GATE AE 2016 Question Paper & Solutions

Verbal & Numerical Aptitude

With increase in airfoil thickness, the critical Mach number for an airfoil is likely to (A) decrease. (B) increase. (C) remain unchanged. (D) be undefined.

Verbal & Numerical Aptitude

Due to a body in potential flow, the velocity at a point A in the flow field is 20 m/s while the free stream velocity is only 10 m/s. The value of coefficient of pressure (C p) at the point A is _________.

Verbal & Numerical Aptitude

Which of the following airfoil will have location of the maximum camber at half chord length from the leading edge? (A) NACA 5212 (B) NACA 1225 (C) NACA 2215 (D) NACA 2512

Verbal & Numerical Aptitude

For a laminar incompressible flow past a flat plate at zero angle of attack, the variation of skin friction drag coefficient  fC with Reynolds number based on the chord length  cRe can be expressed as

Verbal & Numerical Aptitude

Which of the following statement is NOT TRUE across an oblique shock wave?

Verbal & Numerical Aptitude

For a completely subsonic isentropic flow through a convergent nozzle, which of the following statement is TRUE?

Verbal & Numerical Aptitude

Which of the following aircraft engines has the highest propulsive efficiency at a cruising Mach number of less than 0.5? (A) Turbofan engine (B) Turbojet engine (C) Turboprop engine (D) Ramjet engine

Verbal & Numerical Aptitude

Air, with a Prandtl number of 0.7, flows over a flat plate at a high Reynolds number. Which of the following statement is TRUE?

Verbal & Numerical Aptitude

Shaquille O' Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts? (A) 0.2508 (B) 0.2816 (C) 0.2934 (D) 0.6000

Verbal & Numerical Aptitude

If A and B are both non-singular n n matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.

Structural Mechanics

The total number of material constants that are necessary and sufficient to describe the three dimensional Hooke's law for an isotropic material is ____.

Structural Mechanics

Determine the correctness or otherwise of the following statements, [a] and [r]: [a]: In a plane stress problem, the shear strains along the thickness direction of a body are zero but the normal strain along the thickness is not zero. [r]: In a plane stress problem, Poisson effect induces the normal strain along the thickness direction of the body.

Structural Mechanics

Consider four thin -walled beams of different open cross-sections, as shown in the cases (i-iv). A shear force of magnitude 'F' acts vertically downward at the location 'P' in all the beams. In which of the following case, does the shear force induce bending and twisting? Case (i) Case (ii) Case (iii) Case (iv) (A) (i) (B) (ii) (C) (iii) (D) (iv) 3/9

Structural Mechanics

The effective stiffness of the spring-mass system as shown in the figure below is ____ N/mm.

Structural Mechanics

A structural member supports loads, which produce at a particular point, a state of pure shear stress of 50 N/mm 2. At what angles are the principal planes oriented with respect to the plane of pure shear? (A) π/6 and 2π/3 (B) π/4 and 3π/4 (C) π/4 and π/2 (D) π/2 and π

Structural Mechanics

Let x be a positive real number. The function   2 2 x 1x x f  has its minima at x=______.

Structural Mechanics

The vector u is defined as y xeˆx eˆy u   , where xeˆ and yeˆ are the unit vectors along x and y directions, respectively. If the vector  is defined as u    , then      u ______.

Linear Algebra & Differential Equations

The partial differential equation 2 2 x u t u     , where α is a positive constant, is (A) circular. (B) elliptic. (C) hyperbolic. (D) parabolic.

Air-Breathing & Rocket Propulsion

Combustion in gas turbine engines is ideally represented as the following process: (A) Adiabatic (B) Isentropic (C) Isobaric (D) Isochoric

Air-Breathing & Rocket Propulsion

For a given chamber pressure, the thrust of a rocket engine is highest when

Airplane Performance & Stability

The d amping ratio in phugoid motion for gliders is usually less compared to powered aircraft because

Airplane Performance & Stability

During an aircraft cruising flight, the altitude above the ground is usually measured using (A) dynamic pressure. (B) static pressure. (C) radar. (D) laser range finder. 4/9

Airplane Performance & Stability

Indicated airspeed is used by a pilot during (A) take-off. (B) navigation. (C) setting the engine RPM. (D) setting the elevator angle.

Structural Mechanics

The pitch angle and the angle of attack for a fixed wing aircraft are equal during

Incompressible & Compressible Aerodynamics

The load factor of an aircraft turnin g at a constant altitude is 2. The coefficient of lift required for turning flight as compared to level flight at the same speed will be (A) same (B) half (C) double (D) four times Q. 26 - Q. 55 carry two marks each.

Air-Breathing & Rocket Propulsion

An un-mixed turbofan engine with a bypass ratio of 6.0, flies with a velocity of 200 m/s. The core and the bypass nozzles of the engine, that are both convergent nozzles, operate under choked condition and have exhaust static temperatures of 580 K and 295 K, respectively. The specific gas constant and the ratio of specific heats for both the streams are 287 J/kgK and 1.4, respectively. If the fuel-air ratio is negligible, the thrust per unit mass flow rate generated by the engine is _______Ns/kg.

Air-Breathing & Rocket Propulsion

A single-stage gas turbine operates with an axial absolute flow at the entry and exit from the stage. The absolute flow angle at the nozzle exit is 70 o. The turbine stage generates a specific work of 228 kJ/kg when operating with a mean blade speed of 440 m/s. The absolute velocity at the rotor entry is (A) 275.7 m/s (B) 551.5 m/s (C) 1103.0 m/s (D) 1654.5 m/s

Structural Mechanics

An axial compressor operates such that it has an inlet and an exit total temperature of 300 K and 430 K, respectively. The isentropic efficiency of the compressor is 85 %. If the ratio of specific heats is 1.4, then the total pressure ratio across the compressor is ____________.

Incompressible & Compressible Aerodynamics

The maximum value of coefficient of lift ( lC ) for a 2D circular cylinder, provided at least one stagnation point lies on the cylinder surface, is predicted by the potential flow theory to be (A) π/2 (B) π (C) 2π (D) 4π .30 The nozzle AB, as shown below, leading to the test section of a low speed subsonic wind tunnel, has a contraction ratio of 10:1. The pressure difference across the nozzle is maintained at 1000 N/m2 and the density of air is 1.23 kg/m 3. Assuming one-dimensional, steady, inviscid flow, the velocity in the test section as measured at point B is ___________ m/s.

Structural Mechanics

Question 30 from official GATE AE 2016 Examination.

Incompressible & Compressible Aerodynamics

The rate of change of moment coefficient with respect to the angle of attack, d dC m , at half chord point of a thin airfoil, as per approximations from the thin airfoil theory is (A) π/4 radian-1 (B) π/2 radian-1 (C) π radian-1 (D) 2π radian-1

Incompressible & Compressible Aerodynamics

An untwisted wing of elliptic planform and aspect ratio 6 consists of thin symmetric airfoil sections. The coefficient of lift (C L) at o10 angle of attack assuming inviscid incompressible flow is (A) π2/16 (B) π2/12 (C) π2/8 (D) π/2

Air-Breathing & Rocket Propulsion

A gaseous mixture of air and fuel enters a constant area combustion chamber at a velocity of 100 m/s and at a static temperature of 300 K. The heat release due to combustion is 1000 kJ/kg. The specific heat at constant pressure of the calorically perfect gas is 1000 J/kgK. The total temperature of air-fuel mixture after combustion is ______ K.

Incompressible & Compressible Aerodynamics

Consider 1 -D, steady, in viscid, compressible flow through a convergent nozzle . The total temperature and total pressure are oT , oP respectively. The flow through the nozzle is choked with a mass flow rate of om . If the total temperature is increased to oT 4, with total pressure remaining unchanged, then the mass flow rate through the nozzle

Linear Algebra & Differential Equations

Consider a second order linear ordinary differential equation 0 y 4dx dy4 dx y d 2 2   , with the boundary conditions 1dx dy; 1 ) 0 ( y 0 x   . The value of y at x =1 is (A) 0 (B) 1 (C) e (D) e2 6/9

Linear Algebra & Differential Equations

Consider the following system of linear equations: 2x - y + z = 1 3x - 3y + 4z = 6 x - 2y + 3z = 4 This system of linear equations has

Structural Mechanics

A bar made of linear elastic isotropic material is fixed at one end and subjected to an axial force of 1 kN at the other end. The cross-sectional area of the bar is 100 mm 2, length is 100 mm and the Young's Modulus is 1105 N/mm2. The strain energy stored in the bar is ____ Nmm.

Structural Mechanics

A cantilever beam -spring system is shown in the figure. The beam is made with a material of Young's modulus 1105 N/mm 2 and geometry such that its moment of inertia is 100 mm 4 and length l = 100 mm. It is supported by a spring of stiffness K = 30 N/mm and subjected to a load of P = 100 N at the point 'B'. The deflection at the point 'B' due to the load P is ____mm.

Structural Mechanics

Determine the correctness or otherwise of the following statements, [a] and [r], [a]: Ribs, used in airplane wings, increase the column buckling strength of the longitudinal stiffeners. [r]: Ribs distribute concentrated loads into the structure and redistribute stresses around discontinuities.

Structural Mechanics

Question 40 from official GATE AE 2016 Examination.

Linear Algebra & Differential Equations

The governing differential equation of motion of a damped system is given by 0 kxdt dxcdt x dm 2 2   . If m = 1 kg, c = 2 Ns/m and k = 2 N/m then the frequency of the damped oscillation of this system is ____ rad/s.

Structural Mechanics

The two dimensional state of stress in a body is described by the Airy's stress function: 12 yE6 xy72 y x36 y x 12 x5 432 23 4      . The Airy's stress function will satisfy the equilibrium and the compatibility requirements if and only if the value of the coefficient E is ____.

Structural Mechanics

The value of definite integral    0 dx x sin x is _______.

Structural Mechanics

Use Newton-Raphson method to solve the equation: 1 e xx  . Begin with the initial guess 5 . 0 x0  . The solution after one step is x _________.

Structural Mechanics

A wall of thickness 5 mm is heated by a hot gas flowing along the wall. The gas is at a temperature of 3000 K, and the convective heat transfer coefficient is 160 W/m 2K. The wall thermal conductivity is 40 W/mK. If the colder side of the wall is held at 500 K, the temperature of the side exposed to the hot gas is _______ K.

Air-Breathing & Rocket Propulsion

A launch vehicle has a main rocket engine with two identical strap-on motors, all of which fire simultaneously during the operation. The main engine delivers a thrust of 6300 kN with a specific impulse of 428 s. Each strap-on motor delivers a thrust of 12000 kN with specific impulse of 292 s. The acceleration due to gravity is 9.81 m/s 2. The effective (combined) specific impulse of the vehicle is _______ s.

Structural Mechanics

A substance experiences an entropy change of 0 s in a quasi-steady process. The rise in temperature (corresponding to the entropy change s ) is highest for the following process: (A) isenthalpic (B) isobaric (C) isochoric (D) isothermal 8/9

Air-Breathing & Rocket Propulsion

In a particular rocket engine, helium propellant is heated to 6000 K and 95% of its total enthalpy is recovered as kinetic energy of the nozzle exhaust. Consider helium to be a calorically perfect gas with specific heat at constant pressure of 5200 J/kgK. The exhaust velocity for such a rocket for an optimum expansion is _____ m/s.

Airplane Performance & Stability

An aircraft is flying level in the North direction at a velocity of 55 m/s under cross wind from East to West of 5 m/s. For the given aircraft C nβ = 0.012/deg and C nδr = - 0.0072/deg, where δr is the rudder deflection and β is the side slip angle . The rudder deflection exerted by pilot is __________ degrees.

Air-Breathing & Rocket Propulsion

An aircraft weighing 10000 N is flying level at 100 m/s and it is powered by a jet engine. The thrust required for level flight is 1000 N. The maximum possible thrust produced by the jet engine is 5000 N. The minimum time required to climb 1000 m, when flight speed is 100 m/s, is ________s.

Structural Mechanics

The aircraft velocity (m/s) components in body axes are given as [ u, v, w] = [100, 10, 10]. The air velocity (m/s), angle of attack (deg) and sideslip angle (deg) in that order are (A) [120, 0.1, 0.1] (B) [100, 0.1, 0.1] (C) [100.995, 0.1, 5.73] (D) [100.995, 5.71, 5.68]

Structural Mechanics

The Dutch roll motion of the aircraft is described by following relationship                       r 76 . 0 49 . 4 1 26 . 0 r  The undamped natural frequency (rad/s) and damping ratio for the Dutch roll motion in that order are: (A) 4.68, 1.02 (B) 4.49, 1.02 (C) 2.165, 0.235 (D) 2.165, 1.02

Airplane Performance & Stability

A glider weighing 3300 N is flying at 1000 m above sea level. The wing area is 14.1 m2 and the air density is 1.23 kg/m3. Under zero wind conditions, the velocity for maximum range is __________ m/s. α (deg) C L CD C L/CD 11 1.46 0.0865 16.9 9 1.36 0.0675 20.1 7 1.23 0.0535 22.9 5 1.08 0.0440 24.5 3 0.90 0.0350 25.7 1 0.70 0.0275 25.4 -1 0.49 0.0220 22.2 -3 0.25 0.0180 13.8

Incompressible & Compressible Aerodynamics

A rocket, with a total lift-off mass of 10000 kg, moves vertically upward from rest under a constant gravitational acceleration of 9.81 m/s 2. The propellant mass of 8400 kg burns at a constant rate of 1200 kg/s. If the specific impulse of the rocket engine is 240 s, neglecting drag, the burnout velocity in m/s is (A) 3933.7 (B) 4314.6 (C) 4245.9 (D) 4383.3 9/9

Space Dynamics

A satellite is injected at an altitude of 350 km above the Earth's surface, with a velocity of 8.0 km/s parallel to the local horizon. (Earth radius=6378 km, µE (GM=Gravitational constant × Earth mass) = 3.986×1014 m3s-2). The satellite (A) forms a circular orbit. (B) forms an elliptic orbit. (C) escapes from Earth's gravitational field. (D) falls back to earth. END OF THE QUESTION PAPER Q. No Type Section Key Marks 1 MCQ GA C 1 2 MCQ GA B 1 3 MCQ GA B 1 4 MCQ GA B 1 5 MCQ GA C 1 6 NAT GA 120.0 : 120.0 2 7 MCQ GA C 2 8 MCQ GA C 2 9 MCQ GA A 2 10 NAT GA 7.0 : 7.0 2 1 MCQ AE A 1 2 NAT AE -3.0 : -3.0 1 3 MCQ AE D 1 4 MCQ AE C 1 5 MCQ AE D 1 6 MCQ AE C 1 7 MCQ AE C 1 8 MCQ AE A 1 9 MCQ AE B 1 10 MCQ AE B 1 11 NAT AE 2.0 : 2.0 1 12 MCQ AE A 1 13 MCQ AE B 1 14 NAT AE 5.0 : 5.0 1 15 MCQ AE B 1 16 NAT AE 1.0 : 1.0 1 17 NAT AE 0.0 : 0.0 1 18 MCQ AE D 1 19 MCQ AE C 1 20 MCQ AE B 1 21 MCQ AE C 1 22 MCQ AE B 1 23 MCQ AE A 1 24 MCQ AE A 1 25 MCQ AE C 1 26 NAT AE 162 : 166 ; 1147.0 : 1150.0 2 27 MCQ AE B 2 28 NAT AE 2.9 : 3.1 2 29 MCQ AE D 2 30 NAT AE 40.0 : 41.0 2 31 MCQ AE B 2 32 MCQ AE B 2 33 NAT AE 1305 : 1305 2 34 MCQ AE B 2 35 MCQ AE A 2 36 MCQ AE A 2 37 NAT AE 5.0 : 5.0 2 38 NAT AE 1.5 : 1.7 2 39 MCQ AE B 2 40 NAT AE 2.4 : 2.6 2 41 NAT AE 0.99 : 1.01 2 42 NAT AE -11.0 : -11.0 2 43 NAT AE 3.13 : 3.15 2 44 NAT AE 0.56 : 0.58 2 45 NAT AE 548 : 550 2 46 NAT AE 310 : 315 2 47 MCQ AE C 2 48 NAT AE 7690 : 7710 2 49 NAT AE 8.6 : 8.7 2 50 NAT AE 25.0 : 25.0 2 51 MCQ AE D 2 52 MCQ AE C 2 53 NAT AE 20.0 : 21.0 2 54 MCQ AE C 2 55 MCQ AE B 2

Structural Mechanics

Question 56 from official GATE AE 2016 Examination.

Structural Mechanics

Question 57 from official GATE AE 2016 Examination.

Structural Mechanics

Question 58 from official GATE AE 2016 Examination.

Structural Mechanics

Question 59 from official GATE AE 2016 Examination.

Structural Mechanics

Question 60 from official GATE AE 2016 Examination.

Structural Mechanics

Question 61 from official GATE AE 2016 Examination.

Structural Mechanics

Question 62 from official GATE AE 2016 Examination.

Structural Mechanics

Question 63 from official GATE AE 2016 Examination.

Structural Mechanics

Question 64 from official GATE AE 2016 Examination.

Structural Mechanics

Question 65 from official GATE AE 2016 Examination.