GATE AE 2012 Question Paper & Solutions

Verbal Aptitude

The constraint A2 = A on any square matrix A is satisfied for

Verbal Aptitude

The general solution of the differential equation 2 2 20dy d y ydt dt+ -= is

Quantitative Aptitude

An aircraft in trimmed condition has zero pitching moment at

Analytical & Spatial Aptitude

In an aircraft, constant roll rate can be produced using ailerons by applying

Analytical & Spatial Aptitude

For a symmetric airfoil, the lift coefficient for zero degree angle of attack is

Verbal Aptitude

The critical Mach number of an airfoil is attained when

Quantitative Aptitude

The shadowgraph flow visualization technique depends on

Quantitative Aptitude

The Hohmann ellipse used as earth-Mars transfer orbit has

Verbal Aptitude

The governing equation for the static transverse deflection of a beam under an uniformly distributed load, according to Euler-Bernoulli (engineering) beam theory, is a

Analytical & Spatial Aptitude

The Poisson's ratio,ν of most aircraft grade metallic alloys has values in the range:

Linear Algebra

The value of k for which the system of equations 21 ; 28 3xy k z x k yz+ += ++= has no solution is

Linear Algebra

If ()ut is a unit step function, the solution of the differential equation 2 2 ()dxmk x u tdt += in Laplace domain is

Calculus

The general solution of the differential equation 20dy ydx- = is

Differential Equations

During the ground roll manoeuvre of an aircraft, the force(s) acting on it parallel to the direction of motion

Numerical Methods

An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is reached at the same speed, the new rate of climb is

Basic Fluid Mechanics

In an aircraft, the dive manoeuvre can be initiated by:

Airfoil & Wing Theory

In an aircraft, elevator control effectiveness determines

Compressible Flow & Shocks

The Mach angle for a flow at Mach 2.0 is

Compressible Flow & Shocks

For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is (where CL is the lift coefficient)

Wind Tunnel Testing & Instrumentation

Bernoulli's equation is valid under steady state

Atmospheric Flight Mechanics

The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is

Atmospheric Flight Mechanics

The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is

Static Stability & Control

A rocket is to be launched from the bottom of a very deep crater on Mars for earth return. The specific impulse of the rocket, measured in seconds, is to be normalized by the acceleration due to gravity at

Dynamic Stability

In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary carriers of

Space Dynamics & Orbital Mechanics

The logarithmic decrement measured for a viscously damped single degree of freedom system is 0.125. The value of the damping factor in % is closest to

Thermodynamic Cycles of Gas Turbines

The integration 1 3 0 x dx∫ computed using trapezoidal rule with 4n= intervals is ____.

Thermodynamic Cycles of Gas Turbines

An aircraft has a steady rate of climb of 300 m/s at sea level and 150 m/s at 2500 m altitude. The time taken (in sec) for this aircraft to climb from 500 m altitude to 3000 m altitude is ____.

Inlets, Combustors & Nozzles

An airfoil generates a lift of 80 N when operating in a freestream flow of 60 m/s. If the ambient pressure and temperature are 100 kPa and 290 K respectively (specific gas constant is 287 J/kg-K), the circulation on the airfoil in m 2/s is ____.

Compressors and Turbines

A rocket motor has combustion chamber temperature of 2600 K and the products have molecular weight of 25 g/mol and ratio of specific heats 1.2. The universal gas constant is 8314 J/kg-mole-K. The value of theoretical c* (in m/s) is ____.

Rocket Propulsion

The mode shapes of an un-damped two degrees of freedom system are {}10 . 5 T and {}10 . 6 7 5 T - . The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of {}21 T (in mm) and zero initial velocities is ____. 2012 AEROSPACE ENGINEERING - AE AE 5/12 Questions Q.31 to Q.55 are multiple choice type.

Strength of Materials & Elasticity

The nth derivative of the function 1 3y x= + is

Strength of Materials & Elasticity

The volume of a solid generated by rotating the region between semi-circle 211y x=- - and straight line y = 1, about x axis, is

Thin-Walled Structures

One eigenvalue of the matrix 271 0 522 5 16 5 A ⎡ ⎤ ⎢ ⎥=⎢ ⎥ ⎢ ⎥⎣ ⎦ is - 9.33. One of the other eigenvalues is

Structural Dynamics & Aeroelasticity

If an aircraft takes off with 10% less fuel in comparison to its standard configuration, its range is

Aerospace Materials & Fatigue

An aircraft has an approach speed of 144 kmph with a descent angle of 6.6 o. If the aircraft load factor is 1.2 and constant deceleration at touch down is 0.25 g ( g = 9.81 m/s 2), its total landing distance approximately over a 15 m high obstacle is

Linear Algebra

An aircraft is trimmed straight and level at true air speed (TAS) of 100 m/s at standard sea level (SSL). Further, pull of 5 N holds the speed at 90 m/s without re-trimming at SSL (air density = 1.22 kg/m3). To fly at 3000 m altitude (air density = 0.91 kg/m 3) and 120 m/s TAS without re-trimming, the aircraft needs

Calculus

An oblique shock wave with a wave angle β is generated from a wedge angle of θ . The ratio of the Mach number downstream of the shock to its normal component is

Differential Equations

In a closed-circuit supersonic wind tunnel, the c onvergent-divergent (C-D) nozzle and test section are followed by a C-D diffuser to swallow the starting shock. Here, we should have the

Numerical Methods

A vortex flowmeter works on the principle that the Strouhal number of 0.2 is a constant over a wide range of flow rates. If the bluff-body diameter in the flowmeter is 20 mm and the piezo-electric transducer registers the vortex shedding frequency to be 10 Hz, then the velocity of the flow would be measured as

Airfoil & Wing Theory

The stagnation temperatures at the inlet and exit of a combustion chamber are 600 K and 1200 K, respectively. If the heating value of the fuel is 44 MJ/kg and specific heat at constant pressure for air and hot gases are 1.005 kJ/kg.K and 1.147 kJ/kg.K respectively, the fuel-to-air ratio is

Basic Fluid Mechanics

A solid propellant of density 1800 kg/m 3 has a burning rate law r = 6.65 x 10 -3p0.45 mm/s, where p is pressure in Pascals. It is used in a rocket motor with a tubular grain with an initial burning area of 0.314 m 2. The characteristic velocity is 1450 m/s. What should be the nozzle throat diameter to achieve an equilibrium chamber pressure of 50 bar at the end of the ignition transient?

Compressible Flow & Shocks

A bipropellant liquid rocket motor operates at a ch amber pressure of 40 bar with a nozzle throat diameter of 50 mm. The characteristic velocity is 1540 m/s. If the fuel-oxidizer ratio of the propellant is 1.8, and the fuel density is 900 kg/m 3, what should be the minimum fuel tank volume for a burn time of 8 minutes

Airfoil & Wing Theory

The propellant in a single stage sounding rocket occupies 60% of its initial mass. If all of it is expended instantaneously at an equivalent exhaust velocity of 3000 m/s, what would be the altitude attained by the payload when launched vertically? [Neglect drag and assume acceleration due to gravity to be constant at 9.81 m/s 2.]

Compressible Flow & Shocks

The Airy stress function, 22x xy yφ αβγ=++ for a thin square panel of size ll× automatically satisfies compatibility. If the panel is subjected to uniform tensile stress, oσ on all four edges, the traction boundary conditions are satisfied by

Basic Fluid Mechanics

The boundary condition of a rod under longitudinal vibration is changed from fixed-fixed to fixed- free. The fundamental natural frequency of the rod is now k times the original frequency, where k is

Airfoil & Wing Theory

A spring-mass system is viscously damped with a viscous damping constant c. The energy dissipated per cycle when the system is undergoing a harmonic vibration X dCos tω is given by

Atmospheric Flight Mechanics

Buckling of the fuselage skin can be delayed by

Atmospheric Flight Mechanics

The maximum distance that th e centre of gravity can be behind aerodynamic centre without destabilizing the wing-tail combination is

Static Stability & Control

The angle of incidence of tail to trim the wing-tail combination for a 5% static margin is

Dynamic Stability

What is the radial component of the fluid's velocity at a radial location 0.5 m from the pipe axis?

Space Dynamics & Orbital Mechanics

What is the tangential component of the fluid's velocity at the same radial location as above?

Space Dynamics & Orbital Mechanics

The blade angle at the inlet of the rotor is

Thermodynamic Cycles of Gas Turbines

If the mass flow rate is 1 kg/s, the power required to drive the compressor is

Thermodynamic Cycles of Gas Turbines

The internal pressure Yp at yield, based on the von Mises yield criterion, if the vessel is floating in space, is approximately

Inlets, Combustors & Nozzles

If the vessel is evacuated (internal pressure = 0) and subjected to external pressure, yielding according to the von Mises yield criterion (assuming elastic stability until yield)

Compressors and Turbines

Choose the most appropriate alternative from the options given below to complete the following sentence: I ___ to have bought a diamond ring.

Inlets, Combustors & Nozzles

Choose the most appropriate alternative from the options given below to complete the following sentence: Food prices ___ again this month.

Rocket Propulsion

Choose the most appropriate alternative from the options given below to complete the following sentence: The administrators went on to implement yet another unreasonable measure, arguing that the measures were already ___ and one more would hardly make a difference.

Compressors and Turbines

Choose the most appropriate alternative from the options given below to complete the following sentence: To those of us who had always thought him timid, his ___ came as a surprise.

Strength of Materials & Elasticity

The arithmetic mean of five different natural numbers is 12. The largest possible value among the numbers is:

Thin-Walled Structures

Two policemen, A and B, fire once each at the same time at an escaping convict. The probability that A hits the convict is three times the probability that B hits the convict. If the probability of the convict not getting injured is 0.5, the probability that B hits the convict is:

Thin-Walled Structures

The total runs scored by four cricketers P, Q, R, and S in years 2009 and 2010 are given in the following table: Player | 2009 | 2010 P | 802 | 1008 Q | 765 | 912 R | 429 | 619 S | 501 | 701 The player with the lowest percentage increase in total runs is:

Structural Dynamics & Aeroelasticity

If a prime number on division by 4 gives a remainder of 1, then that number can be expressed as:

Aerospace Materials & Fatigue

Two points (4, p) and (0, q) lie on a straight line having a slope of 3/4. The value of (p - q) is:

Aerospace Materials & Fatigue

In the early nineteenth century, theories of social evolution were inspired less by Biology than by the conviction of social scientists that there was a growing improvement in social institutions. Progress was taken for granted and social scientists attempted to discover its laws and phases. Which one of the following inferences may be drawn with the greatest accuracy from the above passage? Social scientists: