GATE AE 2011 Question Paper & Solutions

Verbal Aptitude

Consider x,y,z to be right-handed Cartesian coordinates. A vector function is defined as v = 3x i + 3xy j - yz^2 k. The curl of v is given by:

Verbal Aptitude

Which of the following functions is periodic?

Quantitative Aptitude

The function f(x1, x2, x3) = x1^2 + x2^2 + x3^2 - 2x1 - 4x2 - 6x3 + 14 has its minimum value at:

Analytical & Spatial Aptitude

Consider the function f(x1, x2) = x1^2 + 2x2^2 + e^(x1 - x2). The vector pointing in the direction of maximum increase of the function at (1, -1) is:

Analytical & Spatial Aptitude

Two simultaneous equations given by y = 1/2 + x and y = x - 1/2 have:

Verbal Aptitude

In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain-displacement equations and equations of equilibrium are, respectively:

Quantitative Aptitude

An Euler-Bernoulli beam in bending is assumed to satisfy:

Quantitative Aptitude

A statically indeterminate frame structure has:

Verbal Aptitude

The natural frequency of a spring-mass system of stiffness k and mass m is 10 rad/s. Another single degree of freedom system has spring stiffness 2k and mass 2m. Its natural frequency is:

Analytical & Spatial Aptitude

Consider a single degree of freedom spring-mass system of spring stiffness k1 and mass m which has a natural frequency of 10 rad/s. If another spring of stiffness k2 is connected in parallel, the frequency:

Linear Algebra

Consider a simply supported two-dimensional beam. If the beam is converted into a fixed-fixed beam, then the degree of static indeterminacy will:

Linear Algebra

Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies

Calculus

In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as

Differential Equations

In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as:

Numerical Methods

Lift on an aircraft climbing vertically up is:

Basic Fluid Mechanics

In an aerospace engineering analysis of Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Airfoil & Wing Theory

It is seen that the drag polar of a certain aerofoil is symmetric about the Cd axis. This drag polar could refer to

Compressible Flow & Shocks

It is seen that the drag polar of a certain aerofoil is symmetric about the C_d axis. This drag polar could refer to:

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Wind Tunnel Testing & Instrumentation

In an aerospace engineering analysis of Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

Consider a potential flow with free stream velocity V_inf, over a spinning circular cylinder of radius R and circulation Gamma. The lift per unit span is given by Kutta-Joukowski theorem as:

Atmospheric Flight Mechanics

A main objective of by-pass in a turbo-fan engine is to increase:

Static Stability & Control

Thermodynamic cycle on which the jet engine operates can be Q.24

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

Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young's modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span (L/2) at the center of the cross-section. Unde r the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is

Thermodynamic Cycles of Gas Turbines

P L L/2 2011 AEROSPACE ENGINEERING - AE AE Consider a beam in bending with a solid circular cross-section of 1 mm2, which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm2) is

Thermodynamic Cycles of Gas Turbines

A simp ly supported slender column of square cross section (width=depth= d) has to be designed such that it buckles at the same instant as it yields. Length of the column is given to be 1.57 m and it is made of a material whose Young's modulus is 200 GPa and yield stress is 240 MPa. The width, d, of the column (in cm) should be

Inlets, Combustors & Nozzles

A turbojet powered aircraft is flying at Mach nu mber 0.8 at an altitude of 10 km. The inlet and exit areas of the engine are 0.7 m 2 and 0.4 m 2 respectively. The exhaust gases have velocity of 500 m/s and pressure of 60 kPa. The free stream pressure , density and speed of sound are 26.5 kPa, 0.413 kg/m3 and 299.5 m/s respectively. The thrust of the engine (in kN) is

Compressors and Turbines

A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1 m2. The static pressure difference between th e settling chamber and the test section is 40 cm of water column. Assume , and . The speed of air in the test section (in m/s) is 2m/s 81 . 9g 3kg/m 2 . 1air 3kg/m 1000water

Rocket Propulsion

to Q.55 are multiple choice type. Consider the function . The Newton-Raphson iteration formula to find the root of the function starting from an initial guess at iteration k is ) sin( ) (x x x f  ) 0 (x (A) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (B) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx  

Strength of Materials & Elasticity

) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (D) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   Consider the matrix where a and b are real numbers. The two eigenvalues of this m atrix     2 2 b a 1 and 2 are real and distinct  2 1  when

Strength of Materials & Elasticity

Consider a thin symmetric aerofoil at an angle of attack alpha. According to thin aerofoil theory, the lift coefficient C_l is:

Thin-Walled Structures

4 (2 ) te t (D) 2 1 52( 2 2 )tet t  2011 AEROSPACE ENGINEERING - AE A jet engine is operating at a Mach number of 0.8 at an altitude of 10 km. The efficiency of the air intake is 0.8 and that of the compressor is 0.87. Th e total temperatures (in K) at the exits of the air intake and the compressor respectively are (Ambient pressure = 26.5 kPa; Ambient temperature = 223.3 K; Gas constant,  = 1.4; 8rcp )

Structural Dynamics & Aeroelasticity

The stall speed of an airplane in steady level flight at sea level is V_s0. At an altitude where the density ratio is sigma = 0.25, the true stall speed is:

Aerospace Materials & Fatigue

For an airplane in level turn at bank angle phi, the load factor n is given by:

Linear Algebra

Which of the following Airy's stress functions could satisfy the given boundary conditions, assuming constant values of xx = P, yy = Q and xy = R, along the boundary? (A) RxyyQxP   2 2 22  (B) RxyxQyP   2 2 22 

Calculus

For a gas turbine engine, the specific work output is maximum when the compressor temperature ratio equals:

Differential Equations

A normal shock wave in an ideal gas flow:

Numerical Methods

AE 2011 AEROSPACE ENGINEERING - AE An aircraft with a mass of 5000 kg takes off from sea level with a forward speed of 50 m/s and starts to climb with a climb angle of 15o. The rate of climb and excess thrust available at the start of the climb respectively (assume g = 9.81 ms-2) are (A) 13.40 m/s and 13146.0 N (B) 12.94 m/s and 12694.1 N

Airfoil & Wing Theory

An aircraft with a mass of 5000 kg takes off from sea level with a forward speed of 50 m/s and reaches a climb gradient of 10%. The excess thrust required is approximately:

Basic Fluid Mechanics

The speed of sound in an ideal gas is proportional to:

Compressible Flow & Shocks

An aircraft in level flight encounters a vertical gust, which excites the phugoid mode. The phugoid motion completes 10 cycles in 50 s and its amplitude reduces to half of its maximum value in 25 s. The eigenvalues of the phugoid mode are

Airfoil & Wing Theory

In a convergent-divergent nozzle operating at design conditions, the Mach number at the throat is:

Compressible Flow & Shocks

Consider the inviscid, adiabatic flow of air at free stream conditions M_inf = 2. A wedge of half-angle 10 degrees is placed in the flow. The shock attached to the wedge apex is an:

Basic Fluid Mechanics

Consider a steady two dimensional zero-pressure gradient laminar flow of air over a flat plate. The boundary layer thickness delta scales with distance x from leading edge as:

Airfoil & Wing Theory

In a centrifugal compressor, the pressure rise occurs in:

Atmospheric Flight Mechanics

For an axial compressor stage with 50% reaction, the stator and rotor blade shapes are:

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Static Stability & Control

For a solid rocket motor, the burn rate r of propellant obeys Saint-Robert's law r = a * p_c^n. For stable combustion without motor overpressure explosion, the pressure exponent n must be:

Dynamic Stability

The specific impulse I_sp of a rocket engine is defined as:

Space Dynamics & Orbital Mechanics

In an aerospace engineering analysis of Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

Which of the above materials would you choose such that weight of the shaft subjected to torsion is minimum?

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

For a statically indeterminate beam, the number of compatibility equations required equals:

Inlets, Combustors & Nozzles

AE 2011 AEROSPACE ENGINEERING - AE General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each.

Compressors and Turbines

Choose the word from the options given below that is most nearly opposite in meaning to the given word: Deference

Inlets, Combustors & Nozzles

Choose the most appropriate word(s) from the opt ions given below to complete the following sentence. We lost confidence in him because he never __________ the grandiose promises he had made.

Rocket Propulsion

Choose the word or phrase that best completes the sentence below. ______________ in the frozen wastes of Arctic takes special equipment.

Compressors and Turbines

In how many ways 3 scholarships can be awarded to 4 applicants, when each applicant can receive at most one scholarship?

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

A student attempted to solve a quadratic equation in x twice. In the first attempt, he read the constant term incorrectly and got roots 8 and 2. In the second attempt, he read the coefficient of x incorrectly and got roots -9 and -1. The correct roots of the equation are:

Structural Dynamics & Aeroelasticity

Choose the word that is opposite in meaning to the word 'DORMANT':

Aerospace Materials & Fatigue

Four archers P, Q, R and S try to hit a bull's eye during a tournament consisting of seven rounds. As illustrated in the figure below, a player recei ves 10 points for hitting the bulls' eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle. AE Outer circle 1 point Inner circle 5 points Bull's eye 10 points The final scores received by the play ers during the tournament are listed in the table below. Round P Q R S 1 5 1 10 1 5 10 10 1 2 1 1 1 5 3 10 10 1 1 4 1 5 5 10 5 10 5 1 1 6 5 10 1 1 7 The most accurate and the most consistent players during the tournament are respectively

Aerospace Materials & Fatigue

It can be inferred from the passage that