GATE AE 2012 Question Paper & Solutions

Verbal & Numerical Aptitude

The constraint A2 = A on any square matrix A is satisfied for (A) the identity matrix only. (B) the null matrix only. (C) both the identity matrix and the null matrix. (D) no square matrix A.

Verbal & Numerical Aptitude

The general solution of the differential equation 2 2 20dy d y ydt dt+ -= is (A) 2ttAe Be- + (B) 2ttAe Be-- + (C) 2ttAe Be- + (D) 2ttAe Be+

Verbal & Numerical Aptitude

An aircraft in trimmed condition has zero pitching moment at (A) its aerodynamic centre. (B) its centre of gravity. (C) 25% of its mean aerodynamic chord. (D) 50% of its wing root chord.

Verbal & Numerical Aptitude

In an aircraft, constant roll rate can be produced using ailerons by applying (A) a step input. (B) a ramp input. (C) a sinusoidal input. (D) an impulse input.

Verbal & Numerical Aptitude

For a symmetric airfoil, the lift coefficient for zero degree angle of attack is (A) - 1.0 (B) 0.0 (C) 0.5 (D) 1.0

Verbal & Numerical Aptitude

The critical Mach number of an airfoil is attained when

Verbal & Numerical Aptitude

The shadowgraph flow visualization technique depends on

Verbal & Numerical Aptitude

The Hohmann ellipse used as earth-Mars transfer orbit has (A) apogee at earth and perigee at Mars. (B) both apogee and perigee at earth. (C) apogee at Mars and perigee at earth. (D) both apogee and perigee at Mars.

Verbal & Numerical 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

Verbal & Numerical Aptitude

The Poisson's ratio,ν of most aircraft grade metallic alloys has values in the range: (A) -1 ν≤≤ 0 (B) 0 ν≤≤ 0.2 (C) 0.2 ν≤ ≤ 0.4 (D) 0.4 ν≤≤ 0.5 2012 AEROSPACE ENGINEERING - AE AE 3/12

Structural Mechanics

The value of k for which the system of equations 21 ; 28 3xy k z x k yz+ += ++= has no solution is (A) 0 (B) 2 (C) 4 (D) 8

Linear Algebra & Differential Equations

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

Linear Algebra & Differential Equations

The general solution of the differential equation 20dy ydx- = is (A) 0yx C-+ = (B) 0yxC-+ = (C) 0yx C- += (D) 0yx C-+ =

Incompressible & Compressible Aerodynamics

During the ground roll manoeuvre of an aircraft, the force(s) acting on it parallel to the direction of motion (A) is thrust alone. (B) is drag alone. (C) are both thrust and drag. (D) are thrust, drag and a part of both weight and lift.

Air-Breathing & Rocket Propulsion

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 (A) lower by exactly 10%. (B) lower by more than 10%. (C) lower by less than 10%. (D) an unpredictable quantity.

Air-Breathing & Rocket Propulsion

In an aircraft, the dive manoeuvre can be initiated by (A) reducing the engine thrust alone. (B ) reducing the angle of attack alone. (C) generating a nose down pitch rate. (D) increasing the engine thrust alone.

Airplane Performance & Stability

In an aircraft, elevator control effectiveness determines

Incompressible & Compressible Aerodynamics

The Mach angle for a flow at Mach 2.0 is (A) 30o (B) 45o (C) 60o (D) 90o

Incompressible & Compressible Aerodynamics

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

Structural Mechanics

Bernoulli's equation is valid under steady state

Air-Breathing & Rocket Propulsion

The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is (A) 0.0 (B) 0.5 (C) 1.0 (D) 2.0

Structural Mechanics

The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is (A) 0.25 (B) 0.50 (C) 0.75 (D) 1.0

Air-Breathing & Rocket Propulsion

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 (A) the bottom of the crater on Mars. (B) Mars standard "sea level". (C) earth's standard sea level. (D) the same depth of the crater on earth.

Structural Mechanics

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

Structural 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 (A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0 Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q.30 are numerical answer type. The answer to each of these questions is either a positive whole number, or a positive real number with maximum of 2 decimal places.

Structural Mechanics

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

Structural Mechanics

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 ____.

Incompressible & Compressible Aerodynamics

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 ____.

Air-Breathing & Rocket Propulsion

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 ____.

Structural Mechanics

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.

Structural Mechanics

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

Structural Mechanics

The volume of a solid generated by rotating the region between semi-circle 211y x=- - and straight line y = 1, about x axis, is (A) 2 4 3π π- (B) 2 14 3π π- (C) 2 3 4 π π- (D) 23 4 π π-

Linear Algebra & Differential Equations

One eigenvalue of the matrix 271 0 522 5 16 5 A ⎡ ⎤ ⎢ ⎥=⎢ ⎥ ⎢ ⎥⎣ ⎦ is - 9.33. One of the other eigenvalues is (A) 18.33 (B) -18.33 (C) 18.33 -9.33i (D) 18.33+9.33i

Airplane Performance & Stability

If an aircraft takes off with 10% less fuel in comparison to its standard configuration, its range is (A) lower by exactly 10%. (B) lower by more than 10%. (C) lower by less than 10%. (D) an unpredictable quantity.

Structural Mechanics

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 (A) 1830 m. (B) 1380 m. (C) 830 m. (D) 380 m.

Structural Mechanics

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 (A) 1.95 N upward force. (B) 1.95 N downward force. (C) 1.85 N upward force. (D) 1.75 N downward force.

Incompressible & Compressible Aerodynamics

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 (A) sin(β-θ) (B) cos( β-θ) (C) sin( θ-β) (D) cos(θ -β)

Air-Breathing & Rocket Propulsion

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

Airplane Performance & Stability

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 (A) 0.1 m/s (B) 1 m/s (C) 10 m/s (D) 100 m/s

Air-Breathing & Rocket Propulsion

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 (A) 0.0018 (B) 0.018 (C) 0.18 (D) 1.18

Air-Breathing & Rocket Propulsion

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? (A) 35 mm (B) 38 mm (C) 41 mm (D) 45 mm

Air-Breathing & Rocket Propulsion

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 (A) 1.65 m3 (B) 1.75 m 3 (C) 1.85 m 3 (D) 1.95 m 3

Incompressible & Compressible Aerodynamics

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.] (A) 315 km (B) 335 km (C) 365 km (D) 385 km

Structural Mechanics

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 (A) /2 ; 0 ; /2 .ooα σβγ σ== = (B) ;0 ; .ooα σβ γσ= == (C) 0; / 4; 0.oα βσ γ== = (D) 0; / 2; 0.oα βσ γ= ==

Structural 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 (A) 1 2 (B) 2 (C) 1 2 (D) 2

Structural Mechanics

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 (A) 2 dcXπω (B) 2 d Xπω (C) dcXπω (D) 2 dcXπω

Structural Mechanics

Buckling of the fuselage skin can be delayed by

Structural Mechanics

The maximum distance that th e centre of gravity can be behind aerodynamic centre without destabilizing the wing-tail combination is (A) 0.4 m (B) 1.4 m (C) 2.4 m (D) 3.4 m

Structural Mechanics

The angle of incidence of tail to trim the wing-tail combination for a 5% static margin is (A) -1.4o (B) -0.4o (C) 0.4o (D) 1.4o Common Data for Questions 50 and 51: A thin long circular pipe of 10 mm diameter has porous walls and spins at 60 rpm about its own axis. Fluid is pumped out of the pipe such that it emerges radially relative to the pipe surface at a velocity of 1 m/s. [Neglect the effect of gravity.]

Structural Mechanics

What is the radial component of the fluid's velocity at a radial location 0.5 m from the pipe axis? (A) 0.01 m/s (B) 0.1 m/s (C) 1 m/s (D) 10 m/s

Structural Mechanics

What is the tangential component of the fluid's velocity at the same radial location as above? (A) 0.01 m/s (B) 0.03 m/s (C) 0.10 m/s (D) 0.31 m/s Linked Answer Questions Statement for Linked Answer Questions 52 and 53: Air at a stagnation temperature of 15oC and stagnation pressure 100 kPa enters an axial compressor with an absolute velocity of 120 m/s. Inlet guide vanes direct th is absolute velocity to the rotor inlet at an angle of 18o to the axial direction. The rotor turning angle is 27 o and the mean blade speed is 200 m/s. The axial velocity is assumed constant through the stage.

Structural Mechanics

The blade angle at the inlet of the rotor is (A) 25.5 o (B) 38.5o (C) 48.5o (D) 59.5o

Structural Mechanics

If the mass flow rate is 1 kg/s, the power required to drive the compressor is (A) 50.5 kW (B) 40.5 kW (C) 30.5 kW (D) 20.5 kW Statement for Linked Answer Questions 54 and 55: A thin-walled spherical vessel (1 m inner diameter a nd 10 mm wall thickness) is made of a material with 500 MPaYσ = in both tension and compression.

Structural Mechanics

The internal pressure Yp at yield, based on the von Mises yield criterion, if the vessel is floating in space, is approximately (A) 500 MPa (B) 250 MPa (C) 100 MPa (D) 20 MPa

Airplane Performance & Stability

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) (A) occurs at about half the pressure Yp . (B) occurs at about double the pressure Yp . (C) occurs at about the same pressure Yp . (D) never occurs. 2012 GENERAL APTITUDE - GA_AN_Online General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each. Choose the most appropriate alternative from the options given below to complete the following sentence: I ___ to have bought a diamond ring. (A) have a liking (B) should have liked

Structural Mechanics

(C) would like (D) may like Choose the most appropriate alternative from the options given below to complete the following sentence: Food prices ___ again this month. (A) have raised (B) have been raising

Structural Mechanics

(C) have been rising (D) have arose 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.

Structural Mechanics

(A) reflective (B) utopian (C) luxuriant (D) unpopular 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.

Structural Mechanics

(A) intrepidity (B) inevitability (C) inability (D) inertness The arithmetic mean of five different natural numbers is 12. The largest possible value among the numbers is

Structural Mechanics

Question 60 from official GATE AE 2012 Examination.

Structural Mechanics

(A) 0.14 (B) 0.22 (C) 0.33 (D) 0.40 GA_AN_Online 1/2 2012 GENERAL APTITUDE - GA_AN_Online GA_AN_Online 2/2 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 Mechanics

(A) P (B) Q (C) R (D) S If a prime number on division by 4 gives a remainder of 1, then that number can be expressed as (A) sum of squares of two natural numbers (B) sum of cubes of two natural numbers (C) sum of square roots of two natural numbers

Structural Mechanics

(D) sum of cube roots of two natural numbers Two points (4, p) and (0, q) lie on a straight line having a slope of 3/4. The value of (p - q) is Q.64

Structural Mechanics

Question 64 from official GATE AE 2012 Examination.

Structural Mechanics

(D) emphasized Biology over Social Sciences. END OF THE QUESTION PAPER Paper Question no. Key Paper Question no. Key AE 1C AE 36 B AE 2C AE 37 A AE 3B AE 38 B AE 4D AE 39 B AE 5B AE 40 B AE 6C AE 41 B AE 7C AE 42 B AE 8C AE 43 D AE 9B AE 44 A AE 10 C AE 45 A AE 11 C AE 46 A AE 12 A AE 47 A AE 13 D AE 48 B AE 14 D AE 49 A AE 15 B AE 50 A AE 16 C AE 51 Marks to All AE 17 C AE 52 Marks to All AE 18 A AE 53 Marks to All AE 19 B AE 54 D AE 20 A AE 55 C AE 21 C AE 56 C AE 22 Marks to All AE 57 C AE 23 C AE 58 D AE 24 D AE 59 A AE 25 D AE 60 C AE 26 0.26 to 0.27 AE 61 A AE 27 13 to 14 AE 62 B AE 28 1.1 to 1.2 AE 63 A AE 29 1430 to 1440 AE 64 C AE 30 2 AE 65 A AE 31 A AE 32 A AE 33 A AE 34 B AE 35 Marks to All GATE 2012 ‐ Answer Key ‐ Paper : AE