GATE AE 2013 Question Paper & Solutions

Verbal & Numerical Aptitude

The directional derivative of the function 22 (, ) 5 x xyfx y  in the direction ˆˆ24ija at (, ) ( 1 , 1 )xy  is (A) 1 5  (B) 2 5  (C) 0 (D) 1 5

Verbal & Numerical Aptitude

The value of 5 2 4 2 42 1 x dxxx   is (A) ln 24 11 (B) ln 12 11 (C) ln 2 (D) ln 12 11

Verbal & Numerical Aptitude

At 0x , the function y x is

Verbal & Numerical Aptitude

One of the eigenvectors of the matrix 11 0 01 1 10 1 A   is 1 1 1 v    . The corresponding eigenvalue is ____________

Verbal & Numerical Aptitude

Which one of the following is the most stable configuration of an airplane in roll?

Verbal & Numerical Aptitude

Which one of the following flight instruments is used on an aircraft to determine its attitude in flight?

Verbal & Numerical Aptitude

A supersonic airplane is expected to fly at both subsonic and supersonic speeds during its whole flight course. Which one of the following statements is TRUE?

Verbal & Numerical Aptitude

Which one of the following is favorable for an airplane operation?

Verbal & Numerical Aptitude

Which one of the following is TRUE with respect to Phugoid mode of an aircraft?

Verbal & Numerical Aptitude

The x and y velocity components of a two dimensional flow field are, 2222 , yx cxvyx cyu  , where c is a constant. The streamlines are a family of (A) hyperbolas (B) parabolas (C) ellipses (D) circles 2013 AEROSPACE ENGINEERING - AE AE 6/19

Structural Mechanics

Which one of the following statements is NOT TRUE for a supersonic flow?

Incompressible & Compressible Aerodynamics

Consider a compressible flow where an elemental volume of the fluid is  , moving with velocity V  . Which one of the following expressions is TRUE?

Incompressible & Compressible Aerodynamics

Consider a thin flat plate airfoil at a small angle to an oncoming supersonic stream of air. Assuming the flow to be inviscid, 2 d l C C is

Incompressible & Compressible Aerodynamics

The critical Mach number for a flat plate of zero thickness, at zero angle of attack, is _________

Structural Mechanics

A damped single degree-of-freedom system is vibrating under a harmonic excitation with an amplitude ratio of 2.5 at resonance. The damping ratio of the system is ______________ 2013 AEROSPACE ENGINEERING - AE AE 7/19

Structural Mechanics

The cross-section of a long thin-walled member is as shown in the figure. When subjected to pure twist, point A

Structural Mechanics

The channel section of uniform thickness 2mm shown in the figure is subjected to a torque of 10 Nm. If it is made of a material with shear m odulus of 25 GPa, the twist per unit length in radians/m is _________ 300mm 600mm 300mm A 2013 AEROSPACE ENGINEERING - AE AE 8/19

Structural Mechanics

The stiffened cross-section of a long slender uniform structural member is idealized as shown in the figure below. The lumped areas at A, B, C and D have equal cross-sectional area of 3 cmଶ. The webs AB, BC, CD and DA are each 5 mm thick. The structural member is subjected to a twisting moment of 10 kNm. The magnitudes of the shear flow in the webs, qAB, qBC, qCD, and qDA in kN/m are, respectively

Structural Mechanics

Consider two engines P and Q. In P, the high pressu re turbine blades are cooled with a bleed of 5% from the compressor after the compression process and in Q the turbine blades are not cooled. Comparing engine P with engine Q, which one of the following is NOT TRUE?

Structural Mechanics

The mass flow rate of air through an aircraft e ngine is 10 kg/s. The compressor outlet temperature is 400 K and the turbine inlet temperature is 1800 K. The heating value of the fuel is 42 MJ/kg and the specific heat at constant pressure is 1 kJ/kg- K. The mass flow rate of the fuel in kg/s is approximately ___________

Structural Mechanics

For a given inlet condition, if the turbine inlet temperature is fixed, what value of compressor efficiency given below leads to the lowest amount of fuel added in the combustor of a gas turbine engine? (A) 1 (B) 0.95 (C) 0.85 (D) 0.8 A B C D 200mm 500mm 2013 AEROSPACE ENGINEERING - AE AE 9/19

Structural Mechanics

A gas turbine engine is mounted on an aircraft which can attain a maximum altitude of 11 km from sea level. The combustor volume of this engine is decided based on conditions at (A) sea level (B) 8 km altitude (C ) 5.5 km altitude (D) 11 km altitude

Space Dynamics

Consider the low earth orbit (LEO) and the geo synchronous orbit (GSO). Then

Structural Mechanics

Which one of the following shows the CORRECT variation of stagnation temperature along the axis of an ideal ram jet engine? (A) (B) (C) (D)

Air-Breathing & Rocket Propulsion

A rocket motor has a chamber pressure of 100 bar and chamber temperature of 3000 K. The ambient pressure is 1 bar. Assume that the specifi c heat at constant pressure is 1 kJ/kg-K. Also assume that the flow in the nozzle is isentropic and optimally expanded. The exit static temperature in K is (A) 805 (B) 845 (C) 905 (D) 945 2013 AEROSPACE ENGINEERING - AE AE 10/19 Q. 26 to Q. 55 carry two marks each.

Structural Mechanics

Let 22 2 ˆˆˆˆ ˆ ˆ() ( ) S I yz i zx j xy k x i y j z kd S    , where S denotes the surface of the sphere of unit radius centered at the origin. Here ˆˆˆ, a n d ij k denote three orthogonal unit vectors. The value of I is ____________

Linear Algebra & Differential Equations

Given that the Laplace transform, ࣦ1() ate s a  then ࣦ  53s i n h 5tet = (A) 2 3 10 s s s (B) 2 15 10s s (C) 2 3 10 s s s (D) 2 15 10s s

Linear Algebra & Differential Equations

Values of a, b and c, which render the matrix 11 32 1 0 3 11 32 a Qb c        orthonormal are, respectively

Linear Algebra & Differential Equations

A function ሻ satisfies the differential equation 2 2 20dy d y ydt dt  and is subject to the initial conditions (0 ) 0yt  and (0 ) 1dy tdt   . The value of (1 )yt  is (A) e (B) 0 (C) 1 (D) -1 2013 AEROSPACE ENGINEERING - AE AE 11/19

Incompressible & Compressible Aerodynamics

A glider is launched from a 500m high hilltop. Following data is available for the glider: Zero lift drag coefficient 0 0.02DC  , aspect ratio 10AR and Oswald efficiency factor e = 0.95. The maximum range of the glider in km is _________

Structural Mechanics

Which one of the following criteria leads to maximum turn rate and minimum radius in a level turn flight?

Incompressible & Compressible Aerodynamics

Consider an airplane with rectangular straight wing at dihedral angle 010 . Lift curve slope of wing airfoil section (constant over the whole span of the wing) is 5.4 / .lcr a d  The roll stability derivative, lC in per radian is __________

Incompressible & Compressible Aerodynamics

Consider one-dimensional isentropic flow at a Mach number of 0.5. If the area of cross-section of a streamtube increases by 3% somewhere along the flow, the corresponding percentage change in density is ________

Structural Mechanics

The potential flow model for a storm is represented by the superposition of a sink and a vortex. The stream function can be written in the ( ,r ) system as ln22 r     , where 2100 m /s . Assume a constant air density of 1.2 kg/m 3. The gauge pressure at a distance of 100 m from the storm eye is (A)  (B) 2 1.2  (C) 2 1.2 2 (D) 2 1.2 4

Structural Mechanics

Three identical eagles of wing span s are flying side by side in a straight line with no gap between their wing tips. Assume a single horse shoe vortex model (of equal strength Γ) for each bird. The net downwash experienced by the middle bird is (A) s  (B) 2 s  (C) 3 s  (D) 4 3 s  2013 AEROSPACE ENGINEERING - AE AE 12/19

Incompressible & Compressible Aerodynamics

Streamline pattern of flow past a cylinder is s hown in the figure below. The oncoming flow is steady, irrotational and incompressible. The flow is from left to right. Bernoulli's equation CANNOT be applied between the points (A) 1 and 2 (B) 1 and 5 (C ) 3 and 4 (D) 5 and 6

Incompressible & Compressible Aerodynamics

Consider a supersonic stream at a Mach number M=2, undergoing a gradual expansion. The stream is turned by an angle of 3 degrees due to the expansion. The following data is given. M  (Prandtl-Meyer function) 1.8 20.73 1.9 23.59 2.0 26.38 2.1 29.10 2.2 31.73 2.3 34.28 2.4 36.75 The Mach number downstream of the expansion is (A) 1.88 (B) 2.00 (C ) 2.11 (D) 2.33 1 2 3 4 5 6 2013 AEROSPACE ENGINEERING - AE AE 13/19

Structural Mechanics

The idealized cross-section of a beam is compri sed of four identical booms connected by shear webs. The beam is subjected to a bending moment ܯas shown in the figure. The inclination of the neutral axis to the x-axis in degrees is (A) 45 CW (B) 45 CCW (C) 26.6 CW (D) 63.4 CCW

Structural Mechanics

A composite circular shaft is comprised of a steel core surrounded by an aluminum annulus, perfectly bonded to each other as shown in the fi gure. If it subjected to a pure torque, which one of the following statements is TRUE?

Structural Mechanics

A horizontal rectangular plate ABCD is hinged at points A, B and C. AC and BD are diagonals of the plate. Downward force P is applied at D. The upward reactions RA, RB, and RC at points A, B and C, respectively, are

Structural Mechanics

In the steel structure (Young's modulus = 200 GPa) shown in the figure, all members have a circular cross-section of radius 10 mm. Column BD is pinned at B and D. The support at A is hinged. The minimum value of load ܲat which the column BD may buckle in Newtons is approximately ____________

Structural Mechanics

The thin rectangular plate has dimensions L×b×t. It develops a stress field corresponding to an applied bending moment M as shown in the figure. A valid Airy's stress function is (A) 3 3 2M xtb (B) 3 3 2M ytb (C)  33 3 2M x ytb  (D) 4 3 2M ytb

Structural Mechanics

A cantilever beam of negligible mass is 0.6 m long. It has a rectangular cross-section of width 8 mm and thickness 6 mm and carries a tip mass of 1.4 kg. If the natural frequency of this system is 10 rad/s, Young's modulus of the material of the beam in GPa is ________ x M M L b 2m D 1m 1m A B C P y 2013 AEROSPACE ENGINEERING - AE AE 15/19

Structural Mechanics

A simply supported beam with overhang is loaded by uniformly distributed load of intensity q as shown in the figure. The bending moment at the mid-point of AB is (A) 2 sagging16 qL (B) 2 hogging16 qL (C) 23 hogging16 qL (D) 23 sagging16 qL

Air-Breathing & Rocket Propulsion

Thrust of liquid oxygen - liquid hydrogen rocket engine is 300 kN. The O/F ratio used is 5. If the fuel mass flow rate is 12.5 kg/s, the specific impulse of the rocket motor in Ns/kg is (A) 3800 (B) 4000 (C) 4200 (D) 4400

Structural Mechanics

In a 50 % reaction axial compressor stage, the local blade velocity is 300 m/s and the axial component of velocity is 100 m/s. If the absolute inlet flow angle α1 = 45o, the work per unit mass done on the fluid by the stage in kJ/kg is (A) 30 (B) 40 (C) 50 (D) 60

Incompressible & Compressible Aerodynamics

Consider two rockets P and Q fired vertically up wi th identical specific impulse and a payload of 2 kg. Rocket P has 2 identical stages, and each stage has 200 kg of propellant and 20 kg of structural weight. Rocket Q has a single stage with 400 kg of propellant and 40 kg of structural weight. Neglecting drag and gravity effects, the ratio of the change in velocity of P to that attained by Q is (A) 1.13 (B) 1.23 (C ) 1.33 (D) 1.43 Common Data Questions Common Data for Questions 48 and 49: Data for an airplane are given as follows: weight 30Wk N , thrust available at sea-level 0 4000TN , wing planform area 230Sm , maximum lift coefficient max 1.4LC  , and drag coefficient 20.015 0.024 .D LCC Assume air density at sea-level 31.22 /kg m  .

Structural Mechanics

Stall speed of the airplane in m/s is (A) 17.36 (B) 34.22 (C) 45.52 (D) 119.46

Incompressible & Compressible Aerodynamics

Minimum and maximum speeds of the airplane in level flight condition at sea-level in m/s are respectively (A) 17.36 and 180 (B) 17.36 and 34.22 (C) 34.22 and 119.46 (D) 17.36 and 119.46 L L/2 A B q 2013 AEROSPACE ENGINEERING - AE AE 16/19 Common Data for Questions 50 and 51: An aircraft is flying at Mach number M = 1.5, where the ambient temperature is 250 K. The stagnation temperatur e of gases at the entry to the nozzle is 800 K. The nozzle is choked and always under expanded. Assume the molecular weight of the exhaust gases to be 29, the ratio of specific heats to be 1.4 and the universal gas constant is 8314 J/kmol-K.

Incompressible & Compressible Aerodynamics

For which one of the nozzle exit Mach numbers given below is the propulsive efficiency highest?

Incompressible & Compressible Aerodynamics

For which one of the nozzle exit Mach numbers given below is the thrust highest?

Incompressible & Compressible Aerodynamics

If the circulation at the quarter chord (c/4) of the airfoil is 1 , the normal velocity is zero at (A) c/4 (B) c/2 (C) 3 c/4 (D) all points on the chord

Incompressible & Compressible Aerodynamics

A second identical airfoil is placed behind the first one at a distance of c/2 from the trailing edge of the first. The second airfoil has an unknown circulation 2 placed at its quarter chord. The normal velocity becomes zero at the same chord-wise locations of the respective airfoils as in the previous question. The values of 1 and 2 are respectively (A) 42 ,33 cU cU  (B) 22 ,33 cU cU  (C) 21 ,33 cU cU  (D) 44 ,33 cU cU  2013 AEROSPACE ENGINEERING - AE AE 17/19 Statement for Linked Answer Questions 54 and 55: A wing-body alone configuration airplane with a wing loading of 21000 /W N mS  is flying in cruise condition at a speed V = 90m/s at sea-level (air density at sea-level 31.22 /kg m  ). The zero lift pitching moment coefficient of the airplane is 0 0.06wb mac mCC   and the location of airplane aerodynamic center from the wing leading edge is 0.25 .acXc  Here c is the chord length.

Incompressible & Compressible Aerodynamics

The airplane trim lift coefficient L trimC is (A) 0.502 (B) 0.402 (C) 0.302 (D) 0.202

Structural Mechanics

Distance of center of gravity of the aircraft ( CGX ) from the wing leading edge is (A) 0.447c (B) 0.547c (C) 0.547c (D) 0.25c General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each.

Structural Mechanics

If ൑ 5 and ൑1 1 then which of the following options is TRUE?

Structural Mechanics

The Headmaster ___________ to speak to you. Which of the following options is incorrect to complete the above sentence?

Structural Mechanics

Mahatama Gandhi was known for his humility as

Structural Mechanics

All engineering students should learn mechanics, mathematics and how to do computation. I II III IV Which of the above underlined parts of the sentence is not appropriate? (A) I (B) II (C) III (D) IV

Structural Mechanics

Select the pair that best expresses a relationship similar to that expressed in the pair: water: pipe:: (A) cart: road (B) electricity: wire (C) sea: beach (D) music: instrument Q. 61 to Q. 65 carry two marks each.

Structural Mechanics

Velocity of an object fired directly in upward direction is given by ݐwhere ݐtime) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec? (A) (1, 3/2) (B) (1/2, 1) (C) (1/2, 3/2) (D) (1, 3)

Incompressible & Compressible Aerodynamics

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lo t is found defective, what is the probability that it was manufactured by M2? (A) 0.35 (B) 0.45 (C) 0.5 (D) 0.4

Structural Mechanics

Following table gives data on tourists from different countries visiting India in the year 2011. Country Number of Tourists USA 2000 England 3500 Germany 1200 Italy 1100 Japan 2400 Australia 2300 France 1000 Which two countries contributed to the one third of the total number of tourists who visited India in 2011?

Structural Mechanics

If ൅ 9| ൌ3 then the possible value of ଶ would be: (A) 30 (B) -30 (C) -42 (D) 42

Structural Mechanics

All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments: