GATE AE 2017 Question Paper & Solutions

Quantitative Aptitude

Given the vectors 01 = 1 + 31; 22 = 21 - 4] + 3k, the vector Uz that is perpendicular to both vi and Vz is given by:

Quantitative Aptitude

The eigenvalues An and eigenfunctions Un (x) of the Sturm-Liouville problem d'y dx? - + k7 2y = 0, 0 < x < 1; y(0) = 0, y(1) = 0 are given by:

Quantitative Aptitude

The 3-point Gaussian integration formula is given by: $\int_{-1}^{1} f(x)\,dx \approx \sum_{i=1}^3 A_i f(x_i)$ with $x_1 = 0, x_2 = -x_3 = -\sqrt{3/5}$, and $A_1 = \frac{8}{9}, A_2 = A_3 = \frac{5}{9}$. This formula exactly integrates:

Quantitative Aptitude

Which one of the following statements is NOT true

Quantitative Aptitude

Which one of the following statements is NOT true

Quantitative Aptitude

Correct: 1 Wrong : -0.33 Consider a steady one dimensional flow of a perfect gas with heat transfer in a duct. The T-s diagram (shown below) shows both the static and the stagnation conditions at two locations. A and B, in the duct. At and By denote stagnation conditions for states A and B, respectively. It is known that (AT)a = (AT)B. Ma and Me are the Mach numbers of the flow at locations A and B. T B Which of the following statements is true about the flow.

Quantitative Aptitude

To ensure only the longitudinal static stability (and not the condition for equilibrium) of a low speed aircraft, the aircraft components must be designed to satisfy which one of the following conditions:

Quantitative Aptitude

Which of the following statements) is / are true about the shear centre of a cross-section: P: It is that point in the cross-section through which shear loads produce no twisting. Q: This point is also the centre of twist of sections subjected to pure torsion. R: The normal stress at this point is always zero.

Quantitative Aptitude

Let Nm and No be respectively the non-dimensional locations of the stick-fixed maneuver point and stick-fixed neutral point of a low speed conventional aircraft. These distances are measured with respect to the nose of the fuselage. The numerical value of Na-No

Analytical & Spatial Aptitude

The phenomenon of rudder lock in conventional low speed aircraft is primarily due to

Linear Algebra

Expansion with finite pressure difference with the surrounding. (i1) Compression with infinitesimal pressure difference with the surrounding. (iii) Heat transfer with finite temperature difference with the reservoir. (IV) Heat transfer with infinitesimal temperature difference with the reservoir. Out of these which processes are reversible?

Rocket Propulsion

Among the following engines, which one is expected to have the maximum Specific Impulse?

Basic Fluid Mechanics

For a turbine stage, which one of the following losses occurs due to the turning of the wall boundary layer through an angle due to curved surface?

Inlets, Combustors & Nozzles

In the vane-less space between the impeller and the diffuser vanes in a Centrifugal Compressor, the angular momentum varies in the following manner in the radial direction

Strength of Materials & Elasticity

Which of the following statements about the neutral axis of a beam with unsymmetrical cross section is true:

Strength of Materials & Elasticity

Assuming that the aircraft is flying straight, the top spar cap / flange of a wing is most likely to fail 1n: Top spar cap / flange

Atmospheric Flight Mechanics

An aircraft landing gear can be idealized as a single degree of freedom spring-mass-damper system. The desirable damping characteristics of such a system is:

Strength of Materials & Elasticity

Which of the following statements about the compatibility equations are true: P. Strain compatibility equations must be satisfied in the solution of three-dimensional problems in elasticity. Q. Six strains are defined in terms of three displacement functions and can have arbitrary values. R. Compatibility equations are an expression of the continuity of displacements.

Linear Algebra

(4) Matrix A = and vector (6) = (5) are given. If vector {x) is the solution to the system of equations [A]{x} = {b}, which of the following is true for {x}:

Linear Algebra

Let matrix [A] = [a^2] Then for any non-trivial vector (x) = (xz) which of the following is true for the value of K = {x} [A]{x}:

Calculus

dy de + 6y = f(t); y y(0) = 2,1 = 1 dt t=0 If Y(s) = Jo° y (t)e-st dt and F(s) = Jo° f(t)e-st dt are the Laplace transforms of y(t) and f(t) respectively, then Y (s) is given by: F(s)

Atmospheric Flight Mechanics

The equation x^2 + 5x + 4y = 0 has a solution y (x) that is:

Static Stability & Control

A pilot was flying a single engine propeller aircraft and maintaining a steady level flight at a lift coefficient, Cr=0.5 at an altitude of 500 m. Due to some emergency, at the same altitude (500 m), the pilot had to fully deploy the landing gear. If the pilot wants to maintain steady level flight at the same C1=0.5 and at the same altitude, which of the following control actions should the pilot undertake:

Structural Dynamics & Aeroelasticity

The roots obtained by solving longitudinal characteristic equations of motion for a statically stable aircraft are given below: 21.2 = N^3.4= -2.00=2.50i, where i = V-1 The undamped short-period longitudinal natural frequency (radians/sec) and damping ratio, in that order, are close to

Inlets, Combustors & Nozzles

In a combustor, gaseous Octane (CsHs) and air are to be burned in stoichiometric proportions. If the required flowrate of air is 1 kg/s, what should be the corresponding flow rate of Octane?

Compressors and Turbines

The ninth and the tenth of this month are Monday and Tuesday

Compressors and Turbines

It is _______ to read this year's textbook than the last year's. Choose the correct option to fill in the blanks:

Inlets, Combustors & Nozzles

A rule states that in order to drink beer. one must be over 18 years old. In a bar, there are 4 people. P is 16 years old. Q is 25 years old. R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

Basic Fluid Mechanics

Fatima starts from point P. goes North for 3 km. and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

Rocket Propulsion

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186). Mathematics (295). Chemistry and Physics (83). Chemistry and Mathematics (217). and Physics and Mathematics (63). How many students are taking all 3 subjects?

Strength of Materials & Elasticity

Correct: 2 Wrong: -0.66 "If you are looking for a history of India, or for an account of the rise and fall of the British Raj. or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections. and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters." Which of the following statements best reflects the author's opinion?

Strength of Materials & Elasticity

Each of P. Q. R, S, W. X. Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

Thin-Walled Structures

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

Structural Dynamics & Aeroelasticity

450 515 550 500 500 475 2 km Which of the following is the steepest path leaving from P?

Compressible Flow & Shocks

A strong normal shock wave, with a pressure ratio of 29 across it, is traveling into still air ($T_1 = 300$ K, $\gamma = 1.4$). The Mach number of the shock wave is _________ (round off to 2 decimal places).

Inlets, Combustors & Nozzles

Water exits from a nozzle of diameter 50 mm into atmospheric pressure at a velocity of 20 m/s. The jet strikes a flat vertical plate held perpendicular to the jet. If the density of water is 1000 kg/m$^3$, the horizontal force (in N) required to hold the plate stationary is _________ (round off to the nearest integer).

Basic Fluid Mechanics

A football, meant to be thrown at 100 km/h in sea level air ($\rho = 1.22$ kg/m$^3$, $\mu = 1.8 \times 10^{-5}$ Pa-s), is tested in a water tunnel with a 1:2 scale model. If the kinematic viscosity of water is $1.0 \times 10^{-6}$ m$^2$/s, the water flow speed (in m/s) required for dynamic similarity is _________ (round off to 1 decimal place).

Airfoil & Wing Theory

An aircraft model was tested in a low speed wind-tunnel (Reynolds number based on mean chord $Re = 10^6$). The lift curve slope of the wing is $C_{L\alpha} = 4.5$ rad$^{-1}$. If the aspect ratio of the wing is 6 and Oswald efficiency factor is 0.9, the profile drag coefficient $C_{D0}$ is 0.015. At $C_L = 0.6$, the total drag coefficient $C_D$ of the wing is _________ (round off to 3 decimal places).

Static Stability & Control

A pilot was flying a single engine propeller aircraft and maintained steady level flight at trim. Due to torque reaction and slipstream rotation from a clockwise rotating propeller (viewed from the cockpit), the airplane tends to naturally:

Atmospheric Flight Mechanics

A conventional low speed aircraft had the following aerodynamic characteristics: wing area $S = 20$ m$^2$, weight $W = 30000$ N, and zero-lift drag coefficient $C_{D0} = 0.02$. At sea level with $\rho = 1.225$ kg/m$^3$, if the thrust required at minimum drag speed is 2400 N, the maximum lift-to-drag ratio $(L/D)_{\max}$ of the aircraft is _________ (round off to 1 decimal place).

Strength of Materials & Elasticity

A batch of aluminium alloy yields in uniaxial tension at the stress $\sigma_y = 330$ MPa. Using the von Mises yield criterion, the yield stress in pure shear (in MPa) is _________ (round off to 1 decimal place).

Dynamic Stability

The roots obtained by solving the longitudinal characteristic equation of an airplane are given by $\lambda_{1,2} = -0.005 \pm 0.05i$ and $\lambda_{3,4} = -1.2 \pm 2.5i$. These two pairs of complex conjugate roots correspond respectively to:

Atmospheric Flight Mechanics

An aircraft is to be designed to ensure that it has enough excess power for climb. If the engine produces 500 kW of power and the power required for steady level flight at speed $V$ is 350 kW for an aircraft weight of 12.5 kN, the maximum rate of climb (in m/s) at this speed is _________ (round off to 1 decimal place).

Airfoil & Wing Theory

A conventional aircraft was analyzed to estimate the contribution of the vertical tail to the directional stability derivative $C_{n\beta}$. The vertical tail area is 2 m$^2$, moment arm is 5 m, wing area is 20 m$^2$, and wing span is 10 m. If the lift curve slope of the vertical tail is 4.0 rad$^{-1}$ and tail dynamic pressure ratio is 0.9, the contribution of the vertical tail $C_{n\beta, v}$ is _________ rad$^{-1}$ (round off to 2 decimal places).

Inlets, Combustors & Nozzles

In a combustor, gaseous Octane ($\text{C}_8\text{H}_{18}$) and air are to be burned in a stoichiometric ratio. Assuming air contains 21% $\text{O}_2$ and 79% $\text{N}_2$ by volume, the stoichiometric fuel-to-air mass ratio $(f/a)_{stoich}$ is approximately:

Inlets, Combustors & Nozzles

The given diagram represents the velocity triangle of an axial compressor stage with blade speed $U = 200$ m/s, axial velocity $V_z = 165$ m/s, relative inlet angle $\beta_1 = 45^\circ$, and relative exit angle $\beta_2 = 11^\circ$. The specific work input (in kJ/kg) to the air is _________ (round off to 1 decimal place).

Inlets, Combustors & Nozzles

An aircraft with a turbojet engine, having an inlet area of 1 m$^2$, is flying at a speed of 250 m/s at an altitude where air density is 0.4 kg/m$^3$. The mass flow rate of fuel added is negligible. If the jet exhaust speed is 600 m/s relative to the aircraft, the net thrust (in kN) produced by the engine is _________ (round off to the nearest integer).

Compressors and Turbines

Air, at 450 K stagnation temperature and at a rate of 50 kg/s, enters an axial turbine stage and leaves at 350 K stagnation temperature. Taking specific heat at constant pressure $C_p = 1005$ J/(kg K), the power output (in MW) from the turbine is _________ (round off to 2 decimal places).

Rocket Propulsion

A single stage chemical rocket, having an initial mass of 10,000 kg and structural mass (burnout mass) of 2000 kg, uses a propellant with an effective exhaust velocity of 2500 m/s. The maximum velocity increment $\Delta V$ (in km/s) of the rocket in gravity-free, vacuum space is _________ (round off to 2 decimal places).

Compressors and Turbines

A centrifugal compressor requires 1800 kW of power to compress 10 kg/s of air entering at 300 K stagnation temperature. Taking specific heat $C_p = 1000$ J/(kg K), the stagnation temperature (in K) of air leaving the compressor is _________ K.

Strength of Materials & Elasticity

An aircraft wing is idealized as a cantilever beam of constant width and length $L = 5$ m, carrying a uniformly distributed aerodynamic lift load of $w = 2$ kN/m. If the flexural rigidity of the wing box is $EI = 10^7$ N-m$^2$, the tip deflection (in mm) of the wing is _________ (round off to the nearest integer).

Strength of Materials & Elasticity

For the state of plane stress shown in the figure with $\sigma_x = 80$ MPa, $\sigma_y = -20$ MPa, and $\tau_{xy} = 40$ MPa, the minimum principal stress (in MPa) is _________ (round off to the nearest integer).

Thin-Walled Structures

The maximum normal stress in MN/m$^2$ for the thin-walled beam of square cross-section (side $b = 100$ mm, thickness $t = 2$ mm) under an applied bending moment of $M = 2$ kN-m is _________ (round off to the nearest integer).

Thin-Walled Structures

The idealized cross section of a thin-walled wing box structure has two stringers carrying boom areas $B = 100$ mm$^2$ separated by height $h = 200$ mm and width $w = 400$ mm. If a vertical shear load $V_y = 10$ kN acts at the shear center, the shear flow (in N/mm) in the vertical webs is _________ (round off to the nearest integer).

Structural Dynamics & Aeroelasticity

The natural frequency of the system suspended by two identical vertical springs each of stiffness $k = 1000$ N/m carrying a mass $m = 2$ kg in parallel is _________ rad/s (round off to 1 decimal place).

Quantitative Aptitude

The ninth and the tenth of this month are Monday and Tuesday _________.

Quantitative Aptitude

It is _________ to read this year's textbook than to read last year's textbook.

Quantitative Aptitude

A rule states that in order to drink beer, one must be over 18 years old. In a bar, four people are observed: P: drinking beer Q: drinking coke R: 16 years old S: 25 years old Which person(s) must be checked to confirm that the rule is not being violated?

Quantitative Aptitude

Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. The direct distance (in km) from point P to point Q is _________.

Quantitative Aptitude

500 students are taking one or more courses out of Chemistry, Physics, and Biology. 200 students are taking Chemistry, 220 are taking Physics, and 180 are taking Biology. 80 are taking Chemistry and Physics, 60 are taking Physics and Biology, and 50 are taking Chemistry and Biology. If 20 students are taking all three courses, how many students are taking exactly one course?

Verbal Aptitude

“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, you should look elsewhere. But if you want the story of how ordinary lives were affected by the events, then this book is for you.” Which one of the following statements can be inferred from the passage?

Quantitative Aptitude

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married. P and Q are married. R is the daughter of X. S is the sister of P. Which one of the following MUST be true?

Quantitative Aptitude

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women can build the same bridge in 3 weeks. How many men must be employed to build the bridge in 2 weeks with NO women working?

Quantitative Aptitude

The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is:

Quantitative Aptitude

A contour line joins locations having the same height above the mean sea level. Two contour lines representing heights of 500 m and 550 m are separated by a horizontal distance of 2 km. The average slope (gradient) of the terrain between these two contours is: