GATE AE 2011 Question Paper & Solutions

Verbal & Numerical Aptitude

(A) k iy z32  (B) k jy z32  (C) j iy z32  (D) k iy z32   Which of the following fun ctions is periodic? Q.2

Verbal & Numerical Aptitude

Question 2 from official GATE AE 2011 Examination.

Verbal & Numerical Aptitude

Question 3 from official GATE AE 2011 Examination.

Verbal & Numerical Aptitude

Question 4 from official GATE AE 2011 Examination.

Verbal & Numerical Aptitude

(C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively,

Verbal & Numerical Aptitude

(A) 3, 3 and 3 (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

Verbal & Numerical Aptitude

(D) neither plane strain condition nor plane stress condition 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

Verbal & Numerical Aptitude

(D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k

Verbal & Numerical Aptitude

(A) 24 2 c mk c   (B) 24 c mk c   (C) 2 2 c mk c   (D) 24 2 c mk c   AE 2011 AEROSPACE ENGINEERING - AE Consider a single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 10 rad/s. Con sider another single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 20 rad/s. The spring stiffness is equal to 1k m 2k m 2k

Verbal & Numerical Aptitude

(A) 1k (B) 12k (C) 4 1k (D) 14k Consider a simply support ed two-dimensional beam If the beam is converted into a fixed-fixed beam as then the degree of static indeterminacy will

Incompressible & Compressible Aerodynamics

(A) increase by 3 (B) increase by 2 (C) decrease by 1 (D) decrease by 3 An impulsive launch of a rocket mini mizes the loss of burn-out velocity due to (A) aerodynamic drag force only (B) gravitational force only (C) both aerodynamic drag and gravitational forces

Air-Breathing & Rocket Propulsion

(D) reaction jet control force Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies

Incompressible & Compressible Aerodynamics

(C) propellant masses (D) control system masses In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as

Incompressible & Compressible Aerodynamics

(A)    D L1tan (B)    L D1tan (C)    W L1tan (D)    L W1tan Lift on an aircraft climbing vertically up is (A) equal to its weight (B) zero

Incompressible & Compressible Aerodynamics

(C) equal to the drag (D) equal to the thrust If an aircraft is performing a positive yawing manoeuvre, the side slip angle Q.16 (A) is always zero (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 (A) ahead of wing aerodynamic centre (B) aft of the wing aerodynamic centre

Structural Mechanics

Question 16 from official GATE AE 2011 Examination.

Incompressible & Compressible Aerodynamics

(C) ahead of neutral point (D) aft of neutral point It is seen that the drag polar of a certain aerofoil is symmetric about the Cd axis. This drag polar could refer to

Incompressible & Compressible Aerodynamics

(A) NACA 0012 (B) NACA 4415 (C) NACA 23012 (D) None of the above AE 2011 AEROSPACE ENGINEERING - AE AE The aerodynamic centre of a supersonic aerofoil, with chord c, is located at Q.19 (A) the leading edge (B) 0.25c (C) 0.5c (D) 0.75c Winglets are used on wings to minimize Q.20 (A) skin friction drag (B) profile drag (C) wave drag (D) induced drag 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 (A) R r r Rr V ln21 cos2 2         (B) R r r Rr V ln21 cos2 2        

Structural Mechanics

Question 19 from official GATE AE 2011 Examination.

Structural Mechanics

Question 20 from official GATE AE 2011 Examination.

Structural Mechanics

(C) R r r Rr V ln21 sin2 2         (D) R r r Rr V ln21 sin2 2         A main objective of by-pass in a turbo-fan engine is to increase (A) mass flow rate through engine inlet (B) turbine inlet temperature

Incompressible & Compressible Aerodynamics

(C) mass flow rate through exhaust nozzle (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

Structural Mechanics

(D) mass flow rate in that stage Thermodynamic cycle on which the jet engine operates can be Q.24

Structural Mechanics

Question 24 from official GATE AE 2011 Examination.

Air-Breathing & Rocket Propulsion

(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. 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. Unde r the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is

Structural Mechanics

P L L/2 2011 AEROSPACE ENGINEERING - AE AE Consider a beam in bending with a solid circular cross-section of 1 mm2, which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm2) is

Structural Mechanics

A simp ly 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

Incompressible & Compressible Aerodynamics

A turbojet powered aircraft is flying at Mach nu mber 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

Structural Mechanics

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 th e settling chamber and the test section is 40 cm of water column. Assume , and . The speed of air in the test section (in m/s) is 2m/s 81 . 9g 3kg/m 2 . 1air 3kg/m 1000water

Structural Mechanics

Questions Q.31 to Q.55 are multiple choice type. Consider the function . The Newton-Raphson iteration formula to find the root of the function starting from an initial guess at iteration k is ) sin( ) (x x x f  ) 0 (x (A) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (B) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx  

Linear Algebra & Differential Equations

(C) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (D) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   Consider the matrix where a and b are real numbers. The two eigenvalues of this m atrix     2 2 b a 1 and 2 are real and distinct  2 1  when

Structural Mechanics

(A) 0 and 0ab (B) 0 and 0ab (C) 0 and 0ab  (D) 0 and 0ab The solution of 32tdy y etdt  with initial condition 1 ) 0 (y is given by (A) 21 (3 )9 tet  (B) 2 9 52( 2 2 )tet t 

Incompressible & Compressible Aerodynamics

(C) 2 4 (2 ) te t (D) 2 1 52( 2 2 )tet t  2011 AEROSPACE ENGINEERING - AE 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. Th e 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; 8rcp )

Air-Breathing & Rocket Propulsion

(A) 251.9 and 458.2 (B) 234.9 and 486.8 (C) 251.9 and 486.8 (D) 234.9 and 458.2 A rocket engine is tested on a test bed under th e 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/s2) (A) 175.87 s and 200 kN (B) 203.87 s and 400 kN

Structural Mechanics

(C) 231.87 s and 200 kN (D) 280.87 s and 400 kN A body undergoes deformation under plane strain conditions when subjected to the following stresses (in MPa): 0 , 0 , 75 , 450 , 450 yzxzxyyyxx  . 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. (A) 0 , 0 , 002 . 0 , 00225 . 0 , 00225 . 0 , 0  yzxzxyyyxxzz  (B) 0 , 0 , 001 . 0 , 001 . 0 , 001 . 0 , 300 yzxzxyyyxxzz  (C) 0 , 0 , 001 . 0 , 00225 . 0 , 00225 . 0 , 300 yzxzxyyyxxzz 

Structural Mechanics

(D) 0 , 0 , 002 . 0 , 001 . 0 , 001 . 0 , 0  yzxzxyyyxxzz  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? (A) RxyyQxP   2 2 22  (B) RxyxQyP   2 2 22 

Structural Mechanics

(C) RxyxQyP   2 2 22  (D) RxyyQxP   2 2 22  y x An aircraft is performing a coordinated turn manoeuvre at a bank angle of 30o 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 (B) 3 and 17.6 km

Structural Mechanics

(C) 2 and 0.18 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 configur ation or controls of the aircraft, the nature of the subsequent flight path taken by the aircraft a nd 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

Air-Breathing & Rocket Propulsion

(D) downward circular path with a speed of 25 m/s and radius of 254.8 m/s AE 2011 AEROSPACE ENGINEERING - AE 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 15o. 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 (B) 12.94 m/s and 12694.1 N

Incompressible & Compressible Aerodynamics

(C) 13.40 m/s and 12694.1 N (D) 12.94 m/s and 13146.0 N A glider having a mass of 500 kg is taken to an a ltitude 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 lift- to-drag ratio of 15 are (A) 15.0 km and 1002.2 s respectively (B) 15.0 km and 601.3 s respectively

Space Dynamics

(C) 1.0 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 (B) 0.18 and 1900 km

Linear Algebra & Differential Equations

(C) 0.22 and 8300 km (D) 0.22 and 1900 km 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

Incompressible & Compressible Aerodynamics

(A) -0.05  0.02i (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, p 1 = 1 atm and T 1 = 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 1 M tan ) 1 M (1 1tan1 1) M ( 2 121           Assume air to be calorically perfect with  = 1.4. The Mach number, M 2, downstream of the expansion corner is approximately

Incompressible & Compressible Aerodynamics

(A) 2.00 (B) 1.76 (C) 2.83 (D) 3.14 M1, p1, T1  M2 Consider a steady two dimensional zero-pressure grad ient lami nar 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 kg m -1s-1. The ratio of displacement thic kness to momentum thickness of the boundary layer at a distance of 2 m from the leading edge is 510 8 . 1   

Incompressible & Compressible Aerodynamics

(A) 7.53 (B) 2.59 (C) 2.91 (D) 0.39 Boundary la yer U∞ ∞ p∞ ∞ 2m AE 2011 AEROSPACE ENGINEERING - AE AE 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

Incompressible & Compressible Aerodynamics

(A) P,Q (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, cl, can be written as

Linear Algebra & Differential Equations

(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 02 2 4 4    t wmx wEI , where EI is the flexural stiffness, is the mass per unit length, is the bending displacement, m ) , (t x w x is the coordinate along the beam length, t is time and is the beam length. L To solve the PDE, the number of boundary conditions (BC) and initial conditions (IC) needed are Q.48 (A) 4 BC, 3 IC (B) 2 BC, 2 IC (C) 2 BC, 4 IC (D) 4 BC, 2 IC For the cantilever beam shown in the figure, which of the following CANNOT be a possible boundary condition?

Structural Mechanics

Question 48 from official GATE AE 2011 Examination.

Incompressible & Compressible Aerodynamics

(A) 0 ) , 0 (t w (B) 0 ) , (2 2   t Lx w (C) 0 ) , 0 (2 2   tx w (D) 0 ) , (3 3   t Lx w 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. The shock angle β is

Structural Mechanics

(A) = 20° (B) > 20° and< 30° (C) = 30°  (D) > 30° The total temperature at point P is Q.51 (A) 806.37 K (B) 1128.92 K (C) 1612.74 K (D) 2257.84 K x0x L x L   P 1m M∞ 2011 AEROSPACE ENGINEERING - AE 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, : density): Material E (GPa) y (MPa)  (kg/m3) X 200 550 7700 Y 70 225 2700 Z 110 375 4875 Which of the above materials would you choose such that weight of the shaft is minimum?

Structural Mechanics

Question 51 from official GATE AE 2011 Examination.

Incompressible & Compressible Aerodynamics

(A) X only (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? Q.53 (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      dyy y y Uyy c U yy b b L          2 2 0 0 0 0 0 0 / 4 1  , where U is the free-stream velocity,  is the angle of attack, is the spanwise location,  0y  0 0yL gives the spanwise variation of zero-lift angle, c is the chord, b is the span, and gives the spanwise variation of circulation.  0y The rate of change of circulation with angle of attack      is (A) inversely proportional to  (B) independent of 

Structural Mechanics

Question 53 from official GATE AE 2011 Examination.

Incompressible & Compressible Aerodynamics

(C) a linear function of  (D) a quadratic function of  Given that  dy y C b b L     2 2 , the corresponding lift curve-slope   LC is (A) independent of  (B) a linear function of 

Structural Mechanics

(C) a quadratic function of  (D) a cubic function of  AE 2011 AEROSPACE ENGINEERING - AE General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each.

Structural Mechanics

Choose the word from the options given below that is most nearly opposite in meaning to the given word: Deference

Structural Mechanics

Choose the most appropriate word(s) from the opt ions given below to complete the following sentence. We lost confidence in him because he never __________ the grandiose promises he had made.

Structural Mechanics

Choose the word or phrase that best completes the sentence below. ______________ in the frozen wastes of Arctic takes special equipment.

Structural Mechanics

(A) 4 (B) 12 (C) 64 (D) 81 Choose the most appropriate word from the op tions 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

Structural Mechanics

Question 60 from official GATE AE 2011 Examination.

Structural Mechanics

Question 61 from official GATE AE 2011 Examination.

Structural Mechanics

(A) (-3, 4) (B) (3, -4) (C) (6, 1) (D) (4, 2) AE 2011 AEROSPACE ENGINEERING - AE 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 of children in the queue?

Structural Mechanics

(A) 28 (B) 27 (C) 41 (D) 40

Structural Mechanics

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 recei ves 10 points for hitting the bulls' eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle. AE Outer circle 1 point Inner circle 5 points Bull's eye 10 points The final scores received by the play ers during the tournament are listed in the table below. Round P Q R S 1 5 1 10 1 5 10 10 1 2 1 1 1 5 3 10 10 1 1 4 1 5 5 10 5 10 5 1 1 6 5 10 1 1 7 The most accurate and the most consistent players during the tournament are respectively (A) P and S (B) Q and R (C) Q and Q (D) R and Q Nimbus clouds are dark and ragged, stratus clo uds appear dull in colour and cover the entire sky. Cirrus clouds are thin and delicate, whereas cumulus clouds look like cotton balls.

Structural Mechanics

It can be inferred from the passage that