GATE Solved Question Papers for Aerospace Engineering [AE] by AglaSem.Com

SOLVED PAPERS

GATE AEROSPACE ENGINEERING (AE)

A comprehensive study guide for GATE

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CONTENTS

• • • • • •

Introduction Question Paper Pattern Design of Questions Marking Scheme Syllabus Previous Year Solved Papers o Solved Question Paper 2014 o Answer Key 2014 o Solved Question Paper 2013 o Answer Key 2013 o Solved Question Paper 2012 o Answer Key 2012

Introduction The Graduate Aptitude Test in Engineering (GATE) is the all India level examination conducted by the Indian Institute of Science and seven Indian Institutes of Technology (IITs). A crucial part of GATE preparation is to solve and practice using previous year GATE papers. Solving previous year GATE papers help the candidate in understanding the exam pattern, knowing the level of difficulty of questions, and analyzing preparation. While attempting to solve any previous year GATE paper, it is advisable that it is done in a simulated test environment. This means, that the candidate sets a timer to countdown to test time, makes sure there is no other distraction, and then sits down to take the test as if he / she is in the exam hall. After attempting the paper, check how many questions you could get right in the first attempt. Analyse the strong and weak areas of preparation, and accordingly devise a study schedule or revision pattern. After going through those areas where in the first attempt could not do well, try the next paper. Almost all of the engineering colleges in India take admission in M.Tech courses on the basis of GATE scores. Apart from that, PSUs also recruit students directly on this basis. To score high in this elite examination is tough, but quite achievable.

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Question Paper Pattern In all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10 questions carrying a total of 15 marks are in General Aptitude (GA). In the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI, TF and XE, the Engineering Mathematics will carry around 13% of the total marks, the General Aptitude section will carry 15% of the total marks and the remaining percentage of the total marks is devoted to the subject of the paper. In the papers bearing the codes AR, CY, EY, GG, MA, PH and XL, the General Aptitude section will carry 15% of the total marks and the remaining 85% of the total marks is devoted to the subject of the paper. GATE would contain questions of two different types in various papers: (i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers and sections. These questions are objective in nature, and each will have a choice of four answers, out of which the candidate has to mark the correct answer(s). (ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. For these questions the answer is a real number, to be entered by the candidate using the virtual keypad. No choices will be shown for this type of questions.

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Design of Questions The questions in a paper may be designed to test the following abilities: (i) Recall: These are based on facts, principles, formulae or laws of the discipline of the paper. The candidate is expected to be able to obtain the answer either from his/her memory of the subject or at most from a one-line computation. (ii) Comprehension: These questions will test the candidate's understanding of the basics of his/her field, by requiring him/her to draw simple conclusions from fundamental ideas. (iii) Application: In these questions, the candidate is expected to apply his/her knowledge either through computation or by logical reasoning. (iv) Analysis and Synthesis: In these questions, the candidate is presented with data, diagrams, images etc. that require analysis before a question can be answered. A Synthesis question might require the candidate to compare two or more pieces of information. Questions in this category could, for example, involve candidates in recognising unstated assumptions, or separating useful information from irrelevant information.

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Marking Scheme For 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer. Likewise, for2-marks multiple-choice questions, 2/3 marks will be deducted for a wrong answer. There is no negative marking for numerical answer type questions. General Aptitude (GA) Questions In all papers, GA questions carry a total of 15 marks. The GA section includes 5 questions carrying 1 mark each (sub-total 5 marks) and 5 questions carrying 2 marks each (sub-total 10 marks). Question Papers other than GG, XE and XL These papers would contain 25 questions carrying 1 mark each (sub-total 25 marks) and 30 questions carrying 2 marks each (sub-total 60 marks). The question paper will consist of questions of multiple choice and numerical answer type. For numerical answer questions, choices will not be given. Candidates have to enter the answer (which will be a real number, signed or unsigned, e.g. 25.06, -25.06, 25, -25 etc.) using a virtual keypad. An appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors. GG (Geology and Geophysics) Paper Apart from the General Aptitude (GA) section, the GG question paper consists of two parts: Part A and Part B. Part A is common for all candidates. Part B contains two sections: Section 1 (Geology) and Section 2 (Geo-physics). Candidates will have to attempt questions in Part A and either Section 1 or Section 2 in Part B. Part A consists of 25 multiple-choice questions carrying 1-mark each (sub-total 25 marks and some of these may be numerical answer type questions). Each section in Part B (Section 1 and Section 2) consists of 30 multiple choice questions carrying 2 marks each (sub-total 60 marks and some of these may be numerical answer type questions). XE Paper (Engineering Sciences)


In XE paper, Engineering Mathematics section (Section A) is compulsory. This section contains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each (subtotal 7 marks), and 4 questions carrying 2 marks each (sub-total 8 marks). Some questions may be of numerical answer type questions. Each of the other sections of the XE paper (Sections B through G) contains 22 questions carrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13 questions carrying 2 marks each (sub-total 26 marks). Some questions may be of numerical answer type. XL Paper (Life Sciences) In XL paper, Chemistry section (Section H) is compulsory. This section contains 15 questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks) and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be of numerical answer type. Each of the other sections of the XL paper (Sections I through M) contains 20 questions carrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10 questions carrying 2 marks each (sub-total 20 marks). Some questions may be of numerical answer type. Note on Negative Marking for Wrong Answers For a wrong answer chosen for the multiple choice questions, there would be negative marking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wrong answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a wrong answer. However, there is no negative marking for a wrong answer in numerical answer type questions.


Syllabus for General Aptitude (GA) Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.

Syllabus for Aerospace Engineering (AE) ENGINEERING MATHEMATICS Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors. Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green. Differential Equations: First order linear and nonlinear equations, higher order linear ODEs with constant coefficients, Cauchy and Euler equations, initial and boundary value problems, Laplace transforms. Partial differential equations and separation of variables methods. Numerical methods: Numerical solution of linear and nonlinear algebraic equations, integration by trapezoidal and Simpson rule, single and multi-step methods for differential equations. FLIGHT MECHANICS Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts. Airplane performance: Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing; steady climb & descent,-absolute and service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds. Static stability: Angle of attack, sideslip; roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal tail position and size; directional stability, vertical tail

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position and size; dihedral stability. Wing dihedral, sweep & position; hinge moments, stick forces. Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lat-directional dynamics; longitudinal modes; lateral-directional modes. SPACE DYNAMICS Central force motion, determination of trajectory and orbital period in simple cases. Orbit transfer, in-plane and out-of-plane. Elements of rocket motor performance. AERODYNAMICS Basic Fluid Mechanics: Incompressible irrotational flow, Helmholtz and Kelvin theorem, singularities and superposition, viscous flows, boundary layer on a flat plate. Airfoils and wings: Classification of airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qualitative treatment of low aspect ratio wings. Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulent boundary layer. Compressible Flows: Dynamics and Thermodynamics of I-D flow, isentropic flow, normal shock, oblique shock, Prandtl-Meyer flow, flow in nozzles and diffusers, inviscid flow in a c-d nozzle, flow in diffusers. subsonic and supersonic airfoils, compressibility effects on lift and drag, critical and drag divergence Mach number, wave drag. Wind Tunnel Testing: Measurement and visualisation techniques. STRUCTURES Stress and Strain: Equations of equilibrium, constitutive law, strain-displacement relationship, compatibility equations, plane stress and strain, Airy’s stress function. Flight Vehicle Structures: Characteristics of aircraft structures and materials, torsion, bending and flexural shear. Flexural shear flow in thin-walled sections. Buckling. Failure theories. Loads on aircraft. Structural Dynamics: Free and forced vibration of discrete systems. Damping and resonance. Dynamics of continuous systems. PROPULSION Thermodynamics of Aircraft Gas Turbine engines, thrust and thrust augmentation.


Turbomachinery: Axial

compressors

and

turbines,

centrifugal

pumps

and

compressors. Aerothermodynamics of non rotating propulsion components: Intakes, combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of rocket propulsion.

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GATE Previous Year Solved Papers Aerospace Engineering – AE

2012 - 14


GATE 2014 Solved Paper Aerospace Engineering - AE Duration: 180 minutes

Maximum Marks: 100

Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: “I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition”.


GATE 2014

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. (A) vice

Q.3

(B) virtues

(C) choices

(D) strength

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

Q.5

(B) has a slope of +1 (D) has a slope of −1

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?

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

(B) EPVZB

(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)

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

GATE Previous Year Solved Papers by

Faisal 4 4 5 5

GATE 2014

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

Q.10

(B) 2.5

(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)

(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


GATE 2014

Aerospace - AE


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.

Q.2

The series s =

∞

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 Q.4

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:

(C)

1

∫

0 1

∫

0

dy1 dy5 dx = 0 dx dx 1 dy dy (D) ∫ ( y1 y5 + 1 5 )dx = 0 0 dx dx

y1 y5 dx = 0

(B)

y1 y5 dx ≠ 0

The value of I = (A) 200

Q.6

1

∫ 1000 x 0

4

1

∫

0

dx , obtained by using Simpson’s rule with 2 equally spaced intervals is,

(B) 400

(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? (A)CL =0.15 and Xm = 0.1c (C)CL=0.12 and Xm = 0.18c

Q.7

(B) Bounded and continuous everywhere (D) Continuous and differentiable everywhere

Given the boundary-value problem

(A)

Q.5

(D) R = 1 / 3

(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


GATE 2014

Q.8

Aerospace - AE

Consider supersonic flow near a corner (at an angle θfrom the horizontal) with an attached oblique shock (at an angle β 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)β will decrease if the shock is a weak shock (B)β will decrease if the shock is a strong shock (C)β will increase for both weak and strong shocks (D)β remains unchanged for both weak and strong shocks Q.9

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, �� =

Γ Γ , where strength of the vortex is and r is radial direction. The value of circulation 2�� 2�

along the curve shown in the figure is:

Q.10

(A) Γ

(B) −2Γ

(C) 2Γ

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:

(A) Streamline, streakline and pathline (C) Only a pathline Q.11

(D) 0

(B) Streamline and pathline (D) Only a streakline

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

(B) 40GPa& -0.4 respectively (D) 40GPa& 0.2 respectively


GATE 2014

Q.12

Aerospace - AE

In general, for any given solid subjected to arbitrary loading, which of the following statements is always true: (A) Volume does not vary with loading (C) Density does not vary with loading

Q.13

(B) Mass does not vary with loading (D) Volume, mass and density vary with loading

Which one of the following objects with inclined face at 45� , subjected to the given stresses, are in static equilibrium:

(A)

(B)

a

(D)

(C) Q.14

A damped single degree of freedom system whose undamped natural frequency,��=10Hz, is subjected to sinusoidal external force. Power is half of the maximumfor the two frequencies of 60.9469 rad/s and 64.7168 rad/s. The damping factor associated with the vibrating system (in %) is _______.

Q.15

The boundary conditions for a rod with circular cross-section, under torsional vibration,are changed from fixed-free to fixed-fixed. The fundamental natural frequency of the fixed-fixed rod is k times that of fixed-free rod. The value of k is (A) 1.5

Q.16

Q.17

(B) π

(C) 2.0

(D) 0.5

Match the appropriate engine (in right column) with the corresponding aircraft (in left column) for most efficient performance of the engine. a. Low speed transport aircraft b. High subsonic civilian aircraft c. Supersonic fighter aircraft d. Hypersonic aircraft

i. Ramjet ii. Turboprop iii. Turbojet iv. Turbofan

(A) a – iv, b – iii, c – i, d – ii (C) a – i, b – ii, c – iv, d – iii

(B) a – ii, b – i, c – iii, d – iv (D) a – ii, b – iv, c – iii, d – i

For a given fuel flow rate and thermal efficiency, the take-off thrust for a gas turbine engine burning aviation turbine fuel (considering fuel-air ratiof<<1) is (A) Directly proportional to exhaust velocity (B) Inversely proportional to exhaust velocity (C) Independent of exhaust velocity (D) Directly proportional to the square of the exhaust velocity


GATE 2014 Q.18

Aerospace - AE

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

The thrust produced by a turbojet engine (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

Q.21

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

Q.23

(B) -1

(B) Minimum CL/CD (D) Minimum CD/CL3/2

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

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

(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 ________.

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

(B) -324

(C) 324

(D) 6


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

={

−π < x<0

−2,

0< x<π with f ( x + 2π ) = f ( x) , using

2,

1 1 1 + − +  converges to 3 5 7

π

(C)

3

π

(D)

4

π 5

Let Γ 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 Γ

(A) π Q.29

(B) − π

(C) 1

(D) 0

Solution to the boundary-value problem

d 2u du − 9 2 + u = 5 x, 0 < x < 3 with u (0) = 0, dx dx

(

)

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

(

)

15e − x / 3 e + e x / 3 + 5x 1 + e2 15 sin( x / 3) 5 3 (D) u ( x) = − − x cos(1) 54 (B) u ( x) =

Q.30 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

.

du (0) = 5 is given by: with initial conditions u (0) = 0, dt (A)

Q.31

6 ( s + 1) 2

(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 _____.


GATE 2014 Q.32

Aerospace - AE

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)

Choose the correct combination of statements from the options given above: (A) (i), (iii), (v)

(B) (ii), (iv), (v)

(C) (i), (iv), (v)

(D) (i), (iii)

Q.33

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

(A) 2.95

(B) 0.79

(C) 1.18

(D) 0.64


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

Q.36

(B) (i) & (ii)

(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

Γ2

Γ 2�

+

1 � �Γ 1 ��. 4� ∫−� �� −�1 �2 �2

= 1, where�, Γ� and sare given in figure below.

For theabove semi-elliptic distribution of circulation, Γ, the downwash velocity at any point �1, for

symmetric flight can be obtained as, �(�1 ) =

� �� Γ� [� + �1 �], where � = �1 ∫−� . 4�� 2 −�2 ��−� � 1 � �1 −�

Which of the following options is correct if the induced drag is �� (given ∫

8�Γ2

(A)I=0 and �� = � �

Q.37

(C)I=0 and �� =

��Γ2� 8

−

�2 �2

�� =

�� 2

)

8�Γ2

(B)I= 1 and �� = � � (D)I= 1 and �� =

��Γ2� 8

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 ____.


GATE 2014

Aerospace - AE

Q.38

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

(A) 2.68 Q.40

(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

(A) 19.74 Q.41

(B) 5.36

(B) 9.87

(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

(B) 2.0

(C) 6.9

(D) 4.0


GATE 2014 Q.42

Aerospace - AE

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 = Q.43

(C)�1 = 0,�2 = 0, �3 = �,�4 = −

2

�

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

(A) 3.24 Q.44

�

3�

(B) 20.36

(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

(B) 4.41

(C) 2.67

(D) 3.02

Q.45

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 heatsγ = 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: 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 γ (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 _______.


GATE 2014

Aerospace - AE

Q.47

Air at a stagnation temperature of 300K (ratio of specific heats, γ = 1.4 and specific gas constant R = 287 J/kgK) enters the impeller of a centrifugal compressor in axial direction. The stagnation pressure ratio between the diffuser outlet and impeller inlet is 4.0. The impeller blade radius is 0.3 m and it is rotating at 15000 rev/min. If the slip factor σs (Ratio of tangential component of air velocity at the blade tip to the blade tip speed) is 0.88, the overall efficiency (total-to-total) of the compressor (in %) is ___________.

Q.48

A stationary two stage rocket with initial mass of 16000kg, carrying a payload of 1000kg, is fired in a vertical trajectory from the surface of the earth. Both the stages of the rocket have same specific impulse, Isp, of 300s and same structural coefficient of 0.14. The acceleration due to gravity is 9.8m/s2. Neglecting drag and gravity effects and considering both the stages with same payload ratio, the terminal velocity attained by the payload in m/s is __________________.

Q.49

An aircraft is flying at Mach 3.0 at an altitude where the ambient pressure and temperature are 50 kPa and 200 K respectively. If the converging-diverging diffuser of the engine (considered isentropic with ratio of specific heats, γ = 1.4 and specific gas constant R = 287 J/kgK) has a throat area of 0.05 m2, the mass flow rate through the engine in kg/s is (A) 197

Q.50

(C) 790

(D) 157

A cryogenic rocket has a specific impulse of 455s and characteristic velocity of 2386 m/s. The value of thrust coefficient for this rocket is (A) 1.78

Q.51

(B) 232

(B) 1.73

(C) 1.87

(D) 1.95

For a given airplane with a given wing loading executing a turn in the vertical plane, under what conditions will the turn radius be minimum and the turn rate be maximum? (A) Highest possible CLand lowest possible load factor (B) Lowest possible CLand lowest possible load factor (C) Lowest possible CLand highest possible load factor (D) Highest possible CLand highest possible load factor

Q.52

Lift-off distance for a given aircraft of weight W is SLO. If the take-off weight is reduced by 10%, then the magnitude of percentage change in the lift-off distance (assume all other parameters to remain constant) is _______.

Q.53

Which of the following design parameters influence the maximum rate-of-climb for a jet-propelled airplane? P. Wing loading Q. Maximum thrust-to-weight ratio R. Zero-lift drag coefficient S. Maximum lift-to-drag ratio (A) P and Q alone

(B) P, Q, R and S

(C) P, Q and S alone

(D) Q, R, and S alone


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/∂αa must be negative (αa is absolute angle of attack) CM,cg at zero lift must be negative Slope of CL versus αa 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 Q.55

(B) Q, R, and S 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 (A) 7.20

(B) 5.11

(C) 6.32

(D) 4.23



GATE 2014 - Answer Keys General Aptitude– GA Q. No. 1 2 3 4

Key / Range A B D C

Q. No. 5 6 7 8

Key / Range 1300 to 1300 D B 180 to 180

Q. No. 9 10

Key / Range D B

Key / Range D 0.45 to 0.55 D D B 1.2 to 1.25 A C D A B -5.01 to -4.99 C 1705 to 1720 B C C 0.99 to 1.01 0.12 to 0.13

Q. No. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Key / Range A B D D B D 1880 to 1881 1.10 to 1.25 74 to 76 6050 to 6250 D C D 18 to 20 B C B

Aerospace Engineering – AE Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 ` 14 15 16 17 18 19

Key / Range C B C A D A D B D D A B B 2.95 to 3.05 C D B B C

Q. No. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

GATE 2013

Aerospace - AE

GATE 2013 Solved Paper Aerospace Engineering - AE

Duration: Three Hours

Maximum Marks:100

Paper specific instructions:

1. There are a total of 65 questions carrying 100 marks. Questions are of multiple choice type or numerical answer type. A multiple choice type question will have four choices for the answer with only one correct choice. For numerical answer type questions, the answer is a number and no choices will be given. A number as the answer should be entered using the virtual keyboard on the monitor. 2. Questions Q.1 – Q.25 carry 1mark each. Questions Q.26 – Q.55 carry 2marks each. The 2marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 3. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1mark each, and questions Q.61 – Q.65 carry 2marks each. 4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions will result in NEGATIVE marks. For all 1 mark questions, ̃ mark will be deducted for each wrong answer. For all 2 marks questions, ̄ mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. There is no negative marking for questions of numerical answer type. 5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. 6. Do the rough work in the Scribble Pad provided.


GATE 2013

Aerospace - AE


The directional derivative of the function f ( x, y ) 

x 2  xy 2 in the direction 5

 a  2iˆ  4 ˆj at

( x, y )  (1,1) is

(A) 

Q.2

1 5

(B) 

5

The value of

x 4

(A) ln 24 11

Q.3

2

(C) 0

2 5

(D) 

1 5

x2 dx is  4 x  21 (B) ln 12 11

(C) ln 2

(D) ln 12 11

At x  0 , the function y  x is (A) continuous but not differentiable (B) continuous and differentiable (C) not continuous but differentiable (D) not continuous and not differentiable

Q.4

One of the eigenvectors of the matrix

1  1 1 0    is A   0 1 1  v  1 .  1 0 1  1   The corresponding eigenvalue is ____________

Q.5

Which one of the following is the most stable configuration of an airplane in roll? (A) Sweep back, anhedral and low wing (B) Sweep forward, dihedral and low wing (C) Sweep forward, anhedral and high wing (D) Sweep back, dihedral and high wing


GATE 2013 Q.6

Aerospace - AE

Which one of the following flight instruments is used on an aircraft to determine its attitude in flight? (A) Vertical speed indicator (B) Altimeter (C) Artificial Horizon (D) Turn-bank indicator

Q.7

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? (A) Airplane will experience less stability in pitch at supersonic speeds than at subsonic speeds (B) Airplane will feel no change in pitch stability (C) Airplane will experience more stability in pitch at supersonic speeds than at subsonic speeds (D) Pitch stability cannot be inferred from the information given

Q.8

Which one of the following is favorable for an airplane operation? (A) Tail wind in cruise and head wind in landing (B) Tail wind both in cruise and landing (C) Head wind both in cruise and landing (D) Head wind in cruise and tail wind in landing

Q.9

Which one of the following is TRUE with respect to Phugoid mode of an aircraft? (A) Frequency is directly proportional to flight speed (B) Frequency is inversely proportional to flight speed (C) Frequency is directly proportional to the square root of flight speed (D) Frequency is inversely proportional to the square root of flight speed

Q.10

The x and y velocity components of a two dimensional flow field are,

u

cy cx ,v  2 , where c is a constant. The streamlines are a family of 2 x y x  y2 2

(A) hyperbolas

(B) parabolas

(C) ellipses

(D) circles


GATE 2013 Q.11

Aerospace - AE

Which one of the following statements is NOT TRUE for a supersonic flow? (A) Over a gradual expansion, entropy remains constant (B) Over a sharp expansion corner, entropy can increase (C) Over a gradual compression, entropy can remain constant (D) Over a sharp compression corner, entropy increases

Q.12

Consider a compressible flow where an elemental volume of the fluid is  , moving with velocity  V . Which one of the following expressions is TRUE?  1 D (A)   V   Dt  1 D (B)   (  V )   Dt  DV 1 D  (C)   Dt  Dt   1 D (D) V  (  V )   Dt

Q.13

Consider a thin flat plate airfoil at a small angle Assuming the flow to be inviscid,

 to an oncoming supersonic stream of air.

Cd is C l2

(A) zero (B) independent of  (C) proportional to  (D) proportional to  2

Q.14

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

Q.15

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 ______________


GATE 2013 Q.16

Aerospace - AE

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

A (A) does not move horizontally or axially, but moves vertically (B) does not move axially, but moves both vertically and horizontally (C) does not move horizontally, vertically or axially (D) does not move vertically or axially, but moves horizontally Q.17

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 modulus of 25 GPa, the twist per unit length in radians/m is _________

300mm

600mm

300mm


GATE 2013 Q.18

Aerospace - AE

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 cm . 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

A

D 200mm C

B

500mm (A) 20, 20, 20, 20 (B) 0, 0, 50, 50 (C) 40, 40, 0, 0 (D) 50, 50, 50, 50

Q.19

Consider two engines P and Q. In P, the high pressure 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? (A) Turbine inlet temperature is higher for engine P (B) Specific thrust is higher for engine P (C) Compressor work is the same for both P and Q (D) Fuel flow rate is lower for engine P

Q.20

The mass flow rate of air through an aircraft engine 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 ___________

Q.21

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


GATE 2013 Q.22

Aerospace - AE

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

Q.23

(B) 8 km altitude

(C) 5.5 km altitude

(D) 11 km altitude

Consider the low earth orbit (LEO) and the geo synchronous orbit (GSO). Then (A) V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is lower than that of GSO (B) V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is lower than that of GSO (C) V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is greater than that of GSO (D) V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is greater than that of GSO

Q.24

Q.25

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)

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 specific 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


GATE 2013

Aerospace - AE

Q. 26 to Q. 55 carry two marks each. Q.26

Let I 

 ( y ziˆ z 2

2

xjˆ  x 2 ykˆ)฀( xiˆ  yjˆ  zkˆ)dS , where S denotes the surface of the sphere of unit

S

radius centered at the origin. Here iˆ, ˆj and kˆ denote three orthogonal unit vectors. The value of I is ____________

Q.27

Given that the Laplace transform, (A)

Q.28

3s s  10 s

(B)

2

(e at ) 

 3e5t sinh 5t  =

1 then sa

15 s  10 s

(C)

2

3s s  10 s 2

(D)

15 s  10 s 2

Values of a, b and c, which render the matrix

    Q    

1 3 1 3 1 3

1 2 0 

1 2

 a   b   c 

orthonormal are, respectively (A)

(B)

Q.29

1 2

,

1 2

, 0

1 2 1 ,, 6 6 6

(C) 

1

(D) 

1 2 1 , ,6 6 6

3

, 

1 3

,

1 3

d2y dy A function satisfies the differential equation  2  y  0 and is subject to the initial 2 dt dt dy (t  0)  1. The value of y (t  1) is conditions y (t  0)  0 and dt (A) e

(B) 0

(C) 1

(D) -1


GATE 2013

Aerospace - AE

Q.30

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

Q.31

Which one of the following criteria leads to maximum turn rate and minimum radius in a level turn flight? (A) Highest possible load factor and highest possible velocity (B) Lowest possible load factor and lowest possible velocity (C) Highest possible load factor and lowest possible velocity (D) Lowest possible load factor and highest possible velocity

Q.32

Consider an airplane with rectangular straight wing at dihedral angle   100 . Lift curve slope of wing airfoil section (constant over the whole span of the wing) is cl  5.4 / rad . The roll stability derivative, Cl  in per radian is __________

Q.33

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 ________

Q.34

The potential flow model for a storm is represented by the superposition of a sink and a vortex. The   ln r , where stream function can be written in the ( r ,  ) system as      2 2     100 m 2 /s . Assume a constant air density of 1.2 kg/m3. The gauge pressure at a distance of 100 m from the storm eye is (A) 

Q.35

(B) 

1.2



2

(C) 

1.2 2 2

(D) 

1.2 4 2

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


GATE 2013 Q.36

Aerospace - AE

Streamline pattern of flow past a cylinder is shown 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

4 1

2 3 5 6

(A) 1 and 2

Q.37

(B) 1 and 5

(C) 3 and 4

(D) 5 and 6

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 1.9 2.0 2.1 2.2 2.3 2.4

20.73 23.59 26.38 29.10 31.73 34.28 36.75

The Mach number downstream of the expansion is (A) 1.88

(B) 2.00

(C) 2.11

(D) 2.33


GATE 2013 Q.38

Aerospace - AE

The idealized cross-section of a beam is comprised of four identical booms connected by shear webs. The beam is subjected to a bending moment as shown in the figure. The inclination of the neutral axis to the x-axis in degrees is

M

2a

x

a

(A) 45 CW

Q.39

(B) 45 CCW

a

(C) 26.6 CW

(D) 63.4 CCW

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

(A) Only shear stress is continuous across the steel–aluminum interface (B) Only shear strain is continuous across the steel–aluminum interface (C) Both shear stress and shear strain are continuous across the steel–aluminum interface (D) Both shear stress and shear strain are discontinuous across the steel–aluminum interface Q.40

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 (A) indeterminate (B) P, -P, P (C) 0, P, 0 (D) P/3, P/3, P/3


GATE 2013 Q.41

Aerospace - AE

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 at which the column BD may buckle in Newtons is hinged. The minimum value of load approximately ____________

1m

1m

2m

D

Q.42

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

M

M

b

x L

(A)

Q.43

2M 3 x tb3

(B)

2M 3 y tb3

(C)

2M 3 x  y3  3  tb

(D)

2M 4 y tb3

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 ________


GATE 2013 Q.44

Aerospace - AE

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

q

A

B

L

(A) Q.45

qL2 sagging 16

(C)

3qL2 hogging 16

(D)

3qL2 sagging 16

(B) 4000

(C) 4200

(D) 4400

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

Q.47

qL2 hogging 16

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

Q.46

(B)

L/2

(B) 40

(C) 50

(D) 60

Consider two rockets P and Q fired vertically up with 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 W  30kN , thrust available at sea-level T0  4000 N , wing planform area S  30m 2 , maximum lift coefficient CL max  1.4 , and drag coefficient C D  0.015  0.024C L2 . Assume air density at sea-level    1.22kg / m 3 .

Q.48

Stall speed of the airplane in m/s is (A) 17.36

Q.49

(B) 34.22

(C) 45.52

(D) 119.46

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


GATE 2013

Aerospace - AE

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 temperature 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.

Q.50

For which one of the nozzle exit Mach numbers given below is the propulsive efficiency highest? (A) 1 (B) 1.5 (C) 2 (D) 2.5

Q.51

For which one of the nozzle exit Mach numbers given below is the thrust highest? (A) 1 (B) 1.5 (C) 2 (D) 2.5

Linked Answer Questions Statement for Linked Answer Questions 52 and 53: Circulation theory of lift is assumed for a thin symmetric airfoil at an angle of attack α. Free stream velocity is U.

Q.52

If the circulation at the quarter chord (c/4) of the airfoil is 1 , the normal velocity is zero at (A) c/4

Q.53

(B) c/2

(C) 3c/4

(D) all points on the chord

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)

4 2  cU  ,  cU  3 3

(B)

2 2  cU  ,  cU  3 3

(C)

2 1  cU  ,  cU  3 3

(D)

4 4  cU  ,  cU  3 3


GATE 2013

Aerospace - AE

Statement for Linked Answer Questions 54 and 55: A wing-body alone configuration airplane with a wing loading of W  1000 N / m 2 is flying in cruise condition at a speed V = 90m/s at sea-level (air density S at sea-level    1.22kg / m 3 ). The zero lift pitching moment coefficient of the airplane is wb  Cm 0  0.06 and the location of airplane aerodynamic center from the wing leading edge is Cmac

X ac  0.25c. Here c is the chord length. Q.54

The airplane trim lift coefficient CL trim is

(A) 0.502 Q.55

(B) 0.402

(C) 0.302

(D) 0.202

Distance of center of gravity of the aircraft ( X CG ) from the wing leading edge is (B) 0.547c

(A) 0.447c

(C) 0.547c

(D) 0.25c

General Aptitude (GA) Questions Q. 56 – Q. 60 carry one mark each. Q.56

If

(A)

(B)

(C) (D) Q.57

5 and

then which of the following options is TRUE?

The Headmaster ___________ to speak to you. Which of the following options is incorrect to complete the above sentence? (A) is wanting (B) wants (C) want (D) was wanting

Q.58

Mahatama Gandhi was known for his humility as (A) he played an important role in humiliating exit of British from India. (B) he worked for humanitarian causes. (C) he displayed modesty in his interactions. (D) he was a fine human being.


GATE 2013 Q.59

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

Q.60

Aerospace - AE

(B) II

(C) III

(D) IV

Select the pair that best expresses a relationship similar to that expressed in the pair: water: pipe:: (A) cart: road (C) sea: beach

(B) electricity: wire (D) music: instrument

Q. 61 to Q. 65 carry two marks each. Q.61

Q.62

Velocity of an object fired directly in upward direction is given by 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)

, where

(time)

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 lot is found defective, what is the probability that it was manufactured by M2? (A) 0.35

Q.63

(B) 0.45

(C) 0.5

(D) 0.4

Following table gives data on tourists from different countries visiting India in the year 2011. Country

USA England Germany Italy Japan Australia France

Number of Tourists 2000 3500 1200 1100 2400 2300 1000

Which two countries contributed to the one third of the total number of tourists who visited India in 2011?

(A) USA and Japan (B) USA and Australia (C) England and France (D) Japan and Australia


GATE 2013 Q.64

If |

(A) 30

Q.65

Aerospace - AE |

then the possible value of | (B) -30

|

would be:

(C) -42

(D) 42

All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments: (A) All scientists are researchers (B) All professors are scientists (C) Some researchers are scientists (D) No conclusion follows



GATE 2013 - Answer Keys Aerospace Engineering – AE Q. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key/Range D A A 0 D C C A B A B A B 1 0.2 Marks to All 0.12 to 0.13 D D 0.3 to 0.35 D D

Q. No 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key/Range B B A 0 B D A 9 to 10 C -0.23 to -0.24 1 D C C C A B B 1900 to 2000 B 70 A

Q. No 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key/Range B A B B C A D Marks to All Marks to All D C B C C D B C C C B C


GATE 2012 Solved Paper Aerospace Engineering - AE Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully. 1. The computer allotted to you at the examination center runs a specialized software that permits only one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated and saved on a server periodically and at the end of the examination. 2. To login, enter your Registration Number and password provided in the envelope. Go through the symbols used in the test and understand the meaning before you start the examination. You can view all questions by clicking on the View All Questions button in the screen after the start of the examination. 3. To answer a question, select the question using the selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. To change the answer, just click on another option. If you wish to leave a previously answered question unanswered, click on the button next to the selected option. 4. The examination will automatically stop at the end of 3 hours. 5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a numerical answer, and a number should be entered using the virtual keyboard on the monitor. 6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 8. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For all 1 mark questions, ̃ mark will be deducted for each wrong answer. For all 2 marks questions, ̄ mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the rough work in the Scribble Pad provided. 10. You must sign this sheet and leave it with the invigilators at the end of the examination. ________________________________________________________________________________________ DECLARATION: I hereby declare that I have read and followed all the instructions given in this sheet. Registration Number

AE

Name Signature Verified that the above entries are correct. Invigilator’s signature:


GATE 2012

Aerospace - AE


The constraint A2 = A on any square matrix A is satisfied for (A) the identity matrix only. (C) both the identity matrix and the null matrix.

Q.2 The general solution of the differential equation (A) Ae − t + Be 2t Q.3

(B) Ae −2t + Be − t

(D) Aet + Be 2t

(B) its centre of gravity. (D) 50% of its wing root chord.

(B) a ramp input. (D) an impulse input.

For a symmetric airfoil, the lift coefficient for zero degree angle of attack is (A) – 1.0

Q.6

(C) Ae −2t + Bet

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

Q.5

d 2 y dy + − 2 y = 0 is dt 2 dt

An aircraft in trimmed condition has zero pitching moment at (A) its aerodynamic centre. (C) 25% of its mean aerodynamic chord.

Q.4

(B) the null matrix only. (D) no square matrix A.

(B) 0.0

(C) 0.5

(D) 1.0

The critical Mach number of an airfoil is attained when (A) the freestream Mach number is sonic. (B) the freestream Mach number is supersonic. (C) the Mach number somewhere on the airfoil is unity. (D) the Mach number everywhere on the airfoil is supersonic.

Q.7

The shadowgraph flow visualization technique depends on (A) the variation of the value of density in the flow. (B) the first derivative of density with respect to spatial coordinate. (C) the second derivative of density with respect to spatial coordinate. (D) the third derivative of density with respect to spatial coordinate.

Q.8

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

Q.9

(B) both apogee and perigee at earth. (D) both apogee and perigee at Mars.

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 (A) 2nd order linear homogenous partial differential equation. (B) 4th order linear non-homogenous ordinary differential equation. (C) 2nd order linear non-homogenous ordinary differential equation. (D) 4th order nonlinear homogenous ordinary differential equation.

Q.10

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


GATE 2012 Q.11

Aerospace - AE

The value of k for which the system of equations x + 2 y + kz = 1; solution is (A) 0

Q.12

(B) 2

2 x + ky + 8 z = 3 has no

(C) 4

(D) 8

d 2x If u (t ) is a unit step function, the solution of the differential equation m 2 + kx = u (t ) in dt Laplace domain is (A)

Q.13

1 s (ms 2 + k )

1 ms + k

(B) y − x + C = 0

1 s (ms 2 + k ) 2

y − x +C = 0

(D)

y − x+C = 0

(B) is drag alone. (D) are thrust, drag and a part of both weight and lift.

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 (B) lower by more than 10%. (D) an unpredictable quantity.

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

Q.17

(D)

dy − 2 y = 0 is dx (C)

(A) lower by exactly 10%. (C) lower by less than 10%. Q.16

ms + k 2

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

Q.15

s

(C)

2

The general solution of the differential equation (A) y − x + C = 0

Q.14

(B)

(B) reducing the angle of attack alone. (D) increasing the engine thrust alone.

In an aircraft, elevator control effectiveness determines (A) turn radius. (B) rate of climb. (C) forward-most location of the centre of gravity. (D) aft-most location of the centre of gravity.

Q.18

The Mach angle for a flow at Mach 2.0 is (A) 30o

Q.19

(C) 60o

(D) 90o

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

Q.20

(B) 45o

CL π AR

(B)

CL2 π AR

(C)

CL 2π AR

(D)

CL2 π AR 2

Bernoulli’s equation is valid under steady state (A) only along a streamline in inviscid flow, and between any two points in potential flow. (B) between any two points in both inviscid flow and potential flow. (C) between any two points in inviscid flow, and only along a streamline in potential flow. (D) only along a streamline in both inviscid flow and potential flow.


GATE 2012 Q.21

Aerospace - AE

The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is (A) 0.0

Q.22

(B) 0.5

(B) 0.50

(C) 0.75

(D) 1.0

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. (C) earth’s standard sea level.

Q.24

(D) 2.0

The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is (A) 0.25

Q.23

(C) 1.0

(B) Mars standard “sea level”. (D) the same depth of the crater on earth.

In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary carriers of (A) shear stresses due to an aerodynamic moment component alone. (B) normal (bending) stresses due to aerodynamic forces. (C) shear stresses due to aerodynamic forces alone. (D) shear stresses due to aerodynamic forces and a moment component.

Q.25

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. 1

Q.26

The integration

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

0

Q.27

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 ____.

Q.28

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 m2/s is ____.

Q.29

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 ____.

Q.30

The mode shapes of an un-damped two degrees of freedom system are

{1

{1

0.5}

T

and

− 0.675} . The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum T

amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of

{2 1}

T

(in mm) and zero initial velocities is ____.


GATE 2012

Aerospace - AE

Questions Q.31 to Q.55 are multiple choice type. Q.31

The nth derivative of the function y =

(−1) n n ! (A) ( x + 3) n +1 Q.32

4 3

1 3

(B) 4π 2 − π

(B) −18.33

(B) 1380 m.

(C) 18.33−9.33i

(D) 18.33+9.33i

(B) lower by more than 10%. (D) an unpredictable quantity.

(C) 830 m.

(D) 380 m.

(B) 1.95 N downward force. (D) 1.75 N downward force.

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)

Q.38

3 2 π −π 4

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/m3) and 120 m/s TAS without re-trimming, the aircraft needs (A) 1.95 N upward force. (C) 1.85 N upward force.

Q.37

(D)

An aircraft has an approach speed of 144 kmph with a descent angle of 6.6o. If the aircraft load factor is 1.2 and constant deceleration at touch down is 0.25g (g = 9.81 m/s2), its total landing distance approximately over a 15 m high obstacle is (A) 1830 m.

Q.36

3 4

(C) π 2 − π

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

Q.35

(−1) n n ! (D) ( x + 3) n

⎡ 2 7 10 ⎤ ⎢ ⎥ One eigenvalue of the matrix A = 5 2 25 is – 9.33. One of the other eigenvalues is ⎢ ⎥ ⎢⎣1 6 5 ⎥⎦ (A) 18.33

Q.34

(−1) n (n + 1)! (C) ( x + 3) n

The volume of a solid generated by rotating the region between semi-circle y = 1 − 1 − x 2 and straight line y = 1, about x axis, is (A) π 2 − π

Q.33

(−1) n +1 n ! (B) ( x + 3) n +1

1 is x+3

(B) cos(β–θ)

(C) sin(θ–β)

(D) cos(θ–β)

In a closed-circuit supersonic wind tunnel, the convergent-divergent (C-D) nozzle and test section are followed by a C-D diffuser to swallow the starting shock. Here, we should have the (A) diffuser throat larger than the nozzle throat and the shock located just at the diffuser throat. (B) diffuser throat larger than the nozzle throat and the shock located downstream of the diffuser throat. (C) diffuser throat of the same size as the nozzle throat and the shock located just at the diffuser throat. (D) diffuser throat of the same size as the nozzle throat and the shock located downstream of the diffuser throat.


GATE 2012 Q.39

Aerospace - AE

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

Q.40

(C) 0.18

(D) 1.18

(B) 38 mm

(C) 41 mm

(D) 45 mm

(B) 1.75 m3

(C) 1.85 m3

(D) 1.95 m3

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/s2.] (A) 315 km

Q.44

(B) 0.018

A bipropellant liquid rocket motor operates at a chamber 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/m3, what should be the minimum fuel tank volume for a burn time of 8 minutes (A) 1.65 m3

Q.43

(D) 100 m/s

A solid propellant of density 1800 kg/m3 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 m2. 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

Q.42

(C) 10 m/s

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

Q.41

(B) 1 m/s

(B) 335 km

(C) 365 km

(D) 385 km

The Airy stress function, φ = α x 2 + β xy + γ y 2 for a thin square panel of size l × l automatically satisfies compatibility. If the panel is subjected to uniform tensile stress, σ o on all four edges, the traction boundary conditions are satisfied by

Q.45

(A) α = σ o / 2; β = 0; γ = σ o / 2.

(B) α = σ o ; β = 0; γ = σ o .

(C) α = 0; β = σ o / 4; γ = 0.

(D) α = 0; β = σ o / 2; γ = 0.

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

Q.46

1 2

1 2

(D)

2

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 Cosωd t is given by (A) π cωd X 2

Q.47

(C)

(B) 2

(B) πωd X 2

(C) π cωd X

(D) π cωd2 X

Buckling of the fuselage skin can be delayed by (A) increasing internal pressure. (B) placing stiffeners farther apart. (C) reducing skin thickness. (D) placing stiffeners farther and decreasing internal pressure.


GATE 2012

Aerospace - AE

Common Data Questions Common Data for Questions 48 and 49: A wing and tail are geometrically similar, while tail area is one-third of the wing area and distance between two aerodynamic centres is equal to wing semi-span (b/2). In addition, following data is applicable: ∈α = 0.3, CL = 1.0, CLα = 0.08 / deg., c = 2.5m, b = 30m, CM ac = 0, ηt = 1. The symbols have their usual aerodynamic interpretation. Q.48

The maximum distance that the centre of gravity can be behind aerodynamic centre without destabilizing the wing-tail combination is (A) 0.4 m

Q.49

(B) 1.4 m

(C) 2.4 m

(D) 3.4 m

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.] Q.50

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

Q.51

(B) 0.1 m/s

(C) 1 m/s

(D) 10 m/s

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 this absolute velocity to the rotor inlet at an angle of 18o to the axial direction. The rotor turning angle is 27o and the mean blade speed is 200 m/s. The axial velocity is assumed constant through the stage. Q.52

The blade angle at the inlet of the rotor is (A) 25.5o

Q.53

(B) 38.5o

(C) 48.5o

(D) 59.5o

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 and 10 mm wall thickness) is made of a material with σ Y = 500 MPa in both tension and compression. Q.54

The internal pressure pY 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

Q.55

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 pY . (C) occurs at about the same pressure pY .

(B) occurs at about double the pressure pY . (D) never occurs.


GATE 2012

Aerospace - AE

General Aptitude (GA) Questions Q. 56 – Q. 60 carry one mark each. Q.56

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 (C) would like

Q.57

(B) should have liked (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 (C) have been rising

Q.58

(B) have been raising (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. (A) reflective

Q.59

(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. (A) intrepidity

Q.60

(B) inevitability

(C) inability

(D) inertness

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

(B) 40

(C) 50

(D) 60

Q. 61 - Q. 65 carry two marks each. Q.61

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 (A) 0.14

(B) 0.22

(C) 0.33

(D) 0.40


GATE 2012 Q.62

Aerospace - AE

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 (A) P

Q.63

(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 (D) sum of cube roots of two natural numbers

Q.64

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

Q.65

(B) 0

(C) 3

(D) 4

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 (A) did not question that progress was a fact. (B) did not approve of Biology. (C) framed the laws of progress. (D) emphasized Biology over Social Sciences.



GATE 2012 - Answer Keys Aerospace Engineering – AE Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key / Range C C B D B C C C B C C A D D B C C A B A C Marks to All

Q. No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key / Range C D D 0.26 to 0.27 13 to 14 1.1 to 1.2 1430 to 1440 2 A A A B Marks to All B A B B B B B D A

Q. No. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key / Range A A A B A A Marks to All Marks to All Marks to All D C C C D A C A B A C A

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