GATE AE 2020 Question Paper & Solutions

Verbal Aptitude

The untimely loss of life is a cause of serious global concern as thousands of people get killed _____ accidents every year while many others die _____ diseases like cardio vascular disease, cancer, etc.

Verbal Aptitude

He was not only accused of theft _____ of conspiracy.

Quantitative Aptitude

Select the word that fits the analogy: Explicit: Implicit :: Express: _____

Analytical & Spatial Aptitude

The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements in English lasting 15 seconds, as opposed to informal 5 second messages in French. The French-speaking couple were upset at:

Analytical & Spatial Aptitude

A superadditive function $f(\cdot)$ satisfies the property $f(x_1 + x_2) \ge f(x_1) + f(x_2)$. Which of the following functions is a superadditive function for $x > 1$?

Verbal Aptitude

The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis. Which one of the following sequences shows the correct precedence as per the given passage?

Quantitative Aptitude

It is quarter past three in your watch. The angle between the hour hand and the minute hand is:

Quantitative Aptitude

A circle with centre O has a rectangle PQRS of maximum possible area inscribed within it. If the radius of the circle is $a$, then the area of the shaded portion (circle area minus rectangle area) is:

Verbal Aptitude

$a, b, c$ are real numbers. The quadratic equation $a x^2 - b x + c = 0$ has equal roots, which is $\beta$. Then:

Analytical & Spatial Aptitude

The data of students enrolled in 5 years (2014 to 2018) for two schools P and Q shows average enrollment for school P as 6.9 thousand and average difference between schools P and Q as 2.4 thousand. During this period, the ratio of the average number of students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is:

Linear Algebra

For the function $f(x) = |x|$ defined on $[-1, 1]$, with $f'$ denoting the derivative, Rolle's / Lagrange's Mean Value Theorem is not applicable because:

Linear Algebra

For the Gaussian normal distribution function $f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-z}$, where $z = \frac{(x - \mu)^2}{2\sigma^2}$, and $\sigma, \mu$ are constants, the maximum of $f(x)$ occurs at:

Calculus

The function $y(x) = A e^{mx} + B e^{-mx}$, where $A, B$ and $m$ are constants, is a solution of which differential equation?

Differential Equations

Which of the following statements is true about the effect of an increase in temperature on the dynamic viscosity of water and air, at room temperature?

Numerical Methods

Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute:

Basic Fluid Mechanics

A pair of infinitely long, counter-rotating line vortices of identical circulation strength $\Gamma$ are situated a distance $h$ apart in an inviscid fluid. The vortices will:

Airfoil & Wing Theory

The streamlines of a steady 2D flow through a channel are plotted with upper bounding streamline $\psi = 0.5\text{ m}^2/\text{s}$ and lower bounding streamline $\psi = -0.5\text{ m}^2/\text{s}$. The volumetric flow rate per unit depth through the channel is:

Compressible Flow & Shocks

Which of the following operations will result in an increase in the Mach number of a supersonic flow in a constant-area duct?

Linear Algebra

Given $A = \begin{bmatrix} \sin\theta & \tan\theta \\ 0 & \cos\theta \end{bmatrix}$, the sum of squares of the eigenvalues of $A$ is:

Space Dynamics & Orbital Mechanics

Burnout velocity of a space vehicle in a circular orbit at an angle $5^\circ$ above the local horizon around earth is 13.5 km/s. The velocity vector orientation indicates the orbit trajectory nature is:

Aircraft Equations of Motion

Velocity of an airplane in the body-fixed axes is given as $[u, v, w] = [100, -10, 20]$ m/s. The sideslip angle $\beta$ (in degrees) is _________ (round off to two decimal places).

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Climb, Glide, Ceiling & Turn Performance), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Static Stability & Control

In an aerospace engineering analysis of Static Stability & Control (Longitudinal Static Stability & Neutral Point), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Viscous Flows & Boundary Layers

The similarity solution for the diffusion equation $\frac{\partial u}{\partial t} = \nu \frac{\partial^2 u}{\partial y^2}$ is $u(y, t) = u(\eta)$, where the similarity variable $\eta$ is proportional to:

Maneuvers & Load Factors

An airplane of mass 5000 kg is flying at a constant speed of 360 km/h at the bottom of a vertical circular loop of radius 400 m. Taking $g = 9.8$ m/s$^2$, the lift force (in kN) generated by the wings at the bottom of the loop is _________ (round off to the nearest integer).

Differential Equations

The differential equation $x \frac{dy}{dx} + y = c$, where $c$ is a constant, represents a family of:

Thermodynamic Cycles of Gas Turbines

In an aerospace engineering analysis of Thermodynamic Cycles of Gas Turbines (Turbojet, Turbofan & Turboprop Engine Performance), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Inlets, Combustors & Nozzles

In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Subsonic & Supersonic Inlets), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressors and Turbines

In an aerospace engineering analysis of Compressors and Turbines (Axial Flow Compressor Stage Dynamics & Stall), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Rocket Propulsion

An aerospace system operating under standard sea level conditions is governed by Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Strength of Materials & Elasticity

A load P is applied to the free end of a stepped cantilever beam as shown in the figure. The Young's modulus of the material is E, and the moments of inertia of the two sections of length 2 m and 1 m are / and 3l, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is 2m - Im 31 = 3N 23 243 EI 1 3EI 43 3EI 23 ЗЕІ The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is C C 0 Vy= Y xe Yxy) C C 0 A C 0 C A 0 0 0 0 0 0 0 0 0 0 0 0 0 Ty= 0 BJl [xy A, B and C are compliances which depend on the elastic properties of the material. Which one of the following is correct? c= 4 - B c=1+ B 2 2

Strength of Materials & Elasticity

An aerospace system operating under standard sea level conditions is governed by Strength of Materials & Elasticity (Airframe Structural Analysis & Trusses). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Thin-Walled Structures

An aerospace system operating under standard sea level conditions is governed by Thin-Walled Structures (Shear Flow in Open and Closed Thin-Walled Beams). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Structural Dynamics & Aeroelasticity

For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses? 12 MPa • 4 MPa 18 MPa

Aerospace Materials & Fatigue

In the equation AX = B, A = 1 0 0 11 X= B-?. , where A is -V=] (round off to one an orthogonal matrix, the sum of the unknowns, *+ y+z=_ decimal place). If f(x* - 2x+ 1) dr is evaluated numerically using trapezoidal rule with four intervals, the difference between the numerically evaluated value and the analytical value of the integral is equal to (round off to three decimal places). O.No. 37

Linear Algebra

In an aerospace engineering analysis of Linear Algebra (Systems of Linear Equations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Calculus

In an aerospace engineering analysis of Calculus (Multiple Integrals & Vector Calculus), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Differential Equations

In an aerospace engineering analysis of Differential Equations (Higher Order Linear ODEs with Constant Coefficients), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Numerical Methods

In an aerospace engineering analysis of Numerical Methods (Runge-Kutta Methods for ODEs), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Airfoil & Wing Theory

In an aerospace engineering analysis of Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Basic Fluid Mechanics

In an aerospace engineering analysis of Basic Fluid Mechanics (Viscous Flow & Boundary Layer Equations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (Normal & Oblique Shock Waves), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet's orbit around the sun is planar and elliptic, the value of the eccentricity of the orbit is _________ (round off to three decimal places).

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (Rayleigh & Fanno Flow), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Basic Fluid Mechanics

For a general aviation airplane with tail efficiency n = 0.95, horizontal tail volume ratio Vu = 0.453, downwash angle slope de = 0.35, wing lift curve slope C*a = 4.8 rad"', horizontal tail lift curve slope CLa= 4.4 rad"', shift in neutral point location as a percentage of mean aerodynamic chord is (round off to two decimal places).

Airfoil & Wing Theory

A single engine, propeller driven, general aviation airplane is flying in cruise at sea- level condition (density of air at sea-level is 1.225 kg/m') with speed to cover maximum range. For drag coefficient Cp = 0.025 + 0.049 Ci? and wing loading W/S = 9844 N/m?, the speed of the airplane is _ m/s (round off to one decimal place).

Atmospheric Flight Mechanics

The design flight Mach number of an ideal ramjet engine is 2.8. The stagnation temperature of air at the exit of the combustor is 2400 K. Assuming the specific heat ratio of 1.4 and gas constant of 287 J/(kg K), the velocity of air at the exit of the engine is m/s (round off to one decimal place).

Atmospheric Flight Mechanics

The operating conditions of an aircraft engine combustor are as follows. The rate of total enthalpy of air entering the combustor = 28.94 MJ/s. The rate of total enthalpy of air leaving the combustor = 115.42 MJ/s. Mass flow rate of air = 32 kg/s. Air to fuel mass ratio = 15.6. Lower heating value of the fuel = 46 MJ/kg. The efficiency of the combustor is _% (round off to two decimal places). O.No. 49

Static Stability & Control

An aerospace system operating under standard sea level conditions is governed by Static Stability & Control (Static Margin & Stick-Fixed/Free Stability). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Dynamic Stability

A rocket engine has a sea level specific impulse of 210 s and a nozzle throat area of 0.005 m?. While testing at sea level conditions, the characteristic velocity and pressure for the thrust chamber are 1900 m/s and 50 bar, respectively. Assume the acceleration due to gravity to be 9.8 m/s?. The thrust produced by the rocket engine is kN (round off to one decimal place).

Structural Dynamics & Aeroelasticity

A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio ($\zeta_{new}$) for the overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness ($k_{orig} / k_{new}$), assuming that the other parameters remain unchanged, is _________ (round off to two decimal places).

Space Dynamics & Orbital Mechanics

The two masses of the two degree of freedom system shown in the figure are given initial displacements of 2 cm (xz) and 1.24 cm (x2). The system starts to vibrate in the first mode. The first mode shape of this system is d = [1 a]', where a = . (round off to two decimal places). 1x, (t) 1x3(t)

Bending & Shear of Beams

As shown in the figure, a beam of length 1 m is rigidly clamped at one end ($x = 0$) and simply supported at the other ($x = 1$ m). Under the action of a uniformly distributed downward load of $w = 10$ N/m, the magnitude of the vertical reaction force (in N) at the simply supported end is _________ (round off to two decimal places).

Thermodynamic Cycles of Gas Turbines

An airplane of mass 4000 kg and wing reference area 25 m? flying at sea level has a maximum lift coefficient of 1.65. Assume density of air as 1.225 kg/m' and acceleration due to gravity as 9.8 m/s*. Using a factor of safety of 1.25 to account for additional unsteady lift during a sudden pull-up, the speed at which the airplane reaches a load factor of 3.2 is m/s (round off to two decimal places). A Pitot tube mounted on the wing tip of an airplane flying at an altitude of 3 km measures a pressure of 0.72 bar, and the outside air temperature is 268.66 K. Take the sea level conditions as, pressure = 1.01 bar, temperature = 288.16 K, and density = 1.225 kg/m'. The acceleration due to gravity is 9.8 m/s and the gas constant is 287 J/(kg K). Assuming standard atmosphere, the equivalent airspeed for this airplane is _ _ m/s (round off to two decimal place). Copyright: GATE 2020, IT Delhi

Inlets, Combustors & Nozzles

An aerospace system operating under standard sea level conditions is governed by Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Compressors and Turbines

An aerospace system operating under standard sea level conditions is governed by Compressors and Turbines (Centrifugal Compressors). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Inlets, Combustors & Nozzles

An aerospace system operating under standard sea level conditions is governed by Inlets, Combustors & Nozzles (Combustor Design & Flame Stabilization). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Rocket Propulsion

An aerospace system operating under standard sea level conditions is governed by Rocket Propulsion (Solid, Liquid & Hybrid Rocket Engines). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Compressors and Turbines

An aerospace system operating under standard sea level conditions is governed by Compressors and Turbines (Axial Flow Gas Turbines & Blade Cooling). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Strength of Materials & Elasticity

An aerospace system operating under standard sea level conditions is governed by Strength of Materials & Elasticity (Euler Buckling of Columns & Energy Methods). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Thin-Walled Structures

An aerospace system operating under standard sea level conditions is governed by Thin-Walled Structures (Torsion of Multi-Cell Thin-Walled Tubes). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Thin-Walled Structures

An aerospace system operating under standard sea level conditions is governed by Thin-Walled Structures (Tension Field Beams & Wagner Beams). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Structural Dynamics & Aeroelasticity

An aerospace system operating under standard sea level conditions is governed by Structural Dynamics & Aeroelasticity (Free & Forced Vibrations of Continuous Beams). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Aerospace Materials & Fatigue

An aerospace system operating under standard sea level conditions is governed by Aerospace Materials & Fatigue (Aluminum, Titanium & Aerospace Alloys). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Aerospace Materials & Fatigue

An aerospace system operating under standard sea level conditions is governed by Aerospace Materials & Fatigue (Damage Tolerance & Non-Destructive Testing). Compute the required parameter in standard SI units (rounded off to the acceptable range).