GATE AE 2007-2014 With Answers

ENGINEERING ENGINEER ING MA THEMATICS

Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors.

Calculus: Functions of single variable, limit, continui ty 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 Differe ntial Calculus: 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 e quations.

FLIGHT MECHANICS

Atmo At mo sp spher here: e: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts.

Ai rp rplan lane e perfo per fo rm anc ance: e: Pressure altitude; equivalent, calibrated, ind icated 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 lo iter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds.

Static stability: Angle of attack, sideslip; roll, roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal horizontal tail position and size; directional stability, vertical tail 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 pl ate.

Airf Ai rf oi ls and wi ng ngs: s: Classification of airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qua litative treatment of low aspect ratio wings.

Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulent boundary layer.

Compressible Flows: Dynamics & 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 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 Struct Struct ures: 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.

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 pl ate.

Airf Ai rf oi ls and wi ng ngs: s: Classification of airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qua litative treatment of low aspect ratio wings.

Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulent boundary layer.

Compressible Flows: Dynamics & 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 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 Struct Struct ures: 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. compressors.

Aerot Aer other hermo mody dynam namic ics s of o f n on ro rotat tatin in g pro p ro pu puls ls io ion n com c om po ponen nents ts : Intakes, combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of rocket propulsion.

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2011

AEROSPACE ENGINEERING – AE

AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully.

1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are 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). 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. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ⅓ mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ⅔ mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ⅔ mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. 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. Paper Code: AE Registration No:__________________Name: ___________________________

Signature

AE

2011


Q. 1 – Q. 25 carry one mark each. Q.1

Consider x, y, z to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as v

 3 xi  3 xy j  yz 2k , where

i, j and k are the unit vectors along x, y and

z axes, respectively. The curl of v is given by (A) z i  3 yk

(B) z j  3 yk

2

Q.2

(B) f ( x)

2

The function f ( x1 , x2 , x3 )  x1

2

(A) (1, 2, 3) Q.4

2

(D)

 z 2i  3 yk

Which of the following functions is periodic? (A) f ( x )  x

Q.3

(C) z i  3 y j

2

 log x

(C) f ( x)

(D) f ( x)  const .

 e x

 x22  x32  2 x1  4 x2  6 x3  14 has its minimum value at

(B) (0, 0, 0)

Consider the function f ( x1 , x2 )  x1

2

(C) (3, 2, 1)

 2 x22  e x  x 1

2

(D) (1, 1, 3)

. The vector pointing in the direction of

maximum increase of the function at the point (1, -1) is (A)

Q.5

 2      5 

(B)

 1      5 

Two simultaneous equations given by y

(C)

 2      4 

(B) infinitely many solutions (D) a finite number of multiple solutions

In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, straindisplacement equations and equations of equilibrium are, respectively, (A) 3, 3 and 3

Q.7

(D)

   x and y  x   have

(A) a unique solution (C) no solution Q.6

  0.73      6.73 

(B) 6, 3 and 3

(C) 6, 6 and 3

(D) 6, 3 and 6

An Euler-Bernoulli beam in bending is assumed to satisfy (A) both plane stress as well as plane strain conditions (B) plane strain condition but not plane stress condition (C) plane stress condition but not plane strain condition (D) neither plane strain condition nor plane stress condition

Q.8

A statically indeterminate frame structure has (A) same number of joint degrees of freedom as the number of equilibrium equations (B) number of joint degrees of freedom greater than the number of equilibrium equations (C) number of joint degrees of freedom less than the number of equilibrium equations (D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics

Q.9

Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of m , c and k , respectively. The logarithmic decrement of this system can be calculated using (A)

AE

2 c 4mk  c 2

(B)

 c 4mk  c 2

(C)

2 c mk  c

2

(D)

2 c mk  4c

2

2011

Q.10


Consider a single degree of freedom spring-mass system of spring stiffness k1 and mass m which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness k 2 and mass m which has a natural frequency of 20 rad/s. The spring stiffness

k 2 is equal to (B) 2k 1

(A) k 1

Q.11

(C)

k 1

(D) 4k 1

4

Consider a simply supported two-dimensional beam

If the beam is converted into a fixed-fixed beam as

then the degree of static indeterminacy will (A) increase by 3 Q.12

(B) increase by 2

(C) decrease by 1

(D) decrease by 3

An impulsive launch of a rocket minimizes the loss of burn-out velocity due to (A) aerodynamic drag force only (B) gravitational force only (C) both aerodynamic drag and gravitational forces (D) reaction jet control force

Q.13

Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (C) propellant masses

Q.14

In an un-powered glide of an aircraft having weight W , lift L and drag D, the equilibrium glide angle is defined as (A) tan

Q.15

(B) structural mass efficiencies (D) control system masses

1

 L     D 

(B) tan

1

 D     L 

1

 W     L 

(B) is never zero

(C) is always negative

(D) could be any value

For an airplane to be statically stable, its centre of gravity must always be (B) aft of the wing aerodynamic centre (D) aft of neutral point

It is seen that the drag polar of a certain aerofoil is symmetric about the C d axis. This drag polar could refer to (A) NACA 0012

AE

(D) tan

(B) zero (D) equal to the thrust

(A) ahead of wing aerodynamic centre (C) ahead of neutral point Q.18

 L     W 

If an aircraft is performing a positive yawing manoeuvre, the side slip angle (A) is always zero

Q.17

1

Lift on an aircraft climbing vertically up is (A) equal to its weight (C) equal to the drag

Q.16

(C) tan

(B) NACA 4415

(C) NACA 23012

(D) None of the above

2011

Q.19


The aerodynamic centre of a supersonic aerofoil, with chord c, is located at (A) the leading edge

Q.20

(B) profile drag

(C) wave drag

(D) induced drag

 R 2   r (B) V  r cos  1  2   ln r R 2     R 2   r (D) V  r sin  1  2   ln r R 2   

A main objective of by-pass in a turbo-fan engine is to increase (A) mass flow rate through engine inlet (C) mass flow rate through exhaust nozzle

Q.23

(D) 0.75c

Consider a potential flow with free stream velocity V ∞, over a spinning circular cylinder of radius R and circulation . The stream function, ψ, where ψ = 0 on the cylinder surface, in cylindrical coordinates (r, ) is given by

 R 2   r (A) V  r cos  1  2   ln r R 2     R 2   r (C) V  r sin  1  2   ln r R 2    Q.22

(C) 0.5c

Winglets are used on wings to minimize (A) skin friction drag

Q.21

(B) 0.25c

(B) turbine inlet temperature (D) compressor pressure ratio

The pressure ratio in any one stage of a jet engine compressor is limited by (A) entry stagnation temperature in that stage (B) entry Mach number in that stage (C) pressure gradient induced separation in that stage (D) mass flow rate in that stage

Q.24

Thermodynamic cycle on which the jet engine operates can be (A) open Rankine cycle only (C) open Brayton cycle only

Q.25

(B) either open or closed Rankine cycle (D) either open or closed Brayton cycle

Propulsion efficiency of a jet engine is (A) directly proportional to both the thrust power and the air mass flow rate (B) inversely proportional to both the thrust power and the air mass flow rate (C) directly proportional to the thrust power and inversely proportional to the air mass flow rate (D) inversely proportional to the thrust power and directly proportional to the air mass flow rate

Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Q.26

Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young’s modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span ( L/2) at the center of the cross-section. Under the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is P L/2 L

AE

2011


Q.27

Consider a beam in bending with a solid circular cross-section of 1 mm 2, which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm 2) is

Q.28

A simply supported slender column of square cross section (width=depth= d ) has to be designed such that it buckles at the same instant as it yields. Length of the column is given to be 1.57 m and it is made of a material whose Young’s modulus is 200 GPa and yield stress is 240 MPa. The width, d , of the column (in cm) should be

Q.29

A turbojet powered aircraft is flying at Mach number 0.8 at an altitude of 10 km. The inlet and exit areas of the engine are 0.7 m 2 and 0.4 m 2 respectively. The exhaust gases have velocity of 500 m/s and pressure of 60 kPa. The free stream pressure, density and speed of sound are 26.5 kPa, 0.413 kg/m3 and 299.5 m/s respectively. The thrust of the engine (in kN) is

Q.30

A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1 m2. The static pressure difference between the settling chamber and the test section is 40 cm of water column. Assume g

 9.81 m/s 2 ,  air  1.2 kg/m3 and

 water  1000 kg/m 3 . The

speed of air in the test section (in m/s) is

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

Consider the function f ( x)  x  sin( x) . The Newton-Raphson iteration formula to find the root of the function starting from an initial guess x (A) x (C) x

( k 1)

( k 1)

 

sin x ( k )  x ( k ) cos x k 1  cos x ( k ) sin x ( k )  x ( k ) cos x k 1  cos x

2 b 

Q.32 Consider the matrix

( k )

a



2

Q.33

The solution of

(A)

(C)

AE

1 t e (t  3)2 9 4et (t  2) 2

dy dt

at iteration k is ( k 1)

(B) x

(D) x

( k 1)

 

sin x ( k )  x ( k ) cos x k 1  cos x ( k ) sin x ( k )  x ( k ) cos x k 1  cos x ( k )

where a and b are real numbers. The two eigenvalues of this matrix

 1 and  2 are real and distinct  1 (A) a  0 and b  0

( 0)

  2  when

(B) a  0 and b  0

(C) a  0 and b  0

(D) a  0 and b  0

 y3et t 2 with initial condition y (0)  1 is given by (B)

(D)

9 t 5  2e (t 2  2t  2)

1 t 5  2e (t 2  2t  2)

2011

Q.34


A jet engine is operating at a Mach number of 0.8 at an altitude of 10 km. The efficiency of the air intake is 0.8 and that of the compressor is 0.87. The total temperatures (in K) at the exits of the air intake and the compressor respectively are (Ambient pressure = 26.5 kPa; Ambient temperature = 223.3 K; Gas constant,  = 1.4; prc  8 ) (A) 251.9 and 458.2

Q.35

(B) 234.9 and 486.8

(D) 234.9 and 458.2

A rocket engine is tested on a test bed under the ideal condition of fully expanded jet. The exhaust velocity is 2 km/s through a nozzle of area 2.5 m 2. The mass flow rate is 200 kg/s. The specific impulse of the propellant and the thrust developed respectively are (assume g = 9.81 m/s 2) (A) 175.87 s and 200 kN (C) 231.87 s and 200 kN

Q.36

(C) 251.9 and 486.8

(B) 203.87 s and 400 kN (D) 280.87 s and 400 kN

A body undergoes deformation under plane strain conditions when subjected to the following stresses (in MPa):  xx  450,  yy  450,  xy  75,  xz  0,  yz  0 . What are the remaining components of stresses (in MPa) and strains? Assume the material to be isotropic and linear-elastic with Young’s modulus E = 200 GPa and Poisson’s ratio  = 1/3.

 0,  xx  0.00225,  yy  0.00225,  xy  0.002,  xz  0,  yz  0 (B)  zz  300,  xx  0.001,  yy  0.001,  xy  0.001,  xz  0,  yz  0 (C)  zz  300,  xx  0.00225,  yy  0.00225,  xy  0.001,  xz  0,  yz  0 (D)  zz  0,  xx  0.001,  yy  0.001,  xy  0.002,  xz  0,  yz  0 (A)  zz

Q.37

Which of the following Airy’s stress functions could satisfy the given boundary conditions, assuming constant values of xx = P, yy = Q and xy = R, along the boundary?

y x

(A)   P (C)   P

Q.38

x 2

2 y 2 2

Q Q

y 2

2 x 2 2

 Rxy

(B)   P

 Rxy

(D)   P

2 x 2 2

Q Q

x 2

2 y 2 2

 Rxy  Rxy

An aircraft is performing a coordinated turn manoeuvre at a bank angle of 30 o and forward speed of 100 m/s. Assume g = 9.81 ms -2. The load factor and turn radius respectively are (A) (2/3) and 1.76 km (C) 2 and 0.18 km

Q.39

y 2

(B) 3 and 17.6 km (D) (2/3) and 17.6 km

An aircraft in a steady level flight at forward speed of 50 m/s suddenly rolls by 180 o and becomes inverted. If no other changes are made to the configuration or controls of the aircraft, the nature of the subsequent flight path taken by the aircraft and its characteristic parameter(s) (assume g = 9.81 ms-2) are (A) straight line path with a speed of 50 m/s (B) upward circular path with a speed of 50 m/s and radius of 127.4 m (C) downward circular path with a speed of 50 m/s and radius of 127.4 m/s (D) downward circular path with a speed of 25 m/s and radius of 254.8 m/s

AE

2011

Q.40


An aircraft with a mass of 5000 kg takes off from sea level with a forward speed of 50 m/s and starts to climb with a climb angle of 15 o. The rate of climb and excess thrust available at the start of the climb respectively (assume g = 9.81 ms -2) are (A) 13.40 m/s and 13146.0 N (C) 13.40 m/s and 12694.1 N

Q.41

A glider having a mass of 500 kg is taken to an altitude of 1000 m with a jeep moving on ground at 54 kmph. Upon reaching the required altitude in 50 s, the glider is released and starts its descent. Under the assumption of equilibrium glide, the range and endurance of the glider for a constant liftto-drag ratio of 15 are (A) 15.0 km and 1002.2 s respectively (C) 1.0 km and 601.3 s respectively

Q.42

(B) 12.94 m/s and 12694.1 N (D) 12.94 m/s and 13146.0 N

(B) 15.0 km and 601.3 s respectively (D) 1.0 km and 50 s respectively

An elliptic orbit has its perigee at 400 km above the Earth’s surface and apogee at 3400 km above the Earth’s surface. For this orbit, the eccentricity and semi-major axis respectively are (assume radius of Earth = 6400 km) (A) 0.18 and 8300 km (C) 0.22 and 8300 km

Q.43

An aircraft in level flight encounters a vertical gust, which excites the phugoid mode. The phugoid motion completes 10 cycles in 50 s and its amplitude reduces to half of its maximum value in 25 s. The eigenvalues of the phugoid mode are (A) −0.05  0.02i

Q.44

(B) 0.18 and 1900 km (D) 0.22 and 1900 km

(B) −0.5  0.2i

(C) −0.028  1.26i

(D) 0.028  1.26i

Consider the inviscid, adiabatic flow of air at free stream conditions, M 1 = 2, p1 = 1 atm and T1 = 288 K around a sharp expansion corner ( θ = 20°) as shown below. The Prandtl-Meyer function, ν, is given as a function of Mach number, M, as  (M)  Assume air to be calorically perfect with expansion corner is approximately

 =

  1   1

tan 1

  1   1

(M 2  1)  tan 1 M 2  1

1.4. The Mach number, M 2, downstream of the

M1, p1, T1

 (A) 2.00 Q.45

(B) 1.76

(C) 2.83

M2

(D) 3.14

Consider a steady two dimensional zero-pressure gradient laminar flow of air over a flat plate as shown below. The free stream conditions are U ∞ = 100 ms -1, ρ∞ = 1.2 kg m -3, p∞ = 1 atm and

 

 1.8  105 kg

m-1s-1. The ratio of displacement thickness to momentum thickness of the

boundary layer at a distance of 2 m from the leading edge is Boundary layer

U∞

∞ p∞

∞

(A) 7.53

AE

2m (B) 2.59

(C) 2.91

(D) 0.39

2011

Q.46


In the context of Prandtl’s lifting line theory for a finite wing, which of the following combinations of statements is TRUE? P: The bound vortex is responsible for the lift force Q: The trailing vortices are responsible for the induced drag R: The bound vortex is responsible for the induced drag S: The trailing vortices are responsible for the lift force (A) P,Q

Q.47

(B) Q,R

(C) R,S

(D) P,S

Consider flow over a thin aerofoil at Mach number, M ∞ = 0.5 at an angle of attack, . Using the Prandtl-Glauert rule for compressibility correction, the formula for lift coefficient, c ,l can be written as (A) 5.44

(B) 6.28

(C) 7.26

(D) 14.52

Common Data Questions Common Data for Questions 48 and 49:

The partial differential equation (PDE) governing free vibrations of a uniform Euler-Bernoulli beam is given by

4w  2w EI 4  m 2  0 ,  x t

where EI is the flexural stiffness, m is the mass per unit length,

w( x, t ) is the bending displacement, x is the coordinate along the beam length, t is time and L is the beam length.

x  0

x

x  L

L Q.48

To solve the PDE, the number of boundary conditions (BC) and initial conditions (IC) needed are (A) 4 BC, 3 IC (B) 2 BC, 2 IC (C) 2 BC, 4 IC (D) 4 BC, 2 IC

Q.49

For the cantilever beam shown in the figure, which of the following CANNOT be a possible boundary condition? (A) w(0, t )  0

(B)

2w ( L, t )  0  x 2

(C)

2w (0, t )  0  x 2

(D)

3w ( L, t )  0  x 3

Common Data for Questions 50 and 51:

Consider an inviscid, adiabatic flow of air at free stream Mach Number, M ∞ = 2, across a compression corner (θ = 20°) as shown. The free stream total enthalpy is h 0∞ = 810 kJ kg -1. Assume that air is calorically perfect with γ = 1.4, R = 287 J kg -1 K -1. M∞

P

 Q.50

(B) > 20° and < 30°

(C) = 30°

(D) > 30°

(C) 1612.74 K

(D) 2257.84 K

The total temperature at point P is (A) 806.37 K

AE

1m

The shock angle β is (A) = 20°

Q.51



(B) 1128.92 K

2011


Linked Answer Questions Statement for Linked Answer Questions 52 and 53:

A thin-walled (thickness << radius), hollow shaft of length 1m and mean radius, R = 5 cm has to be designed such that it can transmit a torque, T = 7 kN-m. A survey of different commercially available materials was made and following data was obtained from the suppliers ( E : Young’s modulus,  y: yield stress in shear,  shear,  : density): Material (GPa) E (GPa)  y (MPa)  (kg/m (kg/m3) X 200 550 7700 Y 70 225 2700 Z 110 375 4875 Q.52

Which of the above materials would you choose such that weight of the shaft is minimum? (A) X only

Q.53

(B) Y only

(C) Z only

(D) X or Y

If you assume a factor of safety of 2, what should be the approximate thickness of such a shaft? (A) 0.5 mm

(B) 1 mm

(C) 2 mm

(D) 4 mm

Statement for Linked Answer Questions 54 and 55:

Prandtl’s lifting line equation for a general wing is given by b

 y0  1   y0     L0  y0    U  c y0  4 U 

 /  y  b y0  y dy ,  2

where U  is the free-stream velocity,

 is

the

2

angle of attack, y0 is the spanwise location,  L  0  y0  gives the spanwise variation of zero-lift angle, c is the chord, b is the span, and  y0  gives the spanwise variation of circulation. Q.54

The rate of change of circulation with an gle of attack (A) inversely proportional to  (C) a linear function of 

Q.55

 is 

(B) independent of  (D) a quadratic function of 

b

2

Given that C L

   y dy , the corresponding lift curve-slope 

b

C L is 

2

(A) independent of  (C) a quadratic function of 

AE

 

(B) a linear function of  (D) a cubic function of 

2011


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

Choose the word from the options given below that is most nearly opposite in meaning to the given word: Deference (A) aversion (B) resignation (C) suspicion (D) contempt

Q.57

Choose the most appropriate word(s) from the options given below to complete the following sentence. We lost confidence in him because he never __________ the grandiose promises he had made. (A) delivered (B) delivered on (C) forgot (D) reneged on

Q.58

Choose the word or phrase that best completes the sentence below. ______________ ______________ in the frozen wastes wastes of Arctic takes special equipment. equipment. (A) To survive (B) Surviving (C) Survival (D) That survival

Q.59

In how many ways 3 scholarships can be awarded to 4 applicants, when each applicant can receive any number of scholarships? (A) 4

Q.60

(B) 12

(C) 64

(D) 81

Choose the most appropriate word from the options given below to complete the following sentence. The _________ of eviden ce was on the side of the plaintiff since all but one witness testified that his story was correct. (A) paucity (B) propensity (C) preponderance (D) accuracy

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

If (2y+1) /(y+2) < 1, then which of the following alternatives gives the CORRECT range of y? (A) - 2 < y < 2

Q.62

(C) - 3 < y < 1

(D) - 4 < y < 1

A student attempted to solve a quadratic equation in x twice. However, in the first attempt, he incorrectly wrote the constant term and ended up with the roots as (4, 3). In the second attempt, he incorrectly wrote down the coefficient of x and got the roots as (3, 2). Based on the above information, the roots of the correct quadratic equation are (A) (-3, 4)

AE

(B) - 2 < y < 1

(B) (3, -4)

(C) (6, 1)

(D) (4, 2)

2011

Q.63


L, M and N are waiting in a queue meant for children to enter the zoo. There are 5 children between L and M, and 8 children between M and N. If there are 3 children ahead of N and 21 children behind L, then what is the minimum number number of children in the queue? (A) 28

Q.64

(B) 27

(C) 41

(D) 40

Four archers P, Q, R and S try to hit a bull’s eye during a tournament consisting of seven rounds. As illustrated in the figure below, a player receives 10 points for hitting the bulls’ eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle. Outer circle 1 point Inner circle 5 points Bull’s eye 10 points

The final scores received by the players during the tournament are listed in the table below. Roun d

P

Q

R

S

1

1

5

1

10

2

5

10

10

1

3

1

1

1

5

4

10

10

1

1

5

1

5

5

10

6

10

5

1

1

7

5

10

1

1

The most accurate and the most consistent players during the tournament are respectively (A) P and S Q.65

(B) Q and R

(C) Q and Q

(D) R and Q

Nimbus clouds are dark and and ragged, stratus clouds appear dull in colour a nd cover the entire sky. Cirrus clouds are thin and delicate, whereas cumulus clouds look like cotton balls.

It can be inferred from the passage that (A) A cumulus cloud on the ground is called fog (B) It is easy to predict the weather by studying clouds (C) Clouds are generally of very different shapes, sizes and mass (D) There are four basic cloud types: stratus, nimbus, cumulus and cirrus

END OF THE QUESTION PAPER

AE

www.gateing.com

Official GATE key

D

D

A

B

C

C

D

Marks to All

A

D

A

B

A

B

B

D

C

A

C

D

C

A/C

C

C

C

2.452.55

1.3-1.35

5.956.05

29-32

80-82

A

C

D

C

B

B

C

A

C

B

Marks to All

A

C

C

B

A

C

D

C

D

A

B

D

B

A

D

B

A

C

C

B

C

A

B

D

GATE 2012 Online Examination AE : AEROSPACE ENGINEERING 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, ⅓ mark will be deducted for each wrong answer. For all 2 marks questions, ⅔ 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 t he 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:

2012



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 Q.3

−t

+ Be2t

(B) Ae

−2t

+ Be−t

dy

+

(C) Ae

− 2 y = 0 is

dt −2t

+ Bet

(D) Ae

t

+ Be2t

(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

dt

2

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

Q.5

d2y

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

AE

≤ ν ≤ 0

(B) 0

≤ ν ≤ 0.2

(C) 0.2

≤ ν ≤ 0.4

(D) 0.4

≤ ν ≤ 0.5

2/12

2012

Q.11


The value of k for which the system of equations x + 2 y + kz

= 1; 2 x + ky + 8 z = 3 has no

solution is (A) 0 Q.12

(B) 2

(C) 4

(D) 8

If u (t ) is a unit step function, the solution of the differential equation m

d 2x dt 2

+ kx = u (t ) in

Laplace domain is (A)

Q.13

1 s ( ms + k ) 2

1 ms + k 2

x + C = 0

(B) y − x + C = 0

(D)

1 s (ms 2 + k ) 2

− 2 y = 0 is 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

dx (C)

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

dy

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)

The general solution of the differential equation (A) y −

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 C L is the lift coefficient) (A)

Q.20

(B) 45o

C L π AR

(B)

C L2 π AR

(C)

C L 2π AR

(D)

C L2 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.

AE

3/12

2012

Q.21


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

∫

3

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

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 m 2/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 T

{1 − 0.675}

{1

T

0.5} and

. The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum

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

{2 1} AE

(in mm) and zero initial velocities is ____.

4/12

2012


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

The nth derivative of the function y

(A)

Q.32

( −1) n n ! ( x + 3)n +1

(B)

=

1 x + 3

(−1) n +1 n ! ( x + 3)n +1

is

(C)

( −1) n ( n + 1)! ( x + 3)n

(D)

The volume of a solid generated by rotating the region between semi-circle

( −1) n n ! ( x + 3)n

= 1 − 1 − x 2 and

straight line y = 1, about x axis, is (A) π

Q.33

2

4

− π 3

2

1

− π 3

(B) −18.33

(B) 1380 m.

3 4

π 2 − π

(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

4

(D)

An aircraft is trimmed straight and level at true air speed (TAS) of 100 m/s at standard sea level (SSL). Further, pull of 5 N holds the speed at 90 m/s without re-trimming at SSL (air density = 1.22 kg/m3). To fly at 3000 m altitude (air density = 0.91 kg/m 3) and 120 m/s TAS without re-trimming, the aircraft needs (A) 1.95 N upward force. (C) 1.85 N upward force.

Q.37

3

− π

An aircraft has an approach speed of 144 kmph with a descent angle of 6.6 o. If the aircraft load factor is 1.2 and constant deceleration at touch down is 0.25 g ( g = 9.81 m/s 2), its total landing distance approximately over a 15 m high obstacle is (A) 1830 m.

Q.36

2

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

(C) π

⎡ 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

(B) 4π

(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 t hroat 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.

AE

5/12

2012

Q.39


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

(B) 1 m/s

(B) 0.018

(B) 38 mm

(C) 41 mm

(B) 1.75 m3

(D) 45 mm

(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/s 2.] (A) 315 km

Q.44

(D) 1.18

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/m 3, what should be the minimum fuel tank volume for a burn time of 8 minutes (A) 1.65 m3

Q.43

(C) 0.18

A solid propellant of density 1800 kg/m 3 has a burning rate law r = 6.65 x 10 -3 p0.45 mm/s, where p is pressure in Pascals. It is used in a rocket motor with a tubular grain with an initial burning area of 0.314 m 2. The characteristic velocity is 1450 m/s. What should be the nozzle throat diameter to achieve an equilibrium chamber pressure of 50 bar at the end of the ignition transient? (A) 35 mm

Q.42

(D) 100 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

(C) 10 m/s

(B) 335 km

The Airy stress function, φ

=α

2

(C) 365 km

(D) 385 km

+ 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

= σ o / 2; β = 0; γ = σ o / 2. (C) α = 0; β = σ o / 4; γ = 0.

= σ o ; β = 0; γ = σ o . (D) α = 0; β = σ o / 2; γ = 0.

(A) α

Q.45

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

(C)

(B) 2

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 Cosω d t is given by 2

(A) π cω d X Q.47

(B) α

2

(B) πω d X

(C) π cω d X

2

(D) π cω d 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.

AE

6/12

2012


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, C L = 1.0, C L = 0.08 / deg., c = 2.5 m, b = 30 m, C M = 0, η t =1. The symbols have their usual α

ac

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% s tatic 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 15 oC 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 27 o 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 = 500MPa 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) 500MPa

Q.55

AE

(B) 250MPa

(C) 100MPa

(D) 20MPa

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 .

(B) occurs at about double the pressure pY .

(C) occurs at about the same pressure pY .

(D) never occurs.

7/12

2012

GENERAL APTITUDE - GA_AN_Online


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

GA_AN_Online

(B) 0.22

(C) 0.33

(D) 0.40

1/2

2012

Q.62

GENERAL APTITUDE - GA_AN_Online

The total runs scored by four cricketers P, Q, R, and S following table: Player P Q R S

in years 2009 and 2010 are given in the 2009 802 765 429 501

2010 1008 912 619 701

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 ab ove 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.


GA_AN_Online

2/2

www.gateing.com

Official GATE key

C

C

B

D

B

C

C

C

B

C

C

A

D

D

B

C

C

A

B

A

C

Marks to All

C

D

D

0.26 0.27

13-14

1.1-1.2

1430 1440

2

A

A

A

B

Marks to All

B

A

B

B

B

B

B

D

A

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

What gateing says is correct

0.2656

13.52

1.11

1433.8

C

502m

0.0314

55°

D

2013


AE:AEROSPACE ENGINEERING Duration: Three Hours

Maximum Marks:100

Please read the following instructions carefully: General Instructions:

1. Total duration of examination is 180 minutes (3 hours). 2. The clock will be set at the server. The countdown timer in the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination. 3. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols:

You have not visited the question yet. You have not answered the question. You have answered the question. You have NOT answered the question, but have marked the question for review. You have answered the question, but marked it for review.

The Marked for Review status for a question simply indicates that you would like to look at that question again. If a question is answered and Marked for Review, your answer for that question will be considered in the evaluation. Navigating to a Question

4. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter a number as answer for a numerical type question. c. Click on Save and Next to save your answer for the current question and then go to the next question. d. Click on Mark for Review and Next to save your answer for the current question, mark it for review, and then go to the next question. e. Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number. 5. You can view all the questions by clicking on the Question Paper button. Note that the options for multiple choice type questions will not be shown.

AE

1/19

2013


Answering a Question

6. Procedure for answering a multiple choice type question: a. To select your answer, click on the button of one of the options b. To deselect your chosen answer, click on the button of the chosen option again or click on the Clear Response button c. To change your chosen answer, click on the button of another option d. To save your answer, you MUST click on the Save and Next button e. To mark the question for review, click on the Mark for Review and Next button. If an answer is selected for a question that is Marked for Review, that answer will be considered in the evaluation. 7. Procedure for answering a numerical answer type question: a. To enter a number as your answer, use the virtual numerical keypad b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point c. To clear your answer, click on the Clear Response button d. To save your answer, you MUST click on the Save and Next button e. To mark the question for review, click on the Mark for Review and Next button. If an answer is entered for a question that is Marked for Review, that answer will be considered in the evaluation. 8. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 9. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation.

AE

2/19

2013


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, ⅓ mark will be deducted for each wrong answer. For all 2 marks questions, ⅔ 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.

AE

3/19

2013



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

x 2  xy 2 5



in the direction

a  2iˆ  4 ˆj at

( x, y )  (1,1) is

(A) 

Q.2

1 5

(B) 

x  2

5

The value of

 x 4

2

 4 x  21

(A) ln 24 11

Q.3

At x  0 , the function

2

(C) 0

5

(D) 

1 5

dx is

(B) ln 12 11

(C) ln 2

(D) ln 12 11

 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 0  1   A   0 1 1  is 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

AE

4/19

2013

Q.6


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

Q.8

Which one of the following is favorable for an airplane operation? (A) Tail wind in cruise and head 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 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 proportional to the square root of flight speed speed (D) Frequency is inversely proportional proportional to the square root of flight speed

Q.10

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

u

cy x 2  y 2

,v 

(A) hyperbolas

AE

cx x 2  y 2

, where c is a constant. The streamlines are a family of

(B) parabolas

(C) ellipses

(D) circles

5/19

2013

Q.11


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

(A)  V 

1 D  Dt 

(B)   (  V ) 

1 D  Dt



(C)  

DV DV Dt



 

1 D  Dt

(D) V  (  V ) 

Q.13

1 D  Dt

Consider a thin flat plate airfoil at a small angle  to an oncoming supersonic stream of air. Assuming the flow to be inviscid,

C d C l 2

is

(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 ______________

AE

6/19

2013

Q.16


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

AE

7/19

2013

Q.18


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, q AB, q BC , qCD, and q DA 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

AE

(B) 0.95

(C) 0.85

(D) 0.8

8/19

2013

Q.22


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

AE

(B) 845

(C) 905

(D) 945

9/19

2013



Let I

  ( y 2 ziˆ  z 2 xjˆ  x2 ykˆ)( xiˆ  yjˆ  zkˆ) dS , where S denotes the surface of the sphere of unit S

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

Q.27

Given that the Laplace transform,  (e at ) 

(A)

Q.28

3 s

s 2  10 s

(B)

15 s 2  10 s

1 s  a





5t

then  3e sinh 5t =

(C)

3 s s 2  10 s

(D)

15 s 2  10 s

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

    Q    

1



1

3 1

a

2

  b   c 

0

3 1

1



3

2

orthonormal are, respectively (A)

(B)

1 2 1 6

1

,

,-

(C) 

1

(D) 

1

3

6

, 0

2 2 6

6

1

, 

,

1

,

3

2 6

,

, -

1 3 1 6

Q.29 A function  satisfies the differential equation conditions y (t  0)  0 and

(A) e

AE

dy

(B) 0

dt

d2y dt

2

2

dy

 y  0 and is subject to the initial dt

(t  0)  1. The value of y (t  1) is

(C) 1

(D) -1

10/19

2013


Q.30

A glider is launched from a 500m high hilltop. Following data is available for the glider: Zero lift drag coefficient C D 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, C l  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 stream function can be written in the ( r ,  ) system as   



 



ln r , where 2 2     100 m2 /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

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)

AE

(B) 

  s

(B)

 2 s

(C)

 3 s

(D)

4 3 s

11/19

2013

Q.36


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.

1.8 1.9 2.0 2.1 2.2 2.3 2.4

 (Prandtl-Meyer function) 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

AE

(B) 2.00

(C) 2.11

(D) 2.33

12/19

2013

Q.38


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

y

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 R A, R B, 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

AE

13/19

2013

Q.41


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

A

B

1m

C

1m

P

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 y M

M

b

x L

(A)

Q.43

AE

2 M 3 x tb 3

(B)

2 M 3 y tb 3

(C)

2 M tb3

 x

3

 y3 

(D)

2 M 4 y tb 3

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 ________

14/19

2013

Q.44


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

16

sagging

hogging

(C)

16

hogging

(D)

2 3qL

16

sagging

(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

16

2 3qL

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)

qL2

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

C L max  1.4 , and drag coefficient C D  0.015  0.024 C L2 . Assume air density at sea-level    1.22 kg / m 3 . Q.48

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

Q.49

AE

(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

15/19

2013


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

(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) (C)

AE

(B) c/2

4 3 2 3

 cU  ,  cU  ,

2

 cU 

(B)

 cU 

(D)

3 1 3

2 3 4 3

 cU  ,  cU  ,

2 3 4 3

 cU   cU 

16/19

2013


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 Cmac  C m 0   0.06 and the location of airplane aerodynamic center from the wing leading edge is

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

The airplane trim lift coefficient C L 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


If 3    5 and 8    11 then which of the following options is TRUE? (A)

(B)

(C)

(D) Q.57

 



     

 

 



   

 



  



 

 

 



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.

AE

17/19

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

(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.62

Velocity of an object fired directly in upward direction is given by   80  32  , where  (time) 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)

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

AE

18/19

2013

Q.64


If |2  9|  3 then the possible value of ||    would be: (A) 30

Q.65

(B) -30

(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


AE

19/19

www.gateing.com

Official GATE key

D

A

A

zero

D

C

C

A

B

A

B

A

B

1

0.2

Marks to All

0.120.13

D

D

0.30.35

D

D

B

B

A

zero

B

D

A

9-10

C

-0.23 to -0.24

1

D

C

C

C

A

B

B

19002000

B

70

A

B

A

B

B

C

A

D

C

B

C

C

D

B

B

C

D

C

Marks to All

C

Marks to All

C

GATE 2014: General Instructions during Examination 1. Total duration of the GATE examination is 180 minutes. 2. The clock will be set at the server. The countdown timer at the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You need not terminate the examination or submit your paper. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at the end of the examination. 5. You are allowed to use a non-programmable type calculator, however, sharing of calculators is not allowed. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols:

The Marked for Review status for a question simply indicates that you would like to look at that question again. If a question is answered, but marked for review, then the answer will be considered for evaluation unless the status is modified by the candidate. Navigating to a Question :

7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. b. Select an answer for a multiple choice type question by clicking on the bubble placed before the 4 choices, namely A, B, C and D. Use the virtual numeric keypad to enter a number as answer for a numerical type question. c. Click on Save & Next to save your answer for the current question and then go to the next question. d. Click on Mark for Review & Next to save your answer for the current question and also mark it for review, and then go to the next question.

Caution: Note that your answer for the current question will not be saved, if you navigate

to another question directly by clicking on a question number without saving the answer to the previous question. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question :

8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 9. Procedure for answering a numerical answer type question: a. To enter a number as your answer, use the virtual numerical keypad. b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0' before the decimal point. As many as four decimal points, e.g. 12.5435 or 0.003 or -932.6711 or 12.82 can be entered. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review , that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation.

Choosing a Section :

13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will

only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section.

Changing the Optional Section :

18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section?” If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times.

GATE 2014 Examination AE: Aerospace Engineering 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 entered by 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 of ⅓ 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

SET- 1

General Aptitude -GA


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

2

If y = 5 x + 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

(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

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

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 percentile is the value such that k percent percent of the data fall below that value)

(i) On average, it rains more in July t han 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 r ainfall (A) (i) and (ii) (C) (ii) and (iii)

(B) (i) and (iii) (D) (iii) and (iv)


GA

2/2

GATE 2014

AEROSPACE– AE


For a real symmetric matrix [A], which of the following statements is true: (A) The matrix is (B) The matrix is (C) The matrix is (D) The matrix is

Q.2 The series s

=

always diagonalizable and invertible. always invertible but not necessarily necessarily diagonalizable. always diagonalizable but not necessarily necessarily invertible. always neither diagonalizable nor invertible.

∞

m

2

∑ 3m (x − 2)m 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 f(x) = The function given by 0, x=0 is

{

(A) Unbounded everywhere (C) Bounded but not continuous at x = 0 Q.4

(D) R = 1 / 3

Given the boundary-value problem

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

d  dy   x  + ky = 0, dx  dx 

0 < x < 1 , with y (0) = y (1) = 0 . Then the

solutions of the boundary-value boundary-value problem for k = 1 (given by y1 ) and k = 5 (given by y5 ) satisfy: 1

∫

(A) y1 y5 dx = 0

(B)

0

1

∫

(C) y1 y5 dx ≠ 0

(D)

0

Q.5

The value of I = (A) 200

Q.6

1

∫ 1000 x 0

4

dy1 dy5

0

dx dx

∫

1

∫ ( y y 0

1

5

+

dx = 0 dy1 dy5 dx dx

)dx = 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 C L and X m respectively. For NACA12018 airfoil, which combination of C L and X m given below are correct? (A)C L =0.15 and X m = 0.1c (C)C L=0.12 and X m = 0.18c

Q.7

1

(B)C L =0.12 and X m = 0.2c (D)C L =0.15 and X m = 0.2c

For inviscid, supersonic flow over a di amond 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 experience positive lift and zero drag force (C) The airfoil will experience experience negative lift and zero drag force (D) The airfoil will experience positive lift and positive drag force

AE

1/11

GATE 2014

Q.8

AEROSPACE– AE

Consider supersonic supersonic flow near a corner corner (at an angle angle from the horizontal) horizontal) with an attached attached oblique shock (at an angle with horizontal) as shown in figure. figure. If Mach number M decreases decreases gradually from a high supersonic value, which of the following statements is correct?

(A) β will will decrease if the shock is a weak shock (B) β will will decrease if the shock is a strong shock (C) β will will increase i ncrease for both weak and strong shocks (D) β remains remains unchanged for both weak and strong shocks Q.9

The streamlines of a potential line vortex i s concentric circles with respect to the vortex center as shown in figure. Velocity along these t hese streamlines, outside the core of the vortex can be written as,

 Γ

, where strength of the vortex is

Γ

(B)

=

2

along the curve shown in the figure is:

(A) Q.10

−Γ

2

r

Γ

(C) 2

(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 respectively (C) 80GPa& -0.2 respectively

AE

2

To observe unsteady separated flow in a diverging channel, bubbles are injected at each 10 ms 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

Γ and is radial r adial direction. The value of circulation 

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

2/11

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, =10 Hz, 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 ratio f<<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

AE

3/11

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 t o 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 3/2 (D) Minimum CD/CL

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 3/2 (C) Maximum CD/CL

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 2 R 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

AE

(B) -324

(C) 324

(D) 6

4/11

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

3

1 3

1

1

5

7

={

−2,

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

0< x<π

2,

+ − +  converges to

(C)

π

4

π

(D)

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) Q.29

π

(B) − π

(C) 1

(D) 0

Solution to the boundary-value problem 2

−9

d u dx

2

+ u = 5 x, 0 < x < 3 with u (0) = 0,

(A) u ( x) =

15e

(e−

x / 3

− e x / 3 ) + 5x

1+ e 15 sin( x / 3) 2

(C) u ( x) = −

cos(1)

du dx

= 0 is x =3

(B) u ( x) =

15e

(D) u ( x) = −

+ 5x

(e −

x / 3

+ e x / 3 ) + 5x

1+ e 15 sin( x / 3) 2

cos(1)

Q.30

−

5 54

x

3

2

The Laplace transform L(u(t))=U(s), for the solution u(t) of the problem

d u 2

dt

+2

du dt

+ u = 1, t > 0

.

with initial conditions u (0) = 0,

(A)

Q.31

6 ( s + 1)

2

(B)

du (0) dt

5s + 1 s ( s + 1)

2

= 5 is given by: (C)

1 − 5s s ( s + 1)

2

(D)

5s 2 + 1 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

=

,

wherea and bare constants having unit of (second )-1. If value of a is 5, the value of b is _____.

AE

5/11

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 respectively. Ratio of pressure at point A and is 0.8 and pressure are denoted by 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

AE

(B) 0.79

(C) 1.18

(D) 0.64

6/11

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 i s correct? (A) (i) only

Q.36

(B) (i) & (ii)

(C) (ii) & (iv)

(D) (i), (iii) & (iv)

  along the lifting line can be calculated using the formula  Γ ( ) = −  ∫−  − . Γ  = 1, where, Γ and are given in figure below. Given + Γ  For theabove semi-elliptic distribution of circulation, Γ, the downwash velocity at any point  for   . Γ symmetric flight can be obtained as, ( ) =  [ +   ], where  =  ∫−   − �−   1 −   =  ) Which of the following options is correct if the induced drag is  (given ∫  −  Induced velocity w at a point = 1 4

1

2

2

2

2

1

1

1

s

1,

1

4

1

1

2

2

1

2

2

(A) I=0 and

 Γ   Γ =

2

8

(B) I= 1 and

2

(C) I=0 and Q.37

=

2

 Γ   Γ =

2

8

2

(D) I= 1 and

8

=

8

Two overflowing water reservoirs are connected with a100 m 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

 −   1 −   2

length is =

4

2

2 , where,

 

is a constant pressure gradient along the pipe length,

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

7/11

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 50 N 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 40 mm. Thickness of the wall in Design II has to be determined such that maximum shear stress is the same in both t he 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 I to the mass of shaft using Design II is

(A) 2.68 Q.40

(D) 3.58

− 

(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 (0.5 MPa). The material used for manufacturing this cylinder has a failure stress of 260 MPa. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is (A) 2.8

AE

(C) 1.79

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) 2.0

(C) 6.9

(D) 4.0

8/11

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

          

           − 

Q.43

(A)

1 =

0,

2 =

,

3 =

0,

(C)

1 =

0,

2 =

0,

3 =

,

3

4 =

2

3

2

         −   

(B)

1 =

,

2 =

(D)

1 =

,

2 =

3

3 =

2,

3

2,

0,

3 =

4 =

0,

0

4 =

0

1kg mass is hanging from a spring of stiffness 500 N/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

4 =

(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 = 287 J/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 _______.

AE

9/11

GATE 2014

Q.47

AEROSPACE– AE

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 σ s (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, I sp, 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 t he 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 S LO. If the take-off weight is reduced by 10%, then the magnitude of percentage change in the lift-off di stance (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

AE

(B) P, Q, R and S

(C) P, Q and S alone

(D) Q, R, and S alone

10/11

GATE 2014

Q.54

AEROSPACE– AE

Consider the following four statements regarding aircraft longitudinal stability: P. Q. R. S.

C M,cg at zero lift must be positive ∂C M,cg /∂α a must be negative (α a is absolute angle of attack) C M,cg at zero lift must be negative Slope of C L versus α 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 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 = 13000 N , lift coefficient C L = 0.65, drag coefficient C D = 2 0.025 + 0.04C L and power available P av = 100,000 J/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


AE

11/11

GATE AE 2007-2014 With Answers

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