GATE AE 2023 Question Paper & Solutions

Verbal Aptitude

"You are delaying the completion of the task. Send _______ contributions at the earliest."

Verbal Aptitude

References : ______ : : Guidelines : Implement (By word meaning)

Quantitative Aptitude

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

Quantitative Aptitude

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. Based only on the above information, which one of the following statements can be logically inferred with certainty?

Analytical & Spatial Aptitude

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

Verbal Aptitude

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement " Some human beings are not cruel creatures" is FALSE, then which of the following set of statement(s) can be logically inferred with certainty? (i) All human beings are cruel creatures. (ii) Some human beings are cruel creatures. (iii) Some creatures that are cruel are human beings. (iv) No human beings are cruel creatures.

Quantitative Aptitude

Consider the following inequalities: 1. $p^2 - 4q < 4$ 2. $3p + 2q < 6$ where $p$ and $q$ are positive integers. The value of $(p + q)$ is:

Verbal Aptitude

The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sr i Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households. Based only on the above passage, which one of the following statements can be inferred with certainty?

Verbal Aptitude

The coefficient of x4 in the polynomial (x - 1)3(x - 2)3 is equal to _______.

Verbal Aptitude

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

Calculus

The direction in which a scalar field ( , , )x y z has the largest rate of change at any point with position vector ˆˆˆr xi yj zk= + + is the same as that of the vector

Linear Algebra

If a monotonic and continuous function ()y f x= has only one root in the interval 12x x x , then

Calculus

Consider the one-dimensional wave equation 0uu tx  += for x-    , 0t  . For an initial condition 2 ( ,0) xu x e -= , the solution at 1t = is

Strength of Materials & Elasticity

A two-dimensional potential flow solution for flow past an airfoil has a streamline pattern as shown in the figure. Which of the following conditions is additionally required to satisfy the Kutta condition?

Strength of Materials & Elasticity

Consider the Blasius solution for the incompressible laminar flat plate boundary layer. Among the following options, select the correct relation for the development of the momentum thickness  with distance x from the leading edge along the length of the plate.

Strength of Materials & Elasticity

In a two-dimensional potential flow, the doublet is a limit of the superposition of

Atmospheric Flight Mechanics

An ideal glider has drag characteristics given by 0D D D i C C C=+ , where 2 DLi C KC= is the induced drag coefficient, LC is the lift coefficient, and K is a constant. For maximum range of the glider, the ratio 0DD i CC is

Strength of Materials & Elasticity

The figures shown in the options are schematics of airfoil shapes (not to scale). For a civilian transport aircraft designed for a cruise Mach number of 0.8, which among them is aerodynamically best suited as a wing section?

Static Stability & Control

For a longitudinally statically stable aircraft, which one of the following represents the relationship between the coefficient of pitching moment about the center of gravity mcgC and absolute angle of attack a ? (Note: nose-up moment is positive.)

Compressors and Turbines

In a single-spool aviation turbojet engine, which of the following is the correct relationship between the total work output WT of a^2-stage axial turbine and the total work required WC by a 6-stage axial compressor, neglecting losses?

Strength of Materials & Elasticity

For a stage of a 50% reaction ideal axial flow compressor (symmetrical blading), select the correct statement from the options given.

Rocket Propulsion

An aircraft is cruising with a forward speed aV and the jet exhaust speed relative to the engine at the exit is jV . If 2,ajVV = what is the propulsive efficiency?

Strength of Materials & Elasticity

Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical V-n diagram. For one of these flight loading conditions, it is observed that (i) the compressive bending stresses have a maximum value in the bottom aft region (see figure) of the wing cross-section; and (ii) the tensile bending stresses are maximum in the upper forward region (see figure) of the wing cross-section. For the preceding observations, select the corresponding flight loading condition from the options given.

Strength of Materials & Elasticity

Which one of the following figures represents the qualitative variation of absolute deceleration dV dt with altitude h (measured from the mean sea level) for a space vehicle undergoing a ballistic entry into the Earth's atmosphere?

Structural Dynamics & Aeroelasticity

Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system?

Compressors and Turbines

Which of the following statement(s) is/are true about the state of stress in a plane?

Compressors and Turbines

Which of the following statement(s) is/are true about the ribs of an airplane wing with semi-monocoque construction?

Inlets, Combustors & Nozzles

From the options given, select all that are true for turbofan engines with afterburners.

Strength of Materials & Elasticity

Which of the following statement(s) is/are true with respect to eigenvalues and eigenvectors of a matrix?

Rocket Propulsion

For studying wing vibrations, a wing of mass M and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness k and a torsional spring of equivalent stiffness k as shown in the figure. The centre of gravity (CG) of the wing idealized as an airfoil is marked in the figure. The number of degree(s) of freedom for this idealized wing vibration model is _________. (Answer in integer)

Strength of Materials & Elasticity

The system of equations 20 2 4 0 0 x y z x y z x y z - + = + - = - + = has a non-trivial solution for  = ______. (Answer in integer)

Strength of Materials & Elasticity

An airplane weighing 40 kN is landing on a horizontal runway during which it is retarded by an arresting cable mechanism. The tension in the arresting cable at a given instant, as shown in the figure, is 100 kN. Assuming that the thrust from the engine continues to balance airplane drag, the magnitude of horizontal load factor is ________. (round off to one decimal place)

Thin-Walled Structures

The ratio of the speed of sound in H^2 (molecular weight 2 kg/kmol) to that in N^2 (molecular weight 28 kg/kmol) at temperature 300 K and pressure 2 bar is ____. (round off to two decimal places)

Structural Dynamics & Aeroelasticity

Airplane A and Airplane B are cruising at altitudes of 2 km and 4 km, respectively. The free stream density and static pressure at altitude 2 km are 1.01 kg/m3 and 79.50 kPa, respectively, and at altitude 4 km, they are 0.82 kg/m3 and 61.70 kPa, respectively. The differential pressure reading from the pitot-static tubes is 3 kPa for both the airplanes. Assuming incompressible flow, the ratio of cruise speeds of Airplane A to Airplane B is ______. (round off to two decimal places)

Rocket Propulsion

A supersonic vehicle powered by a ramjet engine is cruising at a speed of 1000 m/s. The ramjet engine burns hydrogen in a subsonic combustor to produce thrust. The heat of combustion for hydrogen is 120 MJ/kg. The overall efficiency of the engine o , defined as the ratio of propulsive power to the total heat release in the combustor, is 40%. Taking acceleration due to gravity 0 10g = m/s^2, the specific impulse of the engine is _____________ seconds. (round off to the nearest integer).

Linear Algebra

Given the function ( ) ( 3)( 2)y x x x= + - , for 44 x-   . What is the value of x at which the function has a minimum?

Strength of Materials & Elasticity

A supersonic aircraft has an air intake ramp that can be rotated about the leading edge O such that the shock from the leading edge meets the cowl lip as shown in the figure. Select all the correct statement(s) as per oblique shock theory when the flight Mach number M is increased.

Differential Equations

Two missiles A and B powered by solid rocket motors have identical specific impulse, liftoff mass of 5600 kg each, and burn durations of 30At = s and 70Bt = s, respectively. The propellant mass flow rates, Am and Bm , for missiles A and B, respectively, are given by 120 kg/s, 0 30 70 kg/s, 0 70 A B t t m m =   =   Neglecting gravity and aerodynamic forces, the relationship between the final velocities AV and BV of missiles A and B, respectively, is given by

Differential Equations

A perfect gas stored in a large reservoir exhausts into the atmosphere through a convergent duct. The reservoir pressure is P0 and temperature is T0. The jet emerges from the nozzle at choked conditions with average velocity u, Mach number M, pressure p, temperature T, and density  . If the reservoir pressure is increased, then

Strength of Materials & Elasticity

Consider a general aviation airplane with weight 10 kN and a wing planform area of 15 m^2. The drag coefficient of the airplane is given as 0 2 D D LC C KC=+ with 0 0.025DC = and 0.05K = . For level flight at an altitude where the density is 0.60 kg/m3 and thrust 1 kN, the maximum cruise speed is (rounded off to the nearest integer)

Inlets, Combustors & Nozzles

A scramjet engine features an intake, isolator, combustor, and a nozzle, as shown in the schematic. Station 3 indicates the combustor entry point. Assume stagnation enthalpy to be constant between Stations 1 and 3, and air to be a calorically perfect gas with specific heat ratio γ. Select the correct expression for Mach number M3 at the inlet to the combustor from the options given.

Strength of Materials & Elasticity

Consider the equation sindy ay xdx += , where a and ω are constants. Given 1 at 0yx== , select all correct statement(s) from the following as x → .

Strength of Materials & Elasticity

Given the vectors ˆˆˆ9 5 2 ˆˆˆ11 4 ˆˆˆ7 14 3 A i j k B i j k C i j k = - + = + + = - + - which of the following statement(s) is/are TRUE?

Strength of Materials & Elasticity

Consider a one-dimensional inviscid supersonic flow in a diverging duct with heat addition (Qin) as shown. Which of the following statement(s) is/are always TRUE?

Strength of Materials & Elasticity

Consider the International Standard Atmosphere (ISA) with h being the geopotential altitude (in km) and dT dh being the temperature gradient (in K/m). Which of the following combination(s) of , dTh dh   is/are as per ISA?

Strength of Materials & Elasticity

For an airfoil, which of the relations given about the critical Mach number crM and drag divergence Mach number ddM is/are correct?

Strength of Materials & Elasticity

Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

Strength of Materials & Elasticity

The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is 0.5 . For the shaft reacting to an applied torque, the ratio of the maximum shear stress  to the maximum shear stress thin wall - obtained using the thin-wall approximation is . (round off to one decimal place)

Strength of Materials & Elasticity

A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

Strength of Materials & Elasticity

A cantilever beam of length 2a is loaded at the tip with force F as shown in the figure. The beam is supported in the middle by a roller with a pin. The magnitude of moment reaction at the built -in end of the beam is  Fa, where  is ______ . (round off to one decimal place)

Structural Dynamics & Aeroelasticity

A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time 2 dT , where dT is the period of the damped vibration) , the amplitud e of the displacement is ______ cm. (round off to two decimal place)

Thin-Walled Structures

The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load ys applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

Compressors and Turbines

Consider a thin-walled cylindrical pressure vessel made of an alloy with yield strength of 300 MPa. The vessel has end caps to contain the pressure. The ratio of radius of the vessel to its wall thickness is 100. As per the von Mises yield criterion, the internal pressure that would cause the failure of the vessel is _____ MPa. (round off to two decimal places)

Compressors and Turbines

Consider the differential equation 2 2 2 4 2 0d y dyx x ydx dx+ + = for 1x  with initial conditions 0y = , 1dy dx = at 1x = . The value of y at 2x = is ____ . (round off to two decimal places)

Inlets, Combustors & Nozzles

The operating characteristics of a pump were measured to be 2 PCa = , where power coefficient 35P PC D= ,  is the flow coefficient, a is a constant, D is a length scale,  is the rotation rate,  is fluid density, and P is the power required. The flow coefficient is a dimensionless volume flow rate scaled with  and D . Assuming that the flow rate remains the same, if the rotation rate is increased to 1.25 , the power changes to P . The value of  is ________ . (round off to two decimal places)

Compressors and Turbines

A thin cambered airfoil has lift coefficient 0lc = at an angle of attack o1.1 =- . Assuming that stall occurs at much larger  , the lc at o4 = is _______. (round off to two decimal places)

Inlets, Combustors & Nozzles

In a potential flow, a uniform stream of strength U directed along the x-axis and four line sources (2-dimensional) of strengths , , ,2 3 4 5    -- are placed along the x-axis at x = 0, 1, 2 and 3, respectively. The strength of an additional line source to be placed at 4x = such that a closed streamline encircles all five sources is _____. (round off to two decimal places).

Rocket Propulsion

Enstrophy is defined as the square of the magnitude of vorticity. For the three-dimensional velocity field ( ) ˆˆˆ(4 1.5 2.5 ) (1.5 1.5 ) 0.7V x y z i x y j xy k= - + + - + , the enstrophy at location (1, 1, 1) is ________ . (round off to two decimal places)

Compressors and Turbines

An airplane with wing planform area of 20 m2 and weight 8 kN is flying straight and level with a speed of 100 m/s. The total drag coefficient is 0.026 and the air density is 0.7 kg/m^3. The total thrust required to introduce a steady climb angle of 0.1 radians is ____ N. (round off to the nearest integer)

Strength of Materials & Elasticity

The maximum permissible load factor and the maximum lift force coefficient for an airplane is 7 and 2, respectively. For a wing loading of 6500 N/m2 and air density 1.23 kg/m^3, the speed yielding the highest possible turn rate in the vertical plane is ___________ m/s. (round off to the nearest integer)

Compressors and Turbines

A gas turbine combustor is burning methane and air at an equivalence ratio 0.5 = , where   stoich FA FA = and [] stoichFA is the ratio of mass flow rate of fuel to the mass flow rate of air at stoichiometry. If the air flow rate is 20airm = kg/s then the mass flow rate of methane is ______ kg/s. (round off to two decimal places)

Thin-Walled Structures

The universal gravitational constant is 116.67 10 - Nm2/kg2. For a planet of mass 236.4169 10 kg and radius 3390 km, the escape velocity is _____ km/s. (round off to one decimal place). Q. 63 A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is 245.98 10 kg and the universal gravitational constant is 116.67 10 - Nm2/kg2. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer)

Space Dynamics & Orbital Mechanics

A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is $5.98 \times 10^{24}$ kg and the universal gravitational constant is $6.67 \times 10^{-11}$ N m$^2$/kg$^2$. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer)

Aerospace Materials & Fatigue

A centrifugal air compressor has inlet root diameter of 0.25 m and the outlet diameter of the impeller is 0.6 m. The pressure ratio is 5.0. The air at the inlet of the rotor is at 1 atm and 25oC. The polytropic efficiency is 0.8 and slip factor is 0.92. Use 1.004pC = kJ/kg-K and 1.4 = . The impeller speed in revolutions per minute (RPM) is _________. (round off to the nearest integer)

Rocket Propulsion

Consider a cryogenic liquid rocket engine using an expander cycle with liquid hydrogen and liquid oxygen as the two propellants. The mass flow rate of hydrogen 2Hm into the combustion chamber is 32 kg/s , and the mass flow rate of oxygen 2Om into the chamber is such that 22 8HOmm = . The combustion of hydrogen and oxygen is at stoichiometry. Assuming that the rate of the forward reaction is much larger than that of the reverse reaction, the rate of formation of H2O is ________ kmol/s. (round off to the nearest integer) END OF QUESTION PAPER