GATE AE 2010 Question Paper & Solutions

Quantitative Aptitude

0) P. - Poss Tos + T, 02-1a P, - Pos 0.2 Two posion vectors are indiares by - fand v, (i If a +b'=1, then the operation 3= a -6) i, amouns to oblining the position vector Ve from V, by

Quantitative Aptitude

An aircraft is climbing al a constant speed in a straight line at a steep angle of climb. The load factor it sustains during the climb is:

Quantitative Aptitude

An aircraft is climbing at a constant speed in a straight line at a steep angle of climb. The load factor it sustains during the climb is:

Quantitative Aptitude

All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:

Quantitative Aptitude

Neglecting the effect of gravity, the rod has

Quantitative Aptitude

The slones sped al wich is.

Quantitative Aptitude

The eigen-values of a real symmetric matrix are always

Quantitative Aptitude

The definite integral fax

Quantitative Aptitude

The absolute ceiling of an aircraft is the altitude above which it:

Analytical & Spatial Aptitude

A thin rectangular plate made of isotropic maerial which satisfies the octahedral (i.e.. Von Mises/ Distortion energy) failure criterion has yield strength of 200 MPa under uniaxial tension. As shown in the figure. if it is loaded with uniform tension of 1S0 MPa along the x-direction, the maximum uniform tensile stress that can be applied along the y-direction before the plate starts yielding is about 1111ttt111, * 0. = 150 MPa THTFTTITTT

Space Dynamics & Orbital Mechanics

The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly eiliptical orbit is

Strength of Materials & Elasticity

A column of length / and flexural rigidity El. has one end fixed and the other end hinged. The critical buckling load for the column is

Structural Dynamics & Aeroelasticity

The natural frequency of bending vibration is highest when

Compressors and Turbines

For a multi-stage axial compressor with consiant diameter hub

Inlets, Combustors & Nozzles

How does the specific thrust, al constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio?

Basic Fluid Mechanics

Cartesian velocity components, then which one of the following combinations is correct? дф до

Rocket Propulsion

Impulse is maximum for a

Compressible Flow & Shocks

For a flow across an oblique shock which of the following statements is true?

Inlets, Combustors & Nozzles

The maximum operating flow rate through a centrifugal compressor at a given RPM is limited by

Wind Tunnel Testing & Instrumentation

A spacecraft of mass 100 kg, moving at an instantaneous speed of 1.8 x 10* m/s, picks up interstellar dust at the rate of 3.2 x 10-* kg/s. Assuming that the dust was initially al rest, the instantaneous rate of retardation of the spacecraft is:

Strength of Materials & Elasticity

Following stress state is proposed for a^2-D problem with no body forces: $\sigma$_xx = 3x^2 y + 4y^3, $\sigma$_yy = 5x^2 + 14y^2, $\tau$_xy = -3xy^2 - 7x^2. It satisfies:

Thin-Walled Structures

Shear center for this section is located al -A. h/2 j. 12 1

Static Stability & Control

The damping ratio 5 is approximately:

Dynamic Stability

If l. j and & are unis vectors along x, y and z, respectively, then al the point * = 5, y = 10 the unit vector in the direction of the steepest slope of the hill will be:

Space Dynamics & Orbital Mechanics

Ignoring compressibility effects, the cruising speed of the aircraft is approximately

Static Stability & Control

The trim curves of an aircraft are of the form Cm.. = (0.05-0.26,) - 0.16, where the elevator deflection angle, o,, is in radians. The static inargin of the aircraft is:

Compressors and Turbines

The function f(x, y) = 2°+ y-sy- 35 has an extremum al the point

Inlets, Combustors & Nozzles

The lift force acting on the wing is

Inlets, Combustors & Nozzles

If the flow through the nozzle is isentropic, what is che mass flow rate of the gases out of the nozzle?

Numerical Methods

Newton-Raphson method achieves an order of convergence equal to:

Strength of Materials & Elasticity

Consider a l-D adiabatic, inviscid, compressible flow of air (R = 287 J/Kg-K, c, = 718 J/Kg-K) through a duct of constant cross-sectional area A=1m'. If the valumetric flow rate is = 680 m/s and stagnation temperature is T, = 580.05 K. then the air temperature inside the duct is

Rocket Propulsion

designed in such a way that the payload ratio and the structural ratio are same for both the stages The second stage of the rocket has following mass distribution : Propellant Mass = 10208 kg Structural Mass = 1134 kg Payload Mass = 1700 kg 8, =9.8 m/s If the rocket is fired from rest and it flies in a zero gravity field and a drag free environment, the final velocity attained by the payload is

Static Stability & Control

2010 AE 0.44 The trim curves of an aircraft are of the form C... = (0.05 - 0.28,) - 0.1C, where ine elevaror deflection angle, ó,, is in radians. The change in elevator deflection needed to increase the lift coefficient from 0.4 10 0.9 is :

Compressors and Turbines

What is the stagnation pressure ratio (Pes) for this compressor?

Strength of Materials & Elasticity

Maximun value of shear stress is

Linear Algebra

The radial and azimuthal velocities on the cylinder surface at 8 = I / 2 are

Basic Fluid Mechanics

The stagnation points are located at

Inlets, Combustors & Nozzles

In a rocket engine test, the stagnation pressure at the inlet of the convergent-divergent nozzle is measured. Given the combustion chamber pressure $p_c = 4.0\text{ MPa}$ and chamber velocity $V_c \approx 0$, the stagnation pressure $p_0$ at the nozzle inlet is:

Differential Equations

Ihrust produced by this engine under the given conditions?

Dynamic Stability

If v= 200 m/s then the wavelength of the phugoid oscillations, assuming 8 = 9.81 m/s*, is. approximately:

Basic Fluid Mechanics

Which of the following options is the closest in meaning to the word below; Circuitous

Compressible Flow & Shocks

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair: Unemployed : Worker

Strength of Materials & Elasticity

Il we manage to our natural resources, we would leave a better planet for our children.

Compressible Flow & Shocks

His rather casual remarks on politics _ his lack of seriousness about the subject.

Basic Fluid Mechanics

Then the number of persons playing neither hockey nor football is:

Airfoil & Wing Theory

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work sllently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the alive passage:

Atmospheric Flight Mechanics

If 137 + 276 = 435 how much is 731 + 6727

Atmospheric Flight Mechanics

§ skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, & semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Static Stability & Control

Core digits 2, 2. 3. 3. 3. 4. 4. 4. 4 how many distinct digit numbers greater than 3000 can be

Dynamic Stability

There are no twin: what order were they born (oldest first'

Basic Fluid 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?

Basic Fluid Mechanics

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

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

In an aerospace engineering analysis of Thermodynamic Cycles of Gas Turbines (Thrust Equations & Specific Fuel Consumption), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Basic Fluid Mechanics

In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?

Basic Fluid Mechanics

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?