GATE AE 2017 Question Paper & Solutions

Verbal Aptitude

Question Number : 1 Correct: 1 Wrong: -0.33 Given the vectors 01 = 1 + 31; 22 = 21 - 4] + 3k, the vector Uz that is perpendicular to both vi and Vz is given by:

Verbal Aptitude

Question Number: 4 Correct: 1 Wrong: 0.33 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

Question Number : 5 Correct: 1 Wrong : 0.33 3-point Gaussian integration formula is given by: I, f(x)dx ~ 2% A, f(x) with x3 = 0,72 = -x3 = - /3: A, = ,A2 = Ag = $ This formula exactly integrates

Analytical & Spatial Aptitude

f (x) = 5 - x? (B) f(x) = 2 + 3x + 6x4 (C) f(x) = 13 + 6x3 + x6 (D) f(x) = e-x2 Question Number : 6 Correct: 1 Wrong : -0.33 Which one of the following statements is NOT true

Analytical & Spatial Aptitude

(B) The pitching moment of any airfoil at any angle of attack is always zero at the aerodynamic center (C) The center of pressure and aerodynamic center coincide for a symmetric airfoil (D) The pitching moment about the aerodynamic center, for any airfoil, does not vary with angle of attack Question Number : 7 Correct: 1 Wrong : 0.33 Which one of the following statements is NOT true

Verbal 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

(B) Flow is supersonic and Ma > MB (C) Flow is subsonic and Ma > MB (D) Flow is supersonic and Ma < MB Question Number : 10 Correct: 1 Wrong: 0.33 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

(D) đCm = 0.0 aCL Question Number : 11 Correct: 1 Wrong: 0.33 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.

Verbal Aptitude

Question Number : 12 Correct: 1 Wrong : -0.33 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

will always be negative (B) will always be positive (C) will always be zero (D) can have any value depending on the location of the center of gravity of the aircraft Question Number : 13 Correct: 1 Wrong : 0.33 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?

Linear Algebra

(1) and (111) (B) (1) and (iv) (C) (ii) and (iii) (D) (11) and (iv) Question Number : 16 Correct: 1 Wrong: 0.33 Among the following engines, which one is expected to have the maximum Specific Impulse?

Calculus

Compressor Surge (C) Choking (B) Rotating Stall (D) Optimum Design Pressure Ratio Question Number : 18 Correct: 1 Wrong: 0.33 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?

Differential Equations

Question Number : 19 Correct: 1 Wrong : 0.33 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

Numerical Methods

Increases (B) Remains constant (C) Decreases (D) First increases and then decreases Question Number : 20 Correct: 1 Wrong : -0.33 Which of the following statements about the neutral axis of a beam with unsymmetrical cross section is true:

Basic Fluid Mechanics

(D) The product of second moment of area about the neutral axis and the normal stress about the neutral axis are always zero. Question Number : 21 Correct: 1 Wrong : -0.33 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

Airfoil & Wing Theory

Question Number : 23 Correct: 1 Wrong: -0.33 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:

Compressible Flow & Shocks

decimal places). Question Number : 25 Correct: 1 Wrong : -0.33 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.

Compressible Flow & Shocks

(D) P, Q and R Question Number : 26 Correct: 2 Wrong: -0.66 (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}:

Wind Tunnel Testing & Instrumentation

Question Number : 27 Correct: 2 Wrong: -0.66 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}:

Atmospheric Flight Mechanics

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

Question Number : 30 Correct: 2 Wrong : -0.66 The equation x 2 + 5x + 4y = 0 has a solution y (x) that is:

Static Stability & Control

Question Number : 39 Correct: 2 Wrong: -0.66 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:

Dynamic Stability

_ (in three decimal places). Question Number : 42 Correct: 2 Wrong : -0.66 The roots obtained by solving longitudinal characteristic equations of motion for a statically stable aircraft are given below: 21.2 = N3.4= -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

Space Dynamics & Orbital Mechanics

characteristics: CLo=0.20, and Cmac, wing = -0.02. The numerical value of Cmow (contribution of the wing to Cmo) about the CG of the aircraft is _ (in two decimal places). Question Number : 45 Correct: 2 Wrong : -0.66 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?

Thermodynamic Cycles of Gas Turbines

Question Number : 56 Correct: 1 Wrong : -0.33 The ninth and the tenth of this month are Monday and Tuesday

Thermodynamic Cycles of Gas Turbines

figuratively (B) retrospectively (C) respectively (D) rightfully Question Number : 57 Correct: 1 Wrong : -0.33 It is

Inlets, Combustors & Nozzles

the last year's. (C) easier, from (D) easiest, from Question Number : 58 Correct: 1 Wrong : -0.33 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?

Compressors and Turbines

(B) Only P's drink and S's age (C) Only S's age (D) Only P's drink. Q's drink and S's age Question Number : 59 Correct: 1 Wrong : -0.33 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

Question Number : 60 Correct: 1 Wrong : 0.33 500 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

(B) Matters are recorded with an impartial perspective. (C) An intimate association offers an impartial perspective. (D) Actors are typically associated with the impartial recording of matters. Question Number : 62 Correct: 2 Wrong: 0.66 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

X is the mother-in-law of R (B) P and R are not married to each other (C) Pis a son of X and Y (D) Q cannot be married to R Question Number : 63 Correct: 2 Wrong : 0.66 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?

Aerospace Materials & Fatigue

An aerospace system operating under standard sea level conditions is governed by Aerospace Materials & Fatigue (Fatigue Crack Growth & S-N Curves). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Linear Algebra

An aerospace system operating under standard sea level conditions is governed by Linear Algebra (Systems of Linear Equations). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Calculus

An aerospace system operating under standard sea level conditions is governed by Calculus (Multiple Integrals & Vector Calculus). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Differential Equations

An aerospace system operating under standard sea level conditions is governed by Differential Equations (Higher Order Linear ODEs with Constant Coefficients). Compute the required parameter in standard SI units (rounded off to the acceptable range).

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

An aerospace system operating under standard sea level conditions is governed by Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Basic Fluid Mechanics

An aerospace system operating under standard sea level conditions is governed by Basic Fluid Mechanics (Viscous Flow & Boundary Layer Equations). Compute the required parameter in standard SI units (rounded off to the acceptable range).

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

An aerospace system operating under standard sea level conditions is governed by Airfoil & Wing Theory (Finite Wing Theory & Induced Drag). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Compressible Flow & Shocks

An aerospace system operating under standard sea level conditions is governed by Compressible Flow & Shocks (Rayleigh & Fanno Flow). Compute the required parameter in standard SI units (rounded off to the acceptable range).

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

An aerospace system operating under standard sea level conditions is governed by Airfoil & Wing Theory (High-Lift Devices & Flaps). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Atmospheric Flight Mechanics

An aerospace system operating under standard sea level conditions is governed by Atmospheric Flight Mechanics (Drag Polar & Aircraft Performance Equations). Compute the required parameter in standard SI units (rounded off to the acceptable range).

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

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

An aerospace system operating under standard sea level conditions is governed by Dynamic Stability (Dutch Roll, Spiral & Roll Subsidence Modes). Compute the required parameter in standard SI units (rounded off to the acceptable range).

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

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

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

An aerospace system operating under standard sea level conditions is governed by Thermodynamic Cycles of Gas Turbines (Thrust Equations & Specific Fuel Consumption). 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 (Convergent & Convergent-Divergent (C-D) Nozzles). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Compressors and Turbines

In an aerospace engineering analysis of Compressors and Turbines (Centrifugal Compressors), 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 (Combustor Design & Flame Stabilization), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Rocket Propulsion

In an aerospace engineering analysis of Rocket Propulsion (Solid, Liquid & Hybrid Rocket Engines), 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 Gas Turbines & Blade Cooling), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Strength of Materials & Elasticity

In an aerospace engineering analysis of Strength of Materials & Elasticity (Euler Buckling of Columns & Energy Methods), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thin-Walled Structures

In an aerospace engineering analysis of Thin-Walled Structures (Torsion of Multi-Cell Thin-Walled Tubes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thin-Walled Structures

In an aerospace engineering analysis of Thin-Walled Structures (Tension Field Beams & Wagner Beams), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Structural Dynamics & Aeroelasticity

In an aerospace engineering analysis of Structural Dynamics & Aeroelasticity (Free & Forced Vibrations of Continuous Beams), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Aerospace Materials & Fatigue

In an aerospace engineering analysis of Aerospace Materials & Fatigue (Aluminum, Titanium & Aerospace Alloys), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Aerospace Materials & Fatigue

In an aerospace engineering analysis of Aerospace Materials & Fatigue (Damage Tolerance & Non-Destructive Testing), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?