GATE AE 2010 Question Paper & Solutions

Verbal 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

Verbal 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

3 (8) 4 (C) 5 (D) 6 0.5 The linear second order parial diferential equation see +3 Jady đy +9 = 0 is

Analytical & Spatial Aptitude

Parabolic (B) Hyperbolic (C) Elliptic (D) None of the above 0.6 All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:

Analytical & Spatial Aptitude

15% (B) 30% (C) 70% (D) 105% 0.7 A vertical slender rod is suspended by a hinge at the top and hangs freely. It is heated unti) it attains a uniform temperature, T. Neglecting the effect of gravity, the rod has

Verbal Aptitude

Stress but no strain (B) Strain but no stress (C) Both stress and strain (D) Neither stress nor strain 0.8 An aircraft saur a ted on a mos i sister and lesed fligh. The slones sped al wich is.

Quantitative Aptitude

28.3 m/s (B) 40.0 m/s (C) 56.6 m/s (D) 80.0 m/s 0.9 The eigen-values of a real symmetric matrix are always

Quantitative Aptitude

The definite integral fax

Verbal Aptitude

does not exist (B) is equal ta 2 (C) is equal to 0 (D) is equal 10 -2 Q.12 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

Linear Algebra

3.5X10" (B) (B) N/m' (C) 10.5x10"N/m (D) 14x10"N/m Q.15 The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly eiliptical orbit is

Linear Algebra

2010 AE Q.16 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

Calculus

T' EI (C) - H'EL (0.70)' (D) (21) Q.17 A horizontal cantilevered stecl beam of rectangutar cross-section having width b and depth d is vibrating in the vertical plane. The natural frequency of bending vibration is highest when

Differential Equations

For a multi-stage axial compressor with consiant diameter hub

Numerical Methods

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

Increases (B) Decreases (C) First increases and then decreases (D) First decreases and then increases Q.22 If @ is the potential function for an incompressible irrotational flow, and u and v are the Cartesian velocity components, then which one of the following combinations is correct? дф до

Airfoil & Wing Theory

дх đẹ (C) i =- ,V= (D) u = 2 дх ду Q.23 Among the choices given below, the Specific Impulse is maximum for a

Compressible Flow & Shocks

2010 Q.24 For a flow across an oblique shock which of the following statements is true?

Compressible Flow & Shocks

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

Wind Tunnel Testing & Instrumentation

Q.26 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:

Atmospheric Flight Mechanics

7.9 × 10* m/s (B) 2.3 × 10-3 m/s (C) zero (D) 5.8 × 10° m/s Q.27 Following stress state is proposed for a 2-D problem with no body forces: 0*=3x'y+4y'. 0=5+1457,509=-3533-7x°. It satisfies

Atmospheric Flight Mechanics

(C) 2.1 R (D) 3.9 R The given thin wall section of uniform thickness, 1, is symmetric about i-axis. Moment of inertia is given to be 1" th'. Shear center for this section is located al -A. h/2 j. 12 1

Static Stability & Control

(C) x=- (D) * =- 28 36 35" Q.32 During an under-damped oscillation of a single degree of freedom system, in the lime-displacement plot the third peak is of magnitude 100 and the lenth peak is of magnitude 10. The damping ratio 5 is approximately:

Dynamic Stability

(D) 2(s -1) (5-1)} +4 Q.34 In a certain region a hill is described by the shape z(x, y) = -x* +y"-ry-3y, where the axes x and y are in the horizontal plane and axis i points vertically upward. 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

i (B) j (C) K (D) i+j+i 0.35 All aircraft is cruising at an alticude of 9 km. The free-stream static pressure and density al this akitude are 3.08 × 10* N/m' and 0.467 kg/m' respectively. A Pitor tube mounted on the wing senses a pressure of 3.31 × 10* N/m Ignoring compressibility effects, the cruising speed of the aircraft is approximately

Thermodynamic Cycles of Gas Turbines

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:

Thermodynamic Cycles of Gas Turbines

0.5 (B) 0.2 (C) 0.1 (D) 0.05 0.37 The function f(x, y) = 2°+ y-sy- 35 has an extremum al the point

Inlets, Combustors & Nozzles

(1,2) (B) (3,0) (C) (2,2) (D) (1.1) Q.38 Consider the flow of air (p = 1.23 kg/m") over a wing of chord length 0.5 m and span 3 m. Let the free stream velocity be U =100 m/s and the average circulation around the wing be F = 10 m%s per unit span. The lift force acting on the wing is

Compressors and Turbines

(C) 3690 N (D) 4920 N 0.39 The stagnation pressure and stagnation temperature inside the combustion chamber of a liquid rocket engine are 1.5 MPa and 2500 K respectively. The burned gases have y = 1.2 and R = 692.83 J/kgK. The rocket has a converging - diverging nozzle with a throat area of 0.025 m' and the flow at the exit of the nozzle is supersonic. If the flow through the nozzle is isentropic, what is che mass flow rate of the gases out of the nozzle?

Rocket Propulsion

18.5 kg/s (B) 31.2 kg/s (C) 29.7 kg/s (D) 19.4 kg/s Q.40 In finding a root of the equation: x* - 6x + 5 = 0 the 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

Strength of Materials & Elasticity

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

Thin-Walled Structures

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 :

Structural Dynamics & Aeroelasticity

(B) -0.125 radians 10) 0.125,1 - (2) radians 10) -0.125, 1- (g) radians Q.47 The inlet stagnation temperature for a single stage axial compressor is 300 K and the stage efficiency is 0.80. Following conditions exist at the mean radius of the rotor blade: Biade speed = 200 m/s Axial flow velocity = 160 mis What is the stagnation pressure ratio (Pes) for this compressor?

Aerospace Materials & Fatigue

(B) M A 0.2PL- -0.3PLT (C) (D) O.2PL+ Q.49 Maximun value of shear stress is

Linear Algebra

AE R where Free stream velocity, V. = 25 m/s Cylinder radius, R= 1 m Circulation, [ = 50m m/s R Q.50 The radial and azimuthal velocities on the cylinder surface at 8 = I / 2 are

Calculus

V, = 0 m/s, Va = -75 m/s (B) V, = 0 m/s. Vo = 75 m/s (C) V, = 0 m/s, ½, = -25 m/s (D) V, = 0 m/s, Va = 25 m/s Q.51 The stagnation points are located at

Differential Equations

(D) 60° and 120° Linked Answer Questions Statement for Linked Answer Questions 52 and 53: An aircraft with an IDEAL Turbojet engine is flying at 200 m/s at an altitude where the ambient pressure is equal to 0.8 bar. The stagnation pressure and temperature at the inler of the curbine are 6 bar and 1400 K respectively. The change in specific enthalpy across the compressor is 335 kJ/kg. Assume the fuel flow rate o be very small in comparison to the air flow rate and consider C. = 1117 J/koK and v = 1.3 Q.52 What is the stagnation pressure at the inlet of the nozzle?

Numerical Methods

2.8 bar (B) 5.7 bar (C) 2.1 bar Q.53 What is the specific Ihrust produced by this engine under the given conditions?

Airfoil & Wing Theory

- ng (в) *V (D) J2r 8 (0) J278 Q.55 If v= 200 m/s then the wavelength of the phugoid oscillations, assuming 8 = 9.81 m/s*, is. approximately:

Basic Fluid Mechanics

Q.56 Which of the following options is the closest in meaning to the word below; Circuitous

Compressible Flow & Shocks

cyclic (B) indirect (C) confusing (D) crooked 0.57 The question below consists of a pair of relued words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed : Worker

Airfoil & Wing Theory

(B) unaware : sleeper (C) wit: jester (D) renovated : house Q.58 Choose the most appropriate word from the options given below so complese the following sentence: Il we manage to our natural resources, we would leave a better planet for our children.

Compressible Flow & Shocks

uphold (B) restrain (C) cherish (D) conserve Q.59 Choose the most appropriate word from the options given below to complete the following sentence: His rather casual remarks on politics _ his lack of seriousness about the subject.

Basic Fluid Mechanics

masked (B) belied (C) betrayed (D) suppressed Q.60 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Airfoil & Wing Theory

Q.61 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

2016) Q.62 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

20 days (B) 18 days (C) 16 days (D) 15 days 0.68 Core digits 2, 2. 3. 3. 3. 4. 4. 4. 4 how many distinct digit numbers greater than 3000 can be

Dynamic Stability

(D) 54 Q.65 Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1" January. The age difference between any two successive siblings (that is born one after another) is less than 3 year Grin ge olonge Fan age + Sain sage. i. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest i. There are no twin: what order were they born (oldest first'

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

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?

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

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?

Inlets, Combustors & Nozzles

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?

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?