GATE AE 2020 Question Paper & Solutions

Verbal Aptitude

15526 гр 16071 гр Q.No. 34 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

Verbal Aptitude

Consider the standard principles of Verbal Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Quantitative Aptitude

Select the word that fits the analogy:

Analytical & Spatial Aptitude

Consider the standard principles of Analytical & Spatial Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Analytical & Spatial Aptitude

A superadditive function f (•) satisfies the following property f (x1 + x2) = f(x1) + f(x2) 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

Quantitative Aptitude

Consider the standard principles of Quantitative Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Quantitative Aptitude

Which one of the following sequences shows the correct precedence as per the given passage? East Asian crisis→ subprime lending crisis →banking crisis→ global financial crisis. Subprime lending crisis→ global financial crisis→ banking crisis → East Asian crisis. Banking crisis→ subprime lending crisis→ global financial crisis → East Asian crisis. Global financial crisis → East Asian crisis → banking crisis → subprime lending crisis. It is quarter past three in your watch. The angle between the hour hand and the minute hand is 0° 7.5° 15° 22.5° A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is P S R

Verbal Aptitude

Consider the standard principles of Verbal Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Analytical & Spatial Aptitude

па? - a? na? - 2a? па? - 3а? a, b, c are real numbers. The quadratic equation ax? - bx + c = 0 has equal roots, which is B, then ß = b/a B? = ac p3 = bc/(2a3) b2 # 4ac

Linear Algebra

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

Linear Algebra

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

Calculus

In an aerospace engineering analysis of Calculus (Limits, Continuity & Differentiability), 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 (First Order ODEs), 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 (Newton-Raphson Method), 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 (Conservation Equations of Mass, Momentum & Energy), 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 (Kutta-Joukowski Theorem & Thin Airfoil Theory), 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?

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Wind Tunnel Testing & Instrumentation

In an aerospace engineering analysis of Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Standard Atmosphere Properties), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

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?

Dynamic Stability

In an aerospace engineering analysis of Dynamic Stability (Short Period & Phugoid Longitudinal Modes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

In an aerospace engineering analysis of Space Dynamics & Orbital Mechanics (Kepler's Laws & Two-Body Problem), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thermodynamic Cycles of Gas Turbines

In an aerospace engineering analysis of Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

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?

Airfoil & Wing Theory

In an aerospace engineering analysis of Airfoil & Wing Theory (Finite Wing Theory & Induced Drag), 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 (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).

Space Dynamics & Orbital Mechanics

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 (§new) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (korg / Knew), 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)

Thermodynamic Cycles of Gas Turbines

Smooth surface As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is N (round off to two decimal places). 7 10 N/m - 1 m

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).