Gate 2011 Aerospace Engineering Question Paper

Consider x,y,z to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as v = 3xi + 3xyj – , where i, j and k are the unit vectors along x, y and zaxes, respectively. The curl of is given by

Which of the following functions is periodic?

The function f has its minimum value at

Consider the function f . The vector pointing in the direction of maximum increase of the function at the point (1, -1) is

Two simultaneous equations given by y = + x and y = x – have

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

An Euler-Bernoulli beam in bending is assumed to satisfy

A statically indeterminate frame structure has

Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of m , c and k , respectively. The logarithmic decrement of this system can be calculated using

Consider a single degree of freedom spring-mass system of spring stiffness and mass m which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness and mass m which has a natural frequency of 20 rad/s. The spring stiffness is equal to

An impulsive launch of a rocket minimizes the loss of burn-out velocity due to

Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise

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

Lift on an aircraft climbing vertically up is

If an aircraft is performing a positive yawing manoeuvre, the side slip angle

For an airplane to be statically stable, its centre of gravity must always be

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

The aerodynamic centre of a supersonic aerofoil, with chord c, is located at

Winglets are used on wings to minimize

Consider a potential flow with free stream velocity V , over a spinning circular cylinder of radius R and circulation . The stream function, , where = 0 on the cylinder surface, in cylindrical coordinates is given by

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

The pressure ratio in any one stage of a jet engine compressor is limited by

Thermodynamic cycle on which the jet engine operates can be

Propulsion efficiency of a jet engine is

Consider the function. The Newton-Raphson iteration formula to find the root of the function starting from an initial guess at iteration k is

Consider the matrix where a and b are real numbers. The two eigenvalues of this matrix are real and distinct when

The solution of with initial condition y(0) = 1 is given by

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. The 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, = 8)

A rocket engine is tested on a test bed under the ideal condition of fully expanded jet. The exhaust velocity is 2 km/s through a nozzle of area 2.5 . The mass flow rate is 200 kg/s. The specific impulse of the propellant and the thrust developed respectively are (assume g = 9.81 )

A body undergoes deformation under plane strain conditions when subjected to the following stresses (in MPa): = 450, = 450, = 75, = 0, = 0. What are the remaining components of stresses (in MPa) and strains? Assume the material to be isotropic and linear-elastic with Young’s modulus E = 200 GPa and Poisson’s ratio v = 1/3.

Which of the following Airy’s stress functions could satisfy the given boundary conditions, assuming constant values of = P = Q and = R, along the boundary?

An aircraft is performing a coordinated turn manoeuvre at a bank angle of and forward speed of 100 m/s. Assume g = 9.81 . and forward speed of 100 m/s. Assume g = 9.81

An aircraft in a steady level flight at forward speed of 50 m/s suddenly rolls by and becomes inverted. If no other changes are made to the configuration or controls of the aircraft, the nature of the subsequent flight path taken by the aircraft and its characteristic parameter(s) (assume g = 9.81 ) are

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 . The rate of climb and excess thrust available at the start of the climb respectively (assume g = 9.81 ) are

A glider having a mass of 500 kg is taken to an altitude of 1000 m with a jeep moving on ground at 54 kmph. Upon reaching the required altitude in 50 s, the glider is released and starts its descent. Under the assumption of equilibrium glide, the range and endurance of the glider for a constant lift-to-drag ratio of 15 are

An elliptic orbit has its perigee at 400 km above the Earth’s surface and apogee at 3400 km above the Earth’s surface. For this orbit, the eccentricity and semi-major axis respectively are (assume radius of Earth = 6400 km)

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

Consider the inviscid, adiabatic flow of air at free stream conditions, atm and = 288 K around a sharp expansion corner as shown below. The Prandtl-Meyer function, ?, is given as a function of Mach number, M, as

Assume air to be calorically perfect with = 1.4. The Mach number, , downstream of the expansion corner is approximately

Consider a steady two dimensional zero-pressure gradient laminar flow of air over a flat plate as shown below. The free stream conditions are = 100 = 1.2 kg = 1 atm and = 1.8 x . The ratio of displacement thickness to momentum thickness of the boundary layer at a distance of 2 m from the leading edge is

In the context of Prandtl’s lifting line theory for a finite wing, which of the following combinations of statements is TRUE?
P: The bound vortex is responsible for the lift force
Q: The trailing vortices are responsible for the induced drag
R: The bound vortex is responsible for the induced drag
S: The trailing vortices are responsible for the lift force

Consider flow over a thin aerofoil at Mach number, = 0.5 at an angle of attack, . Using the Prandtl-Glauert rule for compressibility correction, the formula for lift coefficient, can be written as

Directions for next two questions: The partial differential equation (PDE) governing free vibrations of a uniform Euler-Bernoulli beam is given by = 0 , where EI is the flexural stiffness, m the mass per unit length, w(xt) is the bending displacement, x is the coordinate along the beam length, t is time and L is the beam length.

To solve the PDE, the number of boundary conditions (BC) and initial conditions (IC) needed are

For the cantilever beam shown in the figure, which of the following CANNOT be a possible boundary condition?

Directions for next two questions: Consider an inviscid, adiabatic flow of air at free stream Mach Number, = 2, across a compression corner as shown. The free stream total enthalpy is = 810 kJ . Assume that air is calorically perfect with = 1.4, R = 287 J .

The shock angle is

The total temperature at point P is

Directions for next two questions: A thin-walled (thickness << radius), hollow shaft of length 1m and mean radius, R = 5 cm has to be designed such that it can transmit a torque, T = 7 kN-m. A survey of different commercially available materials was made and following data was obtained from the suppliers (E: Young’s modulus, : yield stress in shear, : density):

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

If you assume a factor of safety of 2, what should be the approximate thickness of such a shaft?

Directions for next two questions: Prandtl’s lifting line equation for a general wing is given by



angle of attack, is the spanwise location, gives the spanwise variation of zero-lift angle, c is the chord, b is the span, and gives the spanwise variation of circulation.

The rate of change of circulation with angle of attack is

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

Deference

Choose the most appropriate word(s) from the options given below to complete the following sentence.

We lost confidence in him because he never ____ the grandiose promises he had made.

Choose the word or phrase that best completes the sentence below.

___ in the frozen wastes of Arctic takes special equipment.

In how many ways 3 scholarships can be awarded to 4 applicants, when each applicant can receive any number of scholarships?

Choose the most appropriate word from the options given below to complete the following sentence.

The ____ of evidence was on the side of the plaintiff since all but one witness testified that his story was correct.

If (2y+1)/(y+2) < 1, then which of the following alternatives gives the CORRECT range of y?

A student attempted to solve a quadratic equation in x twice. However, in the first attempt, he incorrectly wrote the constant term and ended up with the roots as (4, 3). In the second attempt, he incorrectly wrote down the coefficient of x and got the roots as (3, 2). Based on the above information, the roots of the correct quadratic equation are

L, M and N are waiting in a queue meant for children to enter the zoo. There are 5 children between L and M, and 8 children between M and N. If there are 3 children ahead of N and 21 children behind L, then what is the minimum number of children in the queue?

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 receives 10 points for hitting the bulls’ eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle.

The final scores received by the players during the tournament are listed in the table below.


The most accurate and the most consistent players during the tournament are respectively

Nimbus clouds are dark and ragged, stratus clouds appear dull in colour and cover the entire sky. Cirrus clouds are thin and delicate, whereas cumulus clouds look like cotton balls.

It can be inferred from the passage that