GATE AE 2008 Question Paper & Solutions

Quantitative Aptitude

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

Quantitative Aptitude

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

Quantitative Aptitude

LINEAR ordinary differential equation?

Quantitative Aptitude

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

Quantitative Aptitude

The service ceiling of a transport aircraft is defined as the altitude

Quantitative Aptitude

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

NACA 24012 airfoil is

Quantitative Aptitude

An irrotational and inviscid flow can become rotational on passing through a

Quantitative Aptitude

The degree of reaction of an impulse turbine is

Rocket Propulsion

In a convergent-divergent (CD) nozzle of a rocket motor, the wall heat flux is maximum at

Compressible Flow & Shocks

Mach number at the entry to the combustion chamber is around

Rocket Propulsion

The correct order of increasing specific impulse is

Strength of Materials & Elasticity

In the absence of body moments, the symmetry of the stress tensor is derived from

Strength of Materials & Elasticity

In a 3-D orthotropic material, the number of independent elastic constants in the linear stress-strain relationship is:

Strength of Materials & Elasticity

The compatibility conditions in theory of elasticity ensure that

Structural Dynamics & Aeroelasticity

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

Space Dynamics & Orbital Mechanics

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

Space Dynamics & Orbital Mechanics

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

Linear Algebra

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

Atmospheric Flight Mechanics

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

The function f(x) = x^2 - -5x+6

Static Stability & Control

Suppose the non-constant functions F(x) and G(t) satisfy d^2 F/dx^2 + p^2 F = 0 and dG/dt + c^2 p^2 G = 0, where p and c are constants. Then the function u(x,t) = F(x)G(t) definitely satisfies:

Space Dynamics & Orbital Mechanics

The velocity required for a spacecraft to escape earth's gravitational field depends on

Static Stability & Control

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?

Atmospheric Flight Mechanics

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

Compressors and Turbines

Which of the following statements is TRUE regarding aircraft stability?

Atmospheric Flight Mechanics

V-n diagram, what is the minimum speed at which it should be designed to withstand the maximum vertical load factor of 9?

Dynamic Stability

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

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

Atmospheric Flight Mechanics

To maximize range of a jet engine aircraft, it should be flown at a velocity that maximizes

Thin-Walled Structures

The primary function of the fin in the vertical tail of an aircraft is to provide

Static Stability & Control

Which of the following statements about the static stick-fixed stability of this aircraft is true?

Aerospace Materials & Fatigue

Which of the following statements is true for an aircraft flying at a low angle of attack?

Basic Fluid Mechanics

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

Compressible Flow & Shocks

The static pressure along the nozzle downstream of the normal shock

Compressible Flow & Shocks

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

Compressible Flow & Shocks

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

Airfoil & Wing Theory

The variation of downwash along the span of an untwisted wing of elliptic planform is

Airfoil & Wing Theory

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

M. will cause the oblique shock wave to

Airfoil & Wing Theory

The geometrical features of a supercritical airfoil are:

Compressible Flow & Shocks

Which one of the following high lift device results in higher stalling angle?

Basic Fluid Mechanics

The mass flow rate through the bypass duct is

Thermodynamic Cycles of Gas Turbines

A turbojet engine is operating with afterburner off. If the afterburner is switched on, then

Atmospheric Flight Mechanics

If the slip factor is 0.85, the relative velocity at the blade tip is

Inlets, Combustors & Nozzles

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

Compressors and Turbines

The turbine power per unit mass flow is

Dynamic Stability

MJ/kg, the fuel to air ratio is

Rocket Propulsion

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

Compressible Flow & Shocks

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

Strength of Materials & Elasticity

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

Thin-Walled Structures

A thin-walled tube of circular cross-section with mean radius $r$ and wall thickness $t$ has a central vertical web of thickness $t$ which divides it into two equal semicircular cells. Under a twisting moment $T$, the shear flow in the outer walls and central web are related by:

Thin-Walled Structures

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'

Structural Dynamics & Aeroelasticity

What will be the logarithmic decrement if a free vibration test is performed?

Strength of Materials & Elasticity

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

Rocket Propulsion

The maximum value of c for safe loading of the structure, based on von-Mises failure criterion is

Compressors and Turbines

The mass flow rate of fuel is

Rocket Propulsion

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

Numerical Methods

The percentage error (with respect to the exact solution) in estimation of the integral ∫ x^3 dx from 0 to 1 using Simpson's rule is:

Atmospheric Flight Mechanics

The thrust required for steady level flight will be minimum when the aircraft operates at a lift coefficient of

Atmospheric Flight Mechanics

The glide angle that results in maximum range in a power-off glide is

Airfoil & Wing Theory

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. The wing lift coefficient C_L is:

Airfoil & Wing Theory

For the same elliptic wing of aspect ratio 7 at 4 degrees angle of attack with zero-lift angle of -2 degrees, the induced drag coefficient of the wing C_Di is: