GATE AE 2021 Question Paper & Solutions

Verbal Aptitude

(i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun's families is here. (iv) Arun's family is here. Which of the above sentences are grammatically CORRECT?

Verbal Aptitude

PHYLAXIS The mirror image of the above text about the horizontal X-axis (placed below the text) is:

Quantitative Aptitude

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

Analytical & Spatial Aptitude

$\odot$ and $\bullet$ are two operators on numbers $p$ and $q$ such that $p \odot q = p - q$, and $p \bullet q = p \times q$. Then, $(9 \odot (6 \bullet 7)) \odot (7 \bullet (6 \odot 5)) =$

Analytical & Spatial Aptitude

Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

Verbal Aptitude

On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be:

Quantitative Aptitude

The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks." Based on the above passage, which one of the following is TRUE?

Quantitative Aptitude

1. Some football players play cricket. 2. All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

Verbal Aptitude

In a square PQRS of side length $a$, the shaded portion is formed by the intersection of two circular sectors of radius $a$ with centers at diagonally opposite vertices S and Q. The probability that any point picked randomly within the square falls in the shaded area is:

Analytical & Spatial Aptitude

In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in $\text{cm}^2$, is:

Linear Algebra

Consider the differential equation $\frac{d^2 y}{dx^2} + 8\frac{dy}{dx} + 16y = 0$ with boundary conditions $y(0) = 1$ and $\frac{dy}{dx}(0) = 0$. The solution to this equation is:

Linear Algebra

A scalar field $u(x, y)$ is governed by the equation $\frac{\partial^2 u}{\partial x^2} + 6\frac{\partial^2 u}{\partial x \partial y} + 9\frac{\partial^2 u}{\partial y^2} = x + 2y$. The mathematical nature of this equation is:

Calculus

Consider the 2D velocity field $\vec{V} = (2x + 3y)\hat{i} + (3x + 2y)\hat{j}$. The field $\vec{V}$ is:

Differential Equations

In a converging-diverging nozzle, Nozzle A displays oblique shock waves at the exit plane, whereas Nozzle B displays an expansion fan at the exit plane. Nozzles A and B, respectively, are operating in:

Numerical Methods

The combustion process in a turboshaft engine during ideal Brayton cycle operation is considered to be:

Basic Fluid Mechanics

An ideal gas flows steadily through a constant area duct with friction (Fanno flow). As the flow proceeds downstream towards the choking point, the stagnation temperature $T_0$:

Thermodynamics of Aircraft Engines

How does the propulsive efficiency of a turbofan engine, operating at a given cruise altitude and Mach number, vary with bypass ratio (BPR)?

Rocket Propulsion

A solid propellant rocket producing 25 MN thrust is fired for 150 seconds. If the propellant mass consumed during this duration is $1.25 \times 10^6$ kg, the effective exhaust velocity (in m/s) is:

Structural Dynamics & Aeroelasticity

A single degree of freedom spring-mass-damper system is designed to return to its equilibrium position in the shortest possible time without exhibiting oscillatory overshoot. The damping ratio $\zeta$ of this system must be:

Bending & Shear of Beams

Two cantilever beams (Beam 1 and Beam 2) are made of the same homogeneous isotropic material and have identical length $L$. Beam 1 has a solid circular cross-section of radius $R$, while Beam 2 has a hollow circular cross-section with outer radius $R$ and inner radius $R/2$. If identical tip loads $P$ are applied, the ratio of the tip deflection of Beam 2 to that of Beam 1 ($\delta_2 / \delta_1$) is:

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?

Thin-Walled Structures

A thin-walled cylindrical pressure vessel with closed ends, having mean radius $r$ and wall thickness $t$, is subjected to an internal gauge pressure $p$. Under the plane stress assumption, the ratio of the circumferential (hoop) stress $\sigma_h$ to the longitudinal stress $\sigma_l$ is:

Static Stability & Control

For a conventional statically stable airplane, which one of the following combinations of pitching moment parameters about the center of gravity is CORRECT?

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

Q.27 The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:

Calculus

Given that $C$ is the unit circle in the counter-clockwise direction centered at the origin, the value of the contour integral $\oint_C \frac{\cos z}{z}\,dz$ is _________ (round off to 2 decimal places).

Compressors and Turbines

Q.29 The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as: • Tunnel wall

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

Q.31 - Q.36 Multiple Select Question (MSQ), carry TWO mark each (no negative marks). Q.31 (A) (B)

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

Q.33 A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames?

Structural Dynamics & Aeroelasticity

An aerospace system operating under standard sea level conditions is governed by Structural Dynamics & Aeroelasticity (Flutter Phenomenon & Divergence Speed). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Aerospace Materials & Fatigue

Which of the following statement(s) is/are true? (A) Service ceiling is higher than absolute ceiling for a piston-propeller aircraft. (B) For a given aircraft, the stall speed increases with increase in altitude. (C) Everything else remaining the same, a tailwind increases the range of an aircraft. (D) For a jet aircraft constrained to fly at constant altitude, there exists an altitude where its range is maximum.

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

In an aerospace engineering analysis of Basic Fluid Mechanics (Incompressible Potential Flow & Stream Functions), 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 (High-Lift Devices & Flaps), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

Q.47 A single stage axial turbine has a mean blade speed of 340 m/s at design condition with blade angles at inlet and exit of the rotor being 21° and 55°, respectively. The degree of reaction at the mean radius of the rotor is equal to 0.4. The annulus area at the rotor inlet is 0.08 m? and the density

Atmospheric Flight Mechanics

An aerospace system operating under standard sea level conditions is governed by Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Static Stability & Control

Q.49 A rigid horizontal bar ABC, with roller support at A, is pinned to the columns BD and CE at points B and C, respectively as shown in figure. The other end of the column BD is fixed at D, whereas the column CE is pinned at E. A vertical load P is applied on the bar at a distance 'a' from

Dynamic Stability

Q.50 A two-cell wing box is shown in the figure. The cell walls are 1.5 mm thick and the shear modulus G = 27 GPa. If the structure is subjected to a torque of 12 kNm, then the wall AD will experience a shear stress of magnitude

Space Dynamics & Orbital Mechanics

An aerospace system operating under standard sea level conditions is governed by Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Space Dynamics & Orbital Mechanics

Q.52 A 3 m x 1 m signboard is supported by a vertical hollow pole that is fixed to the ground. The pole has a square cross section with outer dimension 250 mm. The yield strength of the pole material is 240 MiPa. To sustain a wind pressure of 7.5 kPa, the dimension d of the pole is _

Thermodynamic Cycles of Gas Turbines

An aerospace system operating under standard sea level conditions is governed by Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Thermodynamic Cycles of Gas Turbines

Q.54 A jet aircraft weighing 10,000 kg has an elliptic wing with a span of 10 m and area 30 m'. The CD, for the aircraft is 0.025. The maximum speed of the aircraft in steady and level flight at sea level is 100 m/s. The density of air at sea level is 1.225 kg/m', and take g = 10 m/s. The maximum thrust

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).