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# GATE 2014 : Aerospace Engineering

14 pages, 65 questions, 19 questions with responses, 27 total responses
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GATE 2014 SET- 1 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding Q.2 (B) meaning (C) concentration (D) stability Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. Q.3 (B) virtues (C) choices (D) strength 20 14 (A) vice Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Q.4 If y = 5x2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (C) is parallel to the x-axis E A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? G AT Q.5 (B) has a slope of +1 (D) has a slope of 1 Q. 6 Q. 10 carry two marks each. Q.6 Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX Q.7 (C) ITZDF (D) OYEIK Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? (A) (B) (C) (D) GA (B) EPVZB Anuj 6 2 4 2 Bhola 2 6 2 4 Chandan 5 5 6 6 Dilip 1 1 3 1 Eswar 3 3 1 3 Faisal 4 4 5 5 1/2

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GATE 2014 SET- 1 General Aptitude -GA Q.8 The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Q.9 One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft? (A) 3.0 (C) 1.5 (D) 1.25 The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value) E 20 14 Q.10 (B) 2.5 G AT (i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (A) (i) and (ii) (C) (ii) and (iii) (B) (i) and (iii) (D) (iii) and (iv) END OF THE QUESTION PAPER GA 2/2

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GATE 2014 AEROSPACE AE Q. 1 Q. 25 carry one mark each. Q.1 For a real symmetric matrix [A], which of the following statements is true: (A) The matrix is always diagonalizable and invertible. (B) The matrix is always invertible but not necessarily diagonalizable. (C) The matrix is always diagonalizable but not necessarily invertible. (D) The matrix is always neither diagonalizable nor invertible. m2 m 3m (x 2) converges for all x with x 2 R given by m =1 (A) R = 0 Q.3 (C) R = (B) R = 3 sin(1 / x ), x 0 x=0 is The function given by f(x) = 0, { (A) Unbounded everywhere (C) Bounded but not continuous at x = 0 d dy x + ky = 0, 0 < x < 1 , with y (0) = y (1) = 0 . Then the dx dx solutions of the boundary-value problem for k = 1 (given by y1 ) and k = 5 (given by y5 ) satisfy: Given the boundary-value problem (C) 1 0 1 0 dy1 dy5 dx = 0 dx dx 1 dy dy (D) ( y1 y5 + 1 5 )dx = 0 0 dx dx E (A) Q.5 y1 y5 dx = 0 (B) y1 y5 dx 0 The value of I = 1 1000 x 0 4 (B) 400 0 (C) 180 (D) 208 For a NACA 5-digit airfoil of chord c, the designed lift coefficient and location of maximum camber along the chord from the leading edge are denoted by CL and Xm respectively. For NACA12018 airfoil, which combination of CL and Xm given below are correct? AE (A)CL =0.15 and Xm = 0.1c (C)CL=0.12 and Xm = 0.18c Q.7 1 dx , obtained by using Simpson s rule with 2 equally spaced intervals is, (G (A) 200 Q.6 (B) Bounded and continuous everywhere (D) Continuous and differentiable everywhere AT Q.4 (D) R = 1 / 3 14 ) The series s = 20 Q.2 (B)CL =0.12 and Xm = 0.2c (D)CL =0.15 and Xm = 0.2c For inviscid, supersonic flow over a diamond shaped airfoil, shown in the figure, which statement is correct among the following? (A) The airfoil will experience zero lift and positive drag force (B) The airfoil will experience positive lift and zero drag force (C) The airfoil will experience negative lift and zero drag force (D) The airfoil will experience positive lift and positive drag force AE 1/11

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GATE 2014 Consider supersonic flow near a corner (at an angle from the horizontal) with an attached oblique shock (at an angle with horizontal) as shown in figure. If Mach number M decreases gradually from a high supersonic value, which of the following statements is correct? (A) will decrease if the shock is a weak shock (B) will decrease if the shock is a strong shock (C) will increase for both weak and strong shocks (D) remains unchanged for both weak and strong shocks Q.9 14 ) Q.8 AEROSPACE AE The streamlines of a potential line vortex is concentric circles with respect to the vortex center as shown in figure. Velocity along these streamlines, outside the core of the vortex can be written as, = , where strength of the vortex is and r is radial direction. The value of circulation 2 2 (A) (B) 2 (C) 2 (D) 0 To observe unsteady separated flow in a diverging channel, bubbles are injected at each 10ms interval at point A as shown in figure. These bubblesact as tracer particles and follow the flow faithfully. The curved line AB shown at any instant represents: AE (G Q.10 AT E 20 along the curve shown in the figure is: (A) Streamline, streakline and pathline (C) Only a pathline Q.11 It is desired to measure the Young s modulus and the Poisson s ratio of a given homogeneous, isotropic material. A bar of length 20cm and square cross-section (10mm 10mm) of this material is subjected to a tensile load of 40kN. Under this load, length increases to 20.1cm while the crosssection reduces to 9.98mm 9.98mm. Young s modulus and Poisson s ratio of the material are: (A) 80GPa& 0.4 respectively (C) 80GPa& -0.2 respectively AE (B) Streamline and pathline (D) Only a streakline (B) 40GPa& -0.4 respectively (D) 40GPa& 0.2 respectively 2/11

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GATE 2014 For a fifty percent reaction axial compressor stage, following statements are given: I. Velocity triangles at the entry and exit of the rotor are symmetrical II. The whirl or swirl component of absolute velocity at the entry of rotor and entry of stator are same. Which of the following options are correct? (A) Both I and II are correct statements (C) I is incorrect but II is correct Q.19 A small rocket having a specific impulse of 200s produces a total thrust of 98kN, out of which 10kN is the pressure thrust. Considering the acceleration due to gravity to be 9.8m/s2, the propellant mass flow rate in kg/s is (A) 55.1 Q.20 (B) I is correct but II is incorrect (D) Both I and II are incorrect (B) 44.9 (C) 50 (D) 60.2 14 ) Q.18 AEROSPACE AE The thrust produced by a turbojet engine 20 (A) Increases with increasing compressor pressure ratio (B) Decreases with increasing compressor pressure ratio (C) Remains constant with increasing compressor pressure ratio (D) First increases and then decreases with increasing compressor pressure ratio The moment coefficient measured about the centre of gravity and about aerodynamic centre of a given wing-body combination are 0.0065 and -0.0235 respectively. The aerodynamic centre lies 0.06 chord lengths ahead of the centre of gravity. The lift coefficient for this wing-body is _____. Q.22 The vertical ground load factor on a stationary aircraft parked in its hangar is: (A) 0 (B) Minimum CL/CD (D) Minimum CD/CL3/2 (G In most airplanes, the Dutch roll mode can be excited by applying (A) a step input to the elevators (C) a sinusoidal input to the aileron (B) a step input to the rudder (D) an impulse input to the elevators Considering R as the radius of the moon, the ratio of the velocities of two spacecraft orbiting moon in circular orbit at altitudes R and 2R above the surface of the moon is ________. AE Q.25 (D) 1 Under what conditionshould a glider be operated to ensure minimum sink rate? (A) Maximum CL/CD (C) Maximum CD/CL3/2 Q.24 (C) Not defined AT Q.23 (B) -1 E Q.21 Q. 26 Q. 55 carry two marks each. Q.26 3 3 2 . Then det ( [ A] + 7[ A] 3[ I ]) is 3 4 If [A] = (A) 0 AE (B) -324 (C) 324 (D) 6 4/11

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GATE 2014 AEROSPACE AE Q.27 For the periodic function given by f ( x ) Fourier series, the sum s = 1 (B) (A) 1 Q.28 ={ < x<0 2, 0< x< with f ( x + 2 ) = f ( x) , using 2, 1 1 1 + + converges to 3 5 7 (C) 3 (D) 4 5 Let be the boundary of the closed circular region A given by x 2 + y 2 1 . Then ( ) I = 3 x 3 9 xy 2 ds (where ds means integration along the bounding curve) is Q.29 (B) (C) 1 Solution to the boundary-value problem d 2u du 9 2 + u = 5 x, 0 < x < 3 with u (0) = 0, dx dx ( ) (B) u ( x) = E Q.30 ( ) 15e x / 3 e + e x / 3 + 5x 1 + e2 15 sin( x / 3) 5 3 (D) u ( x) = x cos(1) 54 20 15e x / 3 e e x / 3 + 5x 1 + e2 15 sin( x / 3) (C) u ( x) = + 5x cos(1) (A) u ( x) = = 0 is x =3 (D) 0 14 ) (A) The Laplace transform L(u(t))=U(s), for the solution u(t) of the problem d 2u du + 2 + u = 1, t > 0 2 dt dt AT . du (0) = 5 is given by: with initial conditions u (0) = 0, dt (B) 5s + 1 s ( s + 1) 2 (C) 1 5s s ( s + 1) 2 5s 2 + 1 (D) s ( s + 1) 2 For a steady, incompressible two-dimensional flow, represented in Cartesian co-ordinates ( , ), a student correctly writes the equation of pathline of any arbitrary particle as, = and = , -1 wherea and bare constants having unit of (second) . If value of a is 5, the value of b is _____. AE Q.31 6 ( s + 1) 2 (G (A) AE 5/11

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GATE 2014 Figures (a) - (d) below show four objects. Dimensions and surface conditions of the objects are shown in the respective figures. All four objects are placed independently in a steady, uniform flow of same velocity and the direction of flow is from left to right as shown in (a). The flow field can be considered as 2-D, viscous and incompressible. Following statements are made regarding the drag that these objects experience. (i) (ii) (iii) (iv) (v) Drag of object (a) is more than the drag of object (d) Drag of object (a) is less than the drag of object (d) Drag of object (b) is more than the drag of object (c) Drag of object (c) is more than the drag of object (b) Drag of object (a) is more than the drag of object (b) 14 ) Q.32 AEROSPACE AE (A) (i), (iii), (v) (B) (ii), (iv), (v) 20 Choose the correct combination of statements from the options given above: (C) (i), (iv), (v) (D) (i), (iii) A student needs to find velocity across a stationary normal shock. He measures density and pressure across the shock as shown in the figure below. 1bar = 105 Pa. (No shock table is needed for the calculations). The value of u1 in m/s is ____. Q.34 For inviscid, compressible flow past a thin airfoil, shown in the figure, free-stream Mach number and pressure are denoted by and respectively. Ratio of pressure at point A and is 0.8 and specific heat ratio is 1.4. If the Mach number at point A is 1.0 and rest of the flow field is subsonic, the value of is AE (G AT E Q.33 (A) 2.95 AE (B) 0.79 (C) 1.18 (D) 0.64 6/11

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GATE 2014 Q.35 AEROSPACE AE A student can measure free-stream velocity of a low-speed wind tunnel using a i. Pitot tube alone aligned with the flow direction. ii. Pitot tube aligned with the flow direction with static pressure measurement at an appropriate position on the tunnel wall. iii. Pitot tube aligned with the flow direction along with barometer pressure reading of the outside ambient. iv. Pitot static tube alone aligned with the flow direction. Considering the above statements, which of the following options is correct? (A) (i) only (C) (ii) & (iv) (D) (i), (iii) & (iv) Induced velocity w at a point = 1 along the lifting line can be calculated using the formula ( 1 ) = Given 2 2 + 1 1 1 . 4 2 2 14 ) Q.36 (B) (i) & (ii) = 1, where , and sare given in figure below. For theabove semi-elliptic distribution of circulation, , the downwash velocity at any point 1, for [ + 1 ], where = 1 2 2 . 4 1 20 symmetric flight can be obtained as, ( 1 ) = 1 2 2 = 2 ) 8 2 2 (C)I=0 and = 8 (G (A)I=0 and = 8 2 2 (D)I= 1 and = 8 (B)I= 1 and = Two overflowing water reservoirs are connected with a100m long pipe of circular cross-section (of radius, R = 0.02m), such that height difference h remains constant as shown in the figure below. The centerline velocity in the pipe is 10m/s. The velocity profile inside the pipe over the entire 2 2 length is = 1 2 , where, is a constant pressure gradient along the pipe length, 4 x is measured from theleft end of the pipe along its central axis and r is radial location inside the pipe with respect to its axis.(Given data: Density and kinematic viscosity of water are 1000kg/m3 and 1x10-6m2/srespectively; acceleration due to gravity is 10m/s2). If all other losses except the frictional losses at the pipe wall are neglected, the value of h in meter is ____. AE Q.37 AT E Which of the following options is correct if the induced drag is (given AE 7/11

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GATE 2014 AEROSPACE AE A 1.8m long steel beam of rectangular cross section (10mm 6mm) is simply supported with a length of 1.2m between the supports and an overhang of 0.3m on either side. Young s modulus for the material of the beam is 200GPa. For a 50N load applied at the center of the beam, magnitude of the slopeof the beam at tip S is _______. Q.39 There are 2 designs proposed for a shaft of length l, with a torque carrying capacity of T.Design I is a solid circular cross-section shaft of diameter30mm. Design II is a thin-walled circular shaft of average diameter 40mm. Thickness of the wall in Design II has to be determined such that maximum shear stress is the same in both the designs for the given torque T(so that same material can be used for manufacturing both the shafts). Ratio of mass of shaft using Design Ito the mass of shaft using Design II is (C) 1.79 (D) 3.58 A structural member of rectangular cross-section 10mm 6mm and length 1m is made of steel (Young s modulus is 200GPa and coefficient of thermal expansion is 12 10 6 / ). It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by which is AE Q.40 (B) 5.36 (G (A) 2.68 AT E 20 14 ) Q.38 (A) 19.74 Q.41 (C) 78.96 (D) 39.48 A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30cm and wall thickness 1mm is subjected to a design maximum internal pressure of 5bar (0.5MPa). The material used for manufacturing this cylinder has a failure stress of 260MPa. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is (A) 2.8 AE (B) 9.87 (B) 2.0 (C) 6.9 (D) 4.0 8/11

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GATE 2014 A cantilevered beam is subjected to a parabolic distribution of shear traction at the right edge while the top and bottom surfaces are traction free. To solve this problem, following Airy s stress function is proposed: = 1 + 2 3 + 3 2 2 + 4 3 . This is an admissible Airy s function that would satisfy the bi-harmonic equation as well as the boundary conditions if and only if (A) 1 = 0, 2 = , 3 = 0, 4 = 2 (C) 1 = 0, 2 = 0, 3 = , 4 = 2 3 (B) 1 = , 2 = 2, 3 (D) 1 = , 2 = 3 = 0, 4 = 0 2, 3 3 = 0, 4 = 0 1kg mass is hanging from a spring of stiffness 500N/m attached to a massless,symmetric beam of length 0.6m, moment of inertia about the bending axis = 8.33 10 10 4 and Young s modulus E=210GPa as shown in the figure. The fundamental natural frequency (in rad/s) of the system is 20 Q.43 3 14 ) Q.42 AEROSPACE AE (C) 22.36 (D) 3.56 A single degree of freedom system is vibrating with initial (first cycle) amplitude of 5cm. The viscous damping factor associated with the vibrating system is 2%. Vibration amplitude of the fifth cycle (in cm) is (A) 1.65 AT Q.44 (B) 20.36 E (A) 3.24 (B) 4.41 (C) 2.67 (D) 3.02 A cruise missile with an ideal ramjet engine is flying at Mach 4.0 at an altitude where the ambient temperature is 100K. Considerratio of specific heats = 1.4 and specific gas constant R = 287J/kgK. If the stagnation temperature in the combustion chamber is equal to 2310K, the speed of the exhaust gases (in m/s) is _____________. Q.46 A gas turbine engine is operating under the following conditions: AE (G Q.45 Stagnation temperature at turbine inlet Stagnation pressure at the turbine inlet Static temperature at turbine exit Velocity at turbine exit Total-to-total efficiency of turbine (ratio of specific heats) CP(specific heat at constant pressure) 1350 K 10 bar 800 K 200 m/s 0.96 1.33 1.147 kJ/kgK The stagnation pressure (in bar) in the nozzle (considering isentropic nozzle) is equal to _______. AE 9/11

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GATE 2014 Q.54 AEROSPACE AE Consider the following four statements regarding aircraft longitudinal stability: P. Q. R. S. CM,cg at zero lift must be positive CM,cg/ a must be negative ( a is absolute angle of attack) CM,cg at zero lift must be negative Slope of CL versus a must be negative Which of the following combination is the necessary criterion for stick fixed longitudinal balance and static stability? (A) Q and R only (C) P and Q only (D) Q and S only Data for a light, single-engine, propeller driven aircraft in steady level flight at sea-level is as follows: velocity V = 40m/s, weight W = 13000N, lift coefficient CL = 0.65, drag coefficient CD = 0.025 + 0.04CL2 and power available Pav = 100,000J/s. The rate of climb possible for this aircraft under the given conditions (in m/s) is (B) 5.11 (C) 6.32 (D) 4.23 20 (A) 7.20 14 ) Q.55 (B) Q, R, and S only AE (G AT E END OF THE QUESTION PAPER AE 11/11

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