GATE AE 2019 Question Paper & Solutions

Verbal Aptitude

The fishermen, government. the flood victims owed their lives, were rewarded by the

Verbal Aptitude

Some students were not involved in the strike. If the above statement is true, which of the following conclusions is/are logically necessary? 1. Some who were involved in the strike were students. 2. No student was involved in the strike. 3. At least one student was involved in the strike. 4. Some who were not involved in the strike were students.

Quantitative Aptitude

The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is

Analytical & Spatial Aptitude

Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below: 1. No two odd or even numbers are next to each other. 2. The second number from the left is exactly half of the left-most number. 3. The middle number is exactly twice the right-most number. Which is the second number from the right?

Analytical & Spatial Aptitude

Until Iran came along, India had never been in kabaddi.

Verbal Aptitude

Q.6 Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates. Which one of the following statements can be inferred from the given passage?

Quantitative Aptitude

interest rates (C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes (D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India Q.7 In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?

Quantitative Aptitude

The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples. Which one of the following pairings is NOT correct?

Verbal Aptitude

Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is AM.

Analytical & Spatial Aptitude

GATE 2019 General Aptitude (GA) Set-8 Q.10 "I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community." Based on the paragraph above, the prestige of a head-hunter depended upon

Linear Algebra

The maximum value of the function f(x) = xe-* (where x is real) is

Linear Algebra

Vector b is obtained by rotating a = î + j by 90º about k, where i, j and k are unit vectors along the x, y and z axes, respectively. b is given by

Calculus

§ (4i - 37) Q.4 The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

Differential Equations

For a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

Numerical Methods

The Mach number increases and the static temperature decreases. (C) The Mach number decreases and the static temperature increases. (D) Both the Mach number and the static temperature decrease. Q.7 For a NACA2415 airfoil of chord length c, which of the following is true?

Basic Fluid Mechanics

Which of the following graphs represents the response of a dynamically unstable airplane? response

Airfoil & Wing Theory

The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

Compressible Flow & Shocks

GATE 2019 Aerospace Engineering Q.12 For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

Compressible Flow & Shocks

CPR of an axial compressor < CPR of centrifugal compressor. (C) CPR of an axial compressor = CPR of centrifugal compressor. (D) CPR of any value can be attained with either an axial or a centrifugal compressor. Q.13 For a beam subjected to a transverse shear load through its shear center,

Wind Tunnel Testing & Instrumentation

01 (see Figure 1). The resulting oblique shock with shock angle ß is then reflected from the top wall. For the reflected shock, the turn angle is 02 and the shock angle is Bz. increasing M M2 Figure 1 Figure 2 Use the weak shock solution from the e-ß-M plot shown in Figure 2 to choose the correct option from the following.

Atmospheric Flight Mechanics

Which of the following statements about adverse yaw of an airplane is/are correct? P. It is caused by flow separation resulting from large rudder deflection. Q. It is caused by dissimilar drag forces acting on the two halves of the wing resulting from aileron deflections of same magnitude. R. It can be eliminated by ensuring that the upward deflection of one aileron is greater than the downward deflection of the opposite aileron.

Atmospheric Flight Mechanics

In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine

Static Stability & Control

200 N P MUNT 100 Nm 0.5m 100 Nm 0.5m MARR

Calculus

A function $f(x)$ is defined by $f(x) = \frac{1}{2}(x + |x|)$. The value of $\int_{-1}^{1} f(x)\,dx$ is _________ (round off to 1 decimal place).

Calculus

The value of the following limit is _________ (round off to 2 decimal places): $\lim_{\theta \to 0} \frac{\theta - \sin\theta}{\theta^3}$

Wind Tunnel Testing & Instrumentation

To simulate the aerodynamic forces on a cylinder of 1 m diameter due to a uniform air flow of 1 m/s at standard temperature and pressure (STP), a scale model of 10 cm diameter is tested in a water tunnel at standard conditions. The required water flow velocity (in m/s) in the water tunnel for Reynolds number similarity is _________ (round off to the nearest integer). (Take $\nu_{air} = 1.5 \times 10^{-5}$ m$^2$/s and $\nu_{water} = 1.0 \times 10^{-6}$ m$^2$/s)

Airplane Performance

The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts from an altitude of 4 km above ground level, is _________ km (round off to the nearest integer).

Aircraft Equations of Motion

For an airplane flying in a vertical plane, the angle of attack is $3^\circ$, the horizontal and vertical components of velocity in wind axes are 300 km/h and 0 km/h, respectively. If the pitch angle is $9^\circ$, the climb angle of the airplane is _________ degrees (round off to the nearest integer).

Airspeed Measurement & Pitot-Static Tube

An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient static pressure are 1.2 kg/m$^3$ and $1.0 \times 10^5$ N/m$^2$, respectively. If the flow is incompressible, the equivalent air speed (in m/s) of the airplane is _________ (round off to 2 decimal places). (Take sea level standard air density $\rho_0 = 1.225$ kg/m$^3$)

Combustion Chambers

For the complete combustion of 1 mole of ethanol ($\text{C}_2\text{H}_5\text{OH}$), the required number of moles of oxygen is _________.

Thermodynamics of Aircraft Engines

One kg of diatomic gas is heated and its temperature increases from 100 K to 600 K. The energy added at constant pressure during this process is 500 kJ. The specific heat at constant volume for the gas is _________ kJ/(kg K) (round off to 2 decimal places).

Theory of Elasticity

The number of independent elastic constants for a homogeneous isotropic linear elastic material is _________.

Theory of Elasticity

A thin plate with Young's modulus 210 GPa and Poisson's ratio 0.3 is loaded under plane stress with $\sigma_x = 100$ MPa and $\sigma_y = -40$ MPa. The absolute value of the normal strain in the z-direction ($|\epsilon_z| \times 10^4$) is _________ (round off to 1 decimal place).

Theory of Elasticity

For the state of stress shown in the figure, the normal stress, $\sigma_n$, on a plane inclined at 45 degrees to the principal planes with $\sigma_1 = 300$ MPa and $\sigma_2 = 200$ MPa is _________ MPa (round off to the nearest integer).

Structural Dynamics & Aeroelasticity

In the spring-mass system, shown in the figure, mass $m = 3$ kg and the spring stiffness $k = 20$ kN/m. The natural frequency (in Hz) of the system is _________ (round off to the nearest integer).

Linear Algebra

The following system of equations: $2x + 3y + z = 5$ $x + y + z = 3$ $3x + 4y + 2z = 8$ (A) has no solution. (B) has a unique solution. (C) has three solutions. (D) has infinitely many solutions.

Compressible Flow & Shocks

A supersonic flow in a constant area duct at Mach number $M_1$ encounters a compression ramp of angle $\theta_1$ generating an oblique shock wave. Which of the following statements is TRUE across the shock wave?

Static Stability & Control

Which of the following statements about adverse yaw of an airplane is/are correct? P. It is caused by the difference in induced drag between the two wings when ailerons are deflected. Q. It causes the airplane to yaw in the direction of the roll. R. It can be counteracted using differential ailerons or Frise ailerons.

Thermodynamics of Aircraft Engines

In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. For a fixed turbine inlet temperature (TIT), how does this affect the turbine work output and the cycle thermal efficiency?

Bending & Shear of Beams

For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentrated bending moment of 100 N-m applied at mid-span, the vertical reaction at the left support is _________ N.

Calculus

For real $x$, the number of points of intersection between the curves $y = x$ and $y = \cos x$ is _________.

Linear Algebra

One of the eigenvalues of the matrix $M = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ is 1. The other eigenvalue is _________.

Differential Equations

The curve $y = f(x)$ is such that its slope is equal to $y^2$ for all real $x$. If the curve passes through $(1, -1)$, the value of $y$ at $x = 0$ is _________ (round off to 1 decimal place).

Potential Flow Theory

The inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius $R$ is given by potential flow theory. If the pressure coefficient at a point on the surface is $C_p = 0$, the angle $\theta$ (in degrees, with $0 \le \theta \le 90^\circ$) measured from the front stagnation point is _________ degrees.

Fluid Statics & Buoyancy

A cylindrical container of radius $R = 50$ cm is filled with water up to a height $h_0$. Upon rotating the cylinder about its central vertical axis at an angular speed $\omega = 10$ rad/s, the free surface depresses at the centre by _________ cm (take $g = 9.81$ m/s$^2$).

Potential Flow Theory

A two-dimensional, incompressible fluid flow is described by the stream function $\psi = x y^3$ m$^2$/s on the Cartesian plane. The magnitude of the velocity vector (in m/s) at the point $(x, y) = (1, 1)$ is _________ (round off to 1 decimal place).

Compressible Flow & Shocks

The static pressure ratio across a stationary normal shock is given by $\frac{P_2}{P_1} = 1 + \frac{2\gamma}{\gamma + 1}(M_1^2 - 1)$, where $M_1$ is the upstream Mach number and $\gamma = 1.4$. If the static pressure ratio across the shock is $\frac{P_2}{P_1} = 29.0$, the upstream Mach number $M_1$ is _________ (round off to 2 decimal places).

Airfoils & Wings

For a symmetric airfoil at an angle of attack of $10^\circ$, assuming thin airfoil theory, the magnitude of the section lift coefficient $C_l$ is _________ (round off to 2 decimal places).

Airfoils & Wings

The span-wise distribution of circulation over a finite wing of span $b = 10$ m is given by $\Gamma(y) = \Gamma_0 \sqrt{1 - (2y/b)^2}$. If $\Gamma_0 = 20$ m$^2$/s and the freestream velocity is 50 m/s at an air density of 1.2 kg/m$^3$, the induced drag (in N) on the wing is _________ (round off to 1 decimal place).

Maneuvers & Load Factors

The airplane shown in the figure starts executing a symmetric pull-up maneuver from steady level flight at $V = 100$ m/s. If the pull-up radius of curvature is $R = 500$ m and $g = 9.81$ m/s$^2$, the load factor $n$ experienced by the airplane is _________ (round off to 2 decimal places).

Airplane Performance

Consider an airplane with a weight of 8000 N, wing area of 16 m$^2$, wing zero-lift drag coefficient of $C_{D0} = 0.02$, Oswald efficiency factor $e = 0.8$, and wing aspect ratio $AR = 8$. At sea level with $\rho = 1.225$ kg/m$^3$, the maximum lift-to-drag ratio $(L/D)_{\max}$ divided by 10 is _________ (round off to 2 decimal places).

Space Dynamics & Orbital Mechanics

The product of earth's mass ($M$) and the universal gravitational constant ($G$) is $GM = 3.986 \times 10^{14}$ m$^3$/s$^2$. The circular orbital speed of a spacecraft at an altitude of 300 km above the Earth's surface (radius of Earth $R_E = 6370$ km) is _________ km/s (round off to 2 decimal places).

Take-Off & Landing

A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84 m$^2$. Assume that the lift coefficient at take-off is 1.2 and air density is 1.225 kg/m$^3$. The lift-off speed (in m/s) of the airplane multiplied by 100 is approximately _________ (round off to the nearest integer).

Static Stability & Control

The design of an airplane is modified to increase the vertical tail area by 20% and decrease the moment arm of the vertical tail by 20%. The ratio of the new directional stability derivative $C_{n\beta}$ (due to the vertical tail) to the original value is _________ (round off to 2 decimal places).

Rocket Propulsion

For a rocket engine, the velocity ratio $r$ is $V_a/V_e$, where $V_a$ is the vehicle velocity and $V_e$ is the exit velocity of the exhaust gases relative to the rocket. The value of $r$ at which the propulsive efficiency $\eta_p$ is maximum is _________.

Rocket Propulsion

The specific impulse of a rocket engine is 3000 N s/kg. The mass of the rocket at burnout is 1000 kg. If the velocity increment $\Delta V$ achieved during the burn is 1500 m/s in gravity-free, drag-free space, the initial mass of the rocket (in kg) divided by 1000 is _________ (round off to 2 decimal places).

Compressors & Turbines

The combustion products of a gas turbine engine can be assumed to be a calorically perfect gas with $\gamma = 1.33$ and $C_p = 1150$ J/(kg K). The total temperature and total pressure at the turbine inlet are 1400 K and 1000 kPa, respectively. If the expansion across the turbine has a total pressure ratio of 4.0, the total temperature (in K) drop across the turbine divided by 10 is _________ (round off to the nearest integer).

Compressors & Turbines

The figure shows the velocity triangles for an axial compressor stage. The axial velocity is constant through the stage at $C_a = 150$ m/s. The rotor blade speed is $U = 200$ m/s. If the rotor blade angles at inlet and exit are $\beta_1 = 45^\circ$ and $\beta_2 = 15^\circ$, the specific work input (in kJ/kg) to the compressor stage is _________ (round off to 2 decimal places).

Theory of Elasticity

As shown in the figure, a rigid slab CD of weight $W$ (distributed uniformly along its length) is hung from a ceiling using three vertical cables of identical length and cross-sectional area. The central cable is made of steel (Young's modulus = $3E$) and the other two outer cables are made of aluminium (Young's modulus = $E$). The percentage of the total weight taken by the central cable is _________ % (round off to the nearest integer).

Structural Stability & Buckling

All the bars in the given truss are elastic with Young's modulus 200 GPa, and have identical cross-sections with moment of inertia $I = 0.1$ cm$^4$. The lowest value of the load $P$ (in kN) at which the truss fails due to buckling of member BC (length $L = 10$ cm) is _________ kN (round off to the nearest integer).

Torsion of Circular & Thin-Walled Shafts

A solid circular shaft is designed to transmit a torque $T$ with a factor of safety of 2. It is proposed to replace the solid shaft by a hollow shaft of the same material and identical outer radius. If the inner radius is half the outer radius, the factor of safety for the hollow shaft is _________ (round off to 1 decimal place).

Theory of Elasticity

In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load (in N) along the z-direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is _________ N (round off to the nearest integer). (Take $AB = 0.55$ m, $BC = 0.50$ m)

Thin-Walled Structures

A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of $T = 1$ kN-m. The walls have uniform thickness $t = 1$ mm and shear modulus $G = 26$ GPa. Assume that the curved portion is semi-circular with radius $R = 50$ mm and straight length $L = 0.5$ m. The shear stress in the wall is _________ MPa (round off to 1 decimal place).

Structural Dynamics & Aeroelasticity

For a damped spring-mass system, mass $m = 10$ kg, stiffness $k = 10^3$ N/m, and damping coefficient $c = 20$ kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is _________ (round off to 1 decimal place).

Structural Dynamics & Aeroelasticity

For the system of springs and masses shown below, $k = 1250$ N/m and $m = 10$ kg. The highest natural frequency, $\omega$, of the system is _________ radians/s (round off to the nearest integer).