???? 3
. The specific impulse of the
motor is 190 ???? and the acceleration due to gravity is 9.8 ???? / ???? 2
. If the propellant burns for a period
of 150 ???? , then the thrust (in ???? ) produced by the rocket motor is ________.
Q.41 A liquid propellant rocket has the following component masses:
Mass of payload kg 180 =
Mass of fuel kg 470 =
Mass of oxidizer kg 1170 =
Mass of structures kg 150 =
Mass of guidance systems kg 20 =
The effective exhaust velocity is 3136 ???? / ???? . The velocity increment (in ???????? / ???? ) of the rocket at
burnout, while operating in outer space, is ________.
Q.42 If all the eigenvalues of a matrix are real and equal, then
(A) the matrix is diagonalizable
(B) its eigenvectors are not necessarily linearly independent
(C) its eigenvectors are linearly independent
(D) its determinant is necessarily zero
Q.43
The value of the integral ( )dx x x x
?
+ + +
2
1
2 3
1 2 3 4 evaluated numerically using Simpson's rule with
one step is
(A) 26.5 (B) 26 (C) 25.5 (D) 25.3
Q.44 The following data is for a single degree of freedom system with viscous damping:
mass, ???? = 10 ???????? ; spring stiffness, ???? = 2.25 ???? / ???????? ;
damping coefficient, ???? = 0.0125 ???? ???? / ???????? .
The ratio of any two successive amplitudes is _____.
GATE 2015 AEROSPACE ? AE
AE 7/8
Q.45 Determine the correctness or otherwise of the following assertion [a] and reason [r]:
Assertion [a]: Aircraft directional static stability can be improved by moving the vertical tail
rearward.
Reason [r]: Moving the vertical tail rearward increases the moment arm from the tail aerodynamic
center to the aircraft center of gravity.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true and [r] is false
Q.46 Consider a 2-D blunt body in an incompressible fluid stream. The flow is irrotational and can be
modeled as a linear combination of a uniform flow and a line source (Rankine half body) as shown
below. Let s
be the distance of the line source from the front stagnation point. Let d be the
upstream distance from the stagnation point to the streamwise location (labeled below as P) where
the oncoming stream reaches 90% of its undisturbed velocity. Then = s d / _____.
Q.47 Following are the operational parameters of an axial compressor stage:
Air mass flow rate = 24 ???????? / ????
Static temperature of air at the rotor inlet = 278 ????
Velocity of air at the rotor inlet (zero whirl velocity) = 140 ???? / ????
Work done on the compressor rotor = 734 ????????
Isentropic efficiency of the compressor stage = 0.86
Ratio of specific heats = 1.4
Specific heat at constant pressure = 1.005 ???????? / ????????????
The stagnation pressure ratio across the axial compressor stage is ________.
Q.48 The thin rectangular tube shown below is made of a material with shear modulus, ???? = 80 ???????????? .
The shear flow is calculated based on the mid-thickness dimensions. If the free end is allowed to
twist no more than 0.0727 ???????????? , then the maximum torque (in ???????? ) which the tube can be subjected
to at its free end is _______.
s
d
uniform flow
line source
Rankine half body
P
GATE 2015 AEROSPACE ? AE
AE 8/8
Q.49 A 200 ???????? long simply-supported column has a 5 ???????? ? 10 ???????? rectangular cross section. The
Young's modulus of the material, ???? = 200 ???????????? . Assuming a factor of safety of 2.5 corresponding
to the buckling load, the maximum load (in ???? ) the column can support in compression is _______.
Q.50 For a level flight at cruise altitude, ???? ???? = 0.018 with drag coefficient at zero lift, ???? ???? ,0
= 0.015.
For a 30? climb at the same altitude and speed, ???? ???? = _____ ? 10
?3
.
Q.51
An aircraft is flying with inertial ground and wind speeds of v
?
???? ???? = (100, 5, 5) ???? / ???? and
v
?
???? ???? = (0, ?5, ?10) ???? / ???? , respectively, as expressed in the body frame. The corresponding sideslip
angle (in degrees) is
(A) 0 (B) 5.65 (C) 8.49 (D) 9.54
Q.52 The elliptical area swept by a satellite is 5.6 ? 10
9
???????? 2
in one full orbit. Its angular speed is
observed to be 0.00125 ???????????? / ???? when it is at a distance of 7,200 ???????? from the center of mass of its
primary. Its orbital period (in Earth days) is _______.
Q.53
For a normal shock, the relation between the upstream Mach number (
1
M ) and the downstream
Mach number (
2
M ) is given by
( )
? ?
?
? +
+ ?
=
1 2
2 1
2
1
2
1
2
2
M
M
M . For an ideal gas with 4 . 1 = ? , the
asymptotic value of the downstream Mach number is _______.
Q.54 A centrifugal air compressor is operating at the following conditions:
Inlet stagnation temperature K 288 =
Inlet stagnation pressure bar 15 . 1 =
Exit stagnation temperature K 454 =
Exit stagnation pressure bar 8 . 4 =
The energy loss due to non-isentropic compression per unit mass of flowing air (ratio of specific
heats, 4 . 1 = ? and specific heat at constant pressure, kgK kJ C
p
/ 005 . 1 = ) is ______ . / kg kJ
Q.55
Hot gas (ratio of specific heats, 33 . 1 = ? ) at a temperature of K 1450 enters into an axial turbine
and expands isentropically. Assume that the kinetic energy of the gas across the turbine is
negligible. If the ratio of inlet to outlet pressures of the turbine is 5 . 9 , then the temperature (in ???? )
of gas exiting the turbine is _______.
FirstRanker.com - FirstRanker's Choice
This post was last modified on 19 December 2019