GATE AE 2008 Question Paper & Solutions

Verbal Aptitude

The function defined by f(x) = sin x, x<0 = 0, x = 0 = 3х , x > 0

Verbal Aptitude

The product of the eigenvalues of the matrix [1 0 0 2 1 [1 1 -3| is

Quantitative Aptitude

4 (B) 0 (C) -6 (D) -9 Which of the following equations is a LINEAR ordinary differential equation?

Analytical & Spatial Aptitude

(C) d'% +x dy + 2y =0 (D) dy) dx + *У + 2y =0 To transfer a satellite from an elliptical orbit to a circular orbit having radius equal to the apogee distance of the elliptical orbit, the speed of the satellite should be

Analytical & Spatial Aptitude

increased at the apogee (B) decreased at the apogee (C) increased at the perigee (D) decreased at the perigee The service ceiling of a transport aircraft is defined as the altitude

Verbal Aptitude

that is halfway between sea-level and absolute ceiling (B) at which it can cruise with one engine operational (C) at which its maximum rate of climb is zero (D) at which its maximum rate of climb is 0.508 m/s Q.6 The drag of an aircraft in steady climbing flight at a given forward speed is

Quantitative Aptitude

In steady, level turning flight of an aircraft at a load factor 'n', the ratio of the horizontal component of lift and aircraft weight is

Quantitative Aptitude

equivalent airspeed and lift coefficient (C) equivalent airspeed and altitude (B) altitude and lift coefficient (D) lift coefficient and aircraft mass Q.9 The maximum thickness to chord ratio for the NACA 24012 airfoil is

Verbal Aptitude

0.5 (B) 1 (С) п (D) ∞0 Q.11 An irrotational and inviscid flow can become rotational on passing through a

Analytical & Spatial Aptitude

trim drag (C) induced drag (B) skin friction drag (D) wave drag Q.13 The degree of reaction of an impulse turbine is

Linear Algebra

1 (B) 0.75 (C) 0.5 (D) 0 Q.14 In a convergent-divergent (CD) nozzle of a rocket motor, the wall heat flux is maximum at

Linear Algebra

the exit of the divergent portion of the CD nozzle (B) the entry to the convergent portion of the CD nozzle (C) the throat of the CD nozzle (D) the mid-length of the divergent portion of the CD nozzle Q.15 In a scramjet engine, the Mach number at the entry to the combustion chamber is around

Calculus

0 (B) 0.3 (C) 2 (D) 6 Q.16 DB denotes double base solid propellant. LOX-RP1 denotes liquid oxygen - kerosene combination. LOX-LH2 denotes liquid oxygen - hydrogen combination. The correct order of increasing specific impulse is

Differential Equations

DB < LOX-RP1 < LOX-LH2 (B) LOX-RP1 < DB < LOX-LH2 (C) LOX-LH2 < DB < LOX-RP1 (D) DB < LOX-LH2 < LOX-RP1 Q.17 In the absence of body moments, the symmetry of the stress tensor is derived from

Numerical Methods

2008 MAIN PAPER - AB Q.18 In a 3-D orthotropic material, the number of elastic constants in linear stress-strain relationship is (D) 21

Basic Fluid Mechanics

3 (B) 5 (C) 9 Q.19 The compatibility conditions in theory of elasticity ensure that

Airfoil & Wing Theory

In a spring-mass-damper single degree of freedom system, the mass is 2 kg and the undamped natural frequency is 20 Hz. The critical damping constant of the system is

Compressible Flow & Shocks

Which of the following quantities remains constant for a satellite in an elliptical orbit around the earth?

Compressible Flow & Shocks

A planet is observed to be at its slowest when it is at a distance r, from the sun and at its fastest when it is at a distance r2 from the sun. The eccentricity e of the planet's orbit is given by

Wind Tunnel Testing & Instrumentation

The value of the line integral (x dy - y dx) taken anticlockwise along a circle of unit radius 2л is

Atmospheric Flight Mechanics

Q.27 Suppose the non-constant functions F(x) and G(t) satisfy d'F dr + p'F= 0, dG dt +c p'G=0, where p and c are constants. Then the function u(x,t) = F(x)G(t) definitely satisfies d'u

Atmospheric Flight Mechanics

no solution (C) two solutions (B) a unique solution (D) infinite solutions Q.29 The function f(x) = x2 - -5x+6

Static Stability & Control

has its maximum value at x = 2.0 (B) has its maximum value at x = 2.5 (C) is increasing on the interval (2.0, 2.5) (D) is increasing on the interval (2.5, 3.0) Q.30 Let Y(s) denote the Laplace transform L(y(t)) of the function y(t) = cosh(at) sin(at) . Then

Dynamic Stability

=sY(s), L(ty(t)) = - ds (C) L -, L(t y(t)) = Y(s -1) (D) L dy = sY(s), L(ty(t)) = e*Y(s) Q.31 The velocity required for a spacecraft to escape earth's gravitational field depends on

Space Dynamics & Orbital Mechanics

MAIN PAPER - AB Q.32 The figure below shows the variation of Cm versus a for an aircraft for three combinations of elevator deflections and locations of centre of gravity. In the figure, lines P and Q are parallel, while lines Q and R have the same intercept on the Cm axis. P Q R Which of the following statements is true?

Thermodynamic Cycles of Gas Turbines

Which of the following statements is TRUE as the altitude increases in stratosphere of International Standard Atmosphere?

Thermodynamic Cycles of Gas Turbines

Temperature increases and dynamic viscosity decreases. (B) Temperature remains constant and pressure increases. (C) Temperature decreases and sound speed decreases. (D) Temperature remains constant and density decreases. Q.34 Which of the following statements is TRUE?

Inlets, Combustors & Nozzles

Wing dihedral reduces roll stability while a low wing increases roll stability. (B) Wing dihedral increases roll stability while a low wing reduces roll stability. (C) Wing dihedral, as well as low wing reduces roll stability. (D) Wing dihedral, as well as low wing increases roll stability. Q.35 An aircraft has a level flight stalling speed of 60 m/s EAS (equivalent air speed). As per the V-n diagram, what is the minimum speed at which it should be designed to withstand the maximum vertical load factor of 9?

Compressors and Turbines

P: Short period mode 1: Coupled roll-yaw oscillations Q: Wing rock 2: Angle of attack remains constant R: Phugoid mode 3: Roll oscillations S: Dutch roll 4: Speed remains constant

Rocket Propulsion

An aircraft is cruising at a true air speed (TAS) of 100 m/s under ISA conditions, at an altitude at which the density of free stream is 0.526 kg/m'. What will be the equivalent air speed (EAS)?

Strength of Materials & Elasticity

2008 MAIN PAPER - AE Q.38 In the definition of the aircraft Euler angles @ (roll), ® (pitch), and v (yaw), the correct sequence of rotations required to make the inertial frame coincide with the aircraft body frame is

Strength of Materials & Elasticity

first y about z axis, second 0 about y axis, third @ about x axis (B) first 0 about y axis, second o about x axis, third y about z axis (C) first p about x axis, second 0 about y axis, third y about z axis (D) first y about z axis, second p about x axis, third 0 about y axis Q.39 To maximize range of a jet engine aircraft, it should be flown at a velocity that maximizes

Thin-Walled Structures

C,/CD (B) CL°S/Cp (C) CL 5/Co (D) C//Co Q.40 The primary function of the fin in the vertical tail of an aircraft is to provide

Structural Dynamics & Aeroelasticity

yaw control (B) yaw stability (C) roll damping (D) roll stability Q.41 An aircraft requires the trailing edge of the elevator to be deflected upwards from its initial position to lower the trim speed. Which of the following statements about the static stick-fixed stability of this aircraft is true?

Aerospace Materials & Fatigue

The aircraft is unstable. (B) The aircraft is neutrally stable. (C) The aircraft is stable. (D) The stability of the aircraft cannot be determined from the given information. Q.42 Which of the following statements is true for an aircraft flying at a low angle of attack?

Linear Algebra

Consider 2-D flow with stream function y = along a unit circle centered at (x = 0, y = 0) is

Calculus

2m (В) т (C) 72/60 (D) 77/90 Q.45 Consider steady, inviscid flow in a convergent-divergent (CD) nozzle, with a normal shock in the divergent portion. The static pressure along the nozzle downstream of the normal shock

Differential Equations

MAIN PAPER - AE 2008 Q.47 If the flow Mach number in a turbulent boundary layer over a flat plate is increased keeping the Reynolds number unchanged, the skin friction coefficient Cr

Numerical Methods

In supersonic wind-tunnel design, an oblique shock diffuser is preferred over a normal shock diffuser because

Airfoil & Wing Theory

it reduces total pressure loss (B) the flow is slowed down more rapidly (C) the flow is accelerated more rapidly (D) it increases total pressure loss Q.49 The variation of downwash along the span of an untwisted wing of elliptic planform is

Basic Fluid Mechanics

Flow past an airfoil is to be modeled using a vortex sheet. The strength of the vortex sheet at the trailing edge will be

Compressible Flow & Shocks

0 (B) 1 (C) 27 (D) co Q.51 Consider a 2-D body in supersonic flow with an attached oblique shock as shown below M. > 1 An increase in free stream Mach number M. will cause the oblique shock wave to

Airfoil & Wing Theory

move closer to the body (B) move away from the body (C) detach from the body (D) become a normal shock Q.52 The geometrical features of a supereritical airfoil are

Compressible Flow & Shocks

rounded leading edge, flat upper surface and high camber at the rear (B) sharp leading edge, curved upper surface and high camber at the rear (C) rounded leading edge, curved upper surface and no camber at the rear D) sharp leading edge, flat upper surface and no camber at the rear Q.53 Which one of the following high lift device results in higher stalling angle?

Basic Fluid Mechanics

split flap (B) Fowler flap (C) plain flap (D) leading edge flap Q.54 A turbofan engine has a bypass ratio of 5 and a total mass flow rate of 120 kg/s. The mass flow rate through the bypass duct is

Airfoil & Wing Theory

2008 MAIN PAPER - AE Q.55 A turbojet engine is operating with afterburner off. If the afterburner is switched on, then

Atmospheric Flight Mechanics

both thrust and sfc decrease (B) thrust increases and sfc decreases (C) thrust decreases and sfe increases (D) both thrust and sfe increase Q.56 A centrifugal compressor operates with a tip blade speed of 340 m/s. The air leaves the impeller with a radial velocity of 88 m/s. If the slip factor is 0.85, the relative velocity at the blade tip is

Atmospheric Flight Mechanics

101.7 m/s (B) 120.3 m/s (C) 132.6 m/s (D) 135.8 m/s Q.57 An ideal ramjet engine is flying at a Mach number M. The exhaust gas static temperature at the outlet of the nozzle is T.. The ambient static temperature is Ta. Gas constant R and specific heat ratio y do not vary through the ramjet. Assuming that nozzle exhaust static pressure is equal to the ambient pressure and fuel air ratio f < <1, the thrust per unit mass flow rate is

Static Stability & Control

(C) M JYRT, (D) M JYRT, T. T. Q.58 A 50 percent degree of reaction axial flow turbine operates with a mean blade speed of 180 m/s. The flow leaves the stator and enters the rotor at an angle of 60 degrees to the axial direction. The axial velocity is 150 m/s, and remains constant throughout the stage. The turbine power per unit mass flow is

Dynamic Stability

(C) (D) y-1 2YRT. y +1 Q.60 Air enters the combustor of a gas turbine engine at total temperature of 500 K and leaves the combustor at total temperature of 1800 K. If cp remains constant at 1.005 kJ/kgK and heating value of the fuel used is 44 MJ/kg, the fuel to air ratio is

Space Dynamics & Orbital Mechanics

The initial temperature sensitivity of burn rate of a solid rocket motor propellant is positive. If the initial temperature increases then

Space Dynamics & Orbital Mechanics

An aircraft is cruising at a Mach number of 0.8 at an altitude where the ambient static pressure is 95 kPa. The diffuser exit total pressure is 140 kPa. Assuming there is no change in the specific heat at constant pressure across the diffuser, and ratio of specific heats is 1.4, the adiabatic efficiency of the intake is

Thermodynamic Cycles of Gas Turbines

Q.64 A column of solid circular cross-section and length L can have various end conditions. Choose the correct set that matches the end conditions (listed in Group I) with the corresponding effective length for buckling (listed in Group II). Group I (end conditions) (P) one end built-in and other end free Q) both ends pinned (R) both ends built-in (S) one end built-in and other end pinned

Thermodynamic Cycles of Gas Turbines

A thin walled tube of circular cross-section with mean radius r has a central web which divides it into two symmetric cells as shown. A torque M is acting on the section. The shear flow q in the central web is M

Inlets, Combustors & Nozzles

shown. A bending moment M, is acting on the cross-section. The ratio of the magnitude of normal stress in the top booms to that of the bottom boom is 1cm I Cl 2 cm 2 cm -- Area = 0.2cmª - Area = 0.1cm'

Compressors and Turbines

5/11 (B) 2/5 (C) 1 (D) 5/2 Q.68 An engineer is asked to test a system which can be idealized as SDOF (single degree of freedom) with viscous damping. A frequency response test was conducted and it is found that the quality factor Q is equal to 10. What will be the logarithmic decrement if a free vibration test is performed?

Inlets, Combustors & Nozzles

Pxy® 4c* 3 Рху 4c where P is a constant. x L The above stress function pertains to a

Rocket Propulsion

Tmax = 7c MPa (B) Tmax = 10c MPa (C) Tmax = 13c MPa (D) Tmax = 15c MPa Q.73 The maximum value of c for safe loading of the structure, based on von-Mises failure criterion is

Compressors and Turbines

2008 MAIN PAPER - AE Common Data for Questions 74 and 75: A liquid rocket engine with oxidizer to fuel ratio of 5:1 produces a thrust of 1 MN. The initial mass of the rocket engine is 100,000 kg and its mass at burn out is 10,000 kg. The characteristic velocity C' and thrust coefficient Cp for the engine are 2386 m/s and 1.4, respectively. Q.74 The mass flow rate of fuel is

Strength of Materials & Elasticity

300.3 kg/s (B) 269.5 kg/s (C) 87.4 kg/s (D) 49.9 kg/s Q.75 Neglecting gravity and drag effects, if the initial velocity of the liquid rocket engine is 2.5 km/s, the velocity of the rocket at burnout is

Thin-Walled Structures

Jf(x) dx on the interval [a, b]. Q.76 Which of the following gives the correct formula for Simpson's rule? (1) (в=а). S(b) + f a+0 (B) The percentage error (with respect to the exact solution) in estimation of the integral §x' dr using Simpson's rule is

Thin-Walled Structures

5.3 (B) 3.5 (C) 2.8 (D) 0 Statement for Linked Answer Questions 78 and 79: An aircraft has a zero-lift drag coefficient CDo = 0.0223, wing aspect ratio ARw = 10.0, and Oswald's efficiency factor e = 0.7 Q.78 The thrust required for steady level flight will be minimum when the aircraft operates at a lift coefficient of

Structural Dynamics & Aeroelasticity

0.65 (B) 0.70 (C) 0.75 (D) 0.80 Q.79 The glide angle that results in maximum range in a power-off glide is

Aerospace Materials & Fatigue

1.82 degrees (B) 2.68 degrees (C) 3.64 degrees (D) 5.01 degrees Statement for Linked Answer Questions 80 and 81: Consider an untwisted wing of elliptical planform in inviscid incompressible irrotational flow at an angle of attack of 4 degrees. The wing aspect ratio is 7 and the zero lift angle of attack is - 2 degrees. Q.80 The wing lift coefficient C, is

Aerospace Materials & Fatigue

0.66 (B) 0.51 (C) 0.44 (D) 0.34 Q.81 The induced drag coefficient of the wing CDi is