GATE AE 2007 Question Paper & Solutions

Verbal Aptitude

Which one of the following engines should be used by a subsonic passenger transport airplane for minimum specific fuel consumption?

Verbal Aptitude

Turbojet engine with afterburner (B) Turbofan engine (C) Ramjet engine (D) Scramjet engine A spring-mass-damper system with a mass of 1 kg is found to have a damping ratio of 0.2 and a natural frequency of 5 rad/s. The damping of the system is given by

Quantitative Aptitude

f (alP) (C) f(a - P) (B) /(a + B) (D) 2x2 zero matrix An artificial satellite remains in orbit and does not fall to the earth because

Analytical & Spatial Aptitude

Ek* = X, - Arx f(x) (C) X+1 = xx - (1/Ar)x f(x) (B) xx., = x, + (Ar /2)x f(x) (D) Xx1 =x, + Arx f(x) The number of natural frequencies of an elastic beam with cantilever boundary conditions is

Analytical & Spatial Aptitude

1 (B) 3 (C) 1000 For maximum range of a glider, which of the following conditions is true? (D) Infinite

Verbal Aptitude

x = 7/2 (C) * = 30/7 (B) x = 7/30 (D) x = 30 Two airplanes are identical except for the location of the wing. The longitudinal static stability of the airplane with low wing configuration will be

Quantitative Aptitude

more than the airplane with high wing configuration (B) less than the airplane with high wing configuration (C) same as the airplane with high wing configuration (D) more if elevator is deflected For a fixed center of gravity location of an airplane, when the propeller is mounted on the nose of the fuselage

Quantitative Aptitude

longitudinal static stability increases (B) longitudinal static stability decreases (C) longitudinal static stability remains same (D) longitudinal static stability is maximum Let an airplane in a steady level flight be trimmed at a certain speed. A level and steady flight at a higher speed could be achieved by changing

Verbal Aptitude

For an elastic anisotropic solid, the number of independent elastic constants in its constitutive equations is

Analytical & Spatial Aptitude

Q.15 Total pressure at a point is defined as the pressure when the flow is brought to rest

Linear Algebra

adiabatically (B) isentropically (C) isothermally (D) isobarically Q.16 The drag divergence Mach number of an airfoil

Linear Algebra

On which one of the following thermodynamic cycles does an ideal ramjet operate?

Calculus

Across a normal shock

Differential Equations

The Joukowskii airfoil is studied in aerodynamics because

Numerical Methods

One of the criteria for high-speed airplanes is that the critical Mach number should be as high as possible. Therefore, high-speed subsonic airplanes are usually designed with

Basic Fluid Mechanics

(C) Es < Eg and Ta > TB (D) Ex > Eg and Ta < TB Let P and @ be two square matrices of same size. Consider the following statements (i) PQ=0 implies P= 0 or Q=0 or both (ii) PQ= 1' implies P= Q*' (ini) (P+Q)* = p* + 2PQ+Q* (iv) (P-Q) = p* -2PQ+Q* where / is the identity matrix. Which of the following statements is correct?

Airfoil & Wing Theory

A 1 kg mass attached to a spring elongates it by 16mm. The mass is then pulled from its equilibrium position by 10mm and released from rest. Assuming the acceleration due to gravity of 9.81 m/s', the response of the mass in mm is given by

Compressible Flow & Shocks

The earth's radius is 6.37x10° m and the acceleration due to gravity on its surface is 9.81 m/s'. A satellite is in a circular orbit at a height of 6.30x10'm above the earth's surface. The minimum additional speed it needs to escape from the earth's gravitational field is

Compressible Flow & Shocks

(C) p = Two pipes of constant sections but different diameters carry water at the same volume flow rate. The Reynolds number, based on the pipe diameter, is

Wind Tunnel Testing & Instrumentation

the same in both pipes (B) is larger in the narrower pipe (C) is smaller in the narrower pipe (D) depends on the material of the pipes Two airfoils of the same family are operating at the same angle of attack. The dimensions of one airfoil are twice as large as the other one. The ratio of the minimum pressure coefficient of the larger airfoil to the minimum pressure coefficient of the smaller airfoil is

Atmospheric Flight Mechanics

Wing A has a constant chord c and span b. Wing B is identical but has a span 4b. When both wings are operating at the same geometric angle of attack at subsonic speed, then:

Atmospheric Flight Mechanics

A spring-mass-damper system is excited by a force F, sinct. The amplitude at resonance is measured to be 1 cm. At half the resonant frequency, the amplitude is 0.5 cm. The damping ratio of the system is

Static Stability & Control

1 and 1/2 (C) 2 and 3 (B) 1 and 1/3 (D) 1/2 and 1/3 The radius of the earth is 6.37 ×10'm and the acceleration due to gravity at its surface is 9.81 m/s'. A satellite is in circular orbit at à height of 35.9x10° m above the earth's surface. This orbit is inclined at 10.5 degrees to the equator. The velocity change needed to make the orbit equatorial is:

Dynamic Stability

561 m/s at 84.75 degrees to the initial direction (B) 561 m/s at 95.25 degrees to the initial direction (C) 281 m/s at 84.75 degrees to the initial direction (D) 281 m/s at 95.25 degrees to the initial direction A piston-prop airplane having propeller efficiency, Пp = 0.8 and weighing 73108 N could achieve maximum climb rate of 15 m/s at flight speed of 50 m/s. The excess Brake Power (BP) at the above flight condition will be

Space Dynamics & Orbital Mechanics

0.07 per deg (B) - 1.065 per deg (C) -0.008 per deg (D) -0.762 per deg The lateral-directional characteristic equation for an airplane gave the following set of roots: 1, = -0.6, 2, = -0.002, 34= -0.06 $ /1.5, where j = V-1. The damping ratio corresponding to the Dutch-roll mode will be

Thermodynamic Cycles of Gas Turbines

3.5 × 10* N/m? (B) 2.0x10* N/m? (C) 2.87×10'N/m? (D) 0.6x10* N/m? If the center of gravity of an airplane is moved forward towards the nose of the airplane; the ma. (maximum value of the lift coefficient) value for which the airplane can be trimmed (C, = 0) will

Thermodynamic Cycles of Gas Turbines

rudder deflection If the contribution of only the horizontal tail of an airplane was considered for estimating да , and if the tail moment arm 4, was doubled, then how many times the original value would the new * become ? да

Inlets, Combustors & Nozzles

two times (B) three times (C) 1.414 times (D) 1.732 times If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be

Compressors and Turbines

Q.40 Let a system of linear equations be as follows: x-y+2z=0 2x + 3y -z = 0 2x -2y + 4z = 0 This system of equations has

Rocket Propulsion

A turbulent boundary layer remains attached over a longer distance on the upper surface of an airfoil than does a laminar boundary layer, because

Strength of Materials & Elasticity

more rapidly (C) turbulence causes the effective coefficient of viscosity to feduce, resulting in less loss of momentum in the boundary layer (D) the turbulent boundary layer is thicker, hence the velocity gradients in it are smaller, therefore viscous losses are less The laminar boundary layer over a large flat plate held parallel to the freestream is 5 mm thick at a point 0.2 m downstream of the leading edge. The thickness of the boundary layer at a point 0.8 m downstream of the leading edge will be

Strength of Materials & Elasticity

If horizontal tail area is increased while the elevator to horizontal tail area ratio is kept same, then

Thin-Walled Structures

Air enters through the eye of a centrifugal compressor with a stagnation temperature 300 K and exits the compressor with a stagnation temperature 424 K. If the isentropic efficiency of the compressor is 0.81 and the ratio of specific heats of the flowing gas (assumed as constant) is 1.4, then the pressure ratio across the compressor is

Structural Dynamics & Aeroelasticity

(B) X1-Y4, X2-Y2, X3-Y3, X4-Y1 (C) X1-Y4, X2-Y1, X3-Y2, X4-Y3 (D) X1-Y4, X2-Y3, X3-Y2, X4-Y1 For an impulse turbine with identical stages, the hot gas exits from the stator blades at the mean blade height at an absolute angle of 70 degrees with the axis of the turbine. If the absolute inlet blade angle with the axis of the turbine at the mean blade height for the rotor blades is 37 degrees, then the absolute exit blade angle with the axis of the turbine at the mean blade height of the rotor blades is

Aerospace Materials & Fatigue

Steel alloy (C) Nickel alloy (B) Titanium alloy (D) Aluminum alloy Q.49 Which one of the following statements is true?

Linear Algebra

An athlete starts running with a speed ½. Subsequently, his speed decreases by an amount that is proportional to the distance that he has already covered. The distance covered will be

Calculus

Linear in time (B) Quadratic in time (C) Exponential in time (D) Logarithmic in time The on-board rocket motor of a satellite of initial mass 2000 kg provides a specific impulse of 280 seconds. If this motor is fired to give a speed increment of 500 m/s along the direction of motion, the mass of propellant consumed is:

Differential Equations

(C) 1666 kg (D) 167 kg Combustion between fuel (octane) and oxidizer (air) occurs inside a combustor with the following stoichiometric chemical reaction: 2C8H18 + (2502 + 94Nz) → 16CO2 + 18H20 + 94Nz. The atomic weights of carbon (C), hydrogen (H), oxygen (O), and nitrogen (N) are 12, 1, 16, and 14, respectively. If the combustion takes place with the fuel to air ratio 0.028, then the equivalence ratio of the fuel-oxidizer mixture is

Numerical Methods

0.094 (B) 0.422 (C) 0.721 (D) 2.371 The von Mises yield criterion or the maximum distortion energy criterion for a plane stress problem with o, and o, as the principal stresses in the plane, and oy as the yield stress, requires

Airfoil & Wing Theory

V: N 21 (h/2) V, (h/2)' (D) Tg = 21, At a stationary point of a multi-variable function, which of the following is true?

Basic Fluid Mechanics

Curl of the function becomes unity (B) Gradient of the function vanishes (C) Divergence of the function vanishes (D) Gradient of the function is maximum In a rocket engine, the hot gas generated in the combustion chamber exits the nozzle with a mass flow rate 719 kg/sec and velocity 1794 m/s. The area of the nozzle exit section is 0.635 m'. If the nozzle expansion is optimum, then the thrust produced by the engine is

Compressible Flow & Shocks

(B) (C) PU:H (D) 2pU3h A gas turbine engine operates with a constant area duct combustor with inlet and outlet stagnation temperatures 540 K and 1104 K respectively. Assume that the flow is one dimensional, incompressible and frictionless and that the heat addition is driving the flow inside the combustor. The pressure loss factor (stagnation pressure loss non-dimensionalized by the inlet dynamic pressure) of the combustor is

Airfoil & Wing Theory

0 (B) 0.489 (C) 1.044 (D) 2.044 The diffuser of an airplane engine decelerates the airflow from the flight Mach number 0.85 to the compressor inlet Mach number 0.38. Assume that the ratio of the specific heats is constant and equal to 1.4. If the diffuser pressure recovery ratio is 0.92, then the isentropic efficiency of the diffuser is

Compressible Flow & Shocks

With-regard to this biplane, which of the following statements is true?

Basic Fluid Mechanics

1 (C) 0.7837 (В) т /4 (D) 0.2536 The purpose of a fuel injection system in the combustor is

Airfoil & Wing Theory

to accelerate the flow in the combustor (B) to increase the stagnation pressure of the fuel-air mixture (C) to ignite the fuel-air mixture (D) to convert the bulk fuel into tiny droplets Which one of the following values is nearer to the vacuum specific impulse of a rocket engine using liquid hydrogen and liquid oxygen as propellants?

Atmospheric Flight Mechanics

49 sec (B) 450 sec (C) 6000 sec (D) 40000 sec A circular cylinder is placed in an uniform stream of ideal fluid with its axis normal to the flow. Relative to the forward stagnation point, the angular positions along the circumference where the speed along the surface of the cylinder is equal to the free stream speed are

Atmospheric Flight Mechanics

The Newton-Raphson iteration formula to find a cube root of a positive number c is 2x, + 2c

Static Stability & Control

The torsion constant J of a thin-walled closed tube of thickness t and mean radius r is given by

Dynamic Stability

(D) J = 2mr* An aerospace system shown in the following figure is designed in such a way that the expansion generated at A is completely absorbed by wall B for P, = Pa, Where Pa corresponds to the design condition. M, > 1, PI Poo B For p, > P. which of the following statements is NOT true?

Space Dynamics & Orbital Mechanics

P 0.8 0.4 0 In the above figure, c, refers to the section lift coefficient, C, refers to the lif coefficient of the wing, y is the coordinate along the span and s is the span of the wing. A designer prefers to use a wing for which the stall begins at the root. Which of the wings will he choose?

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

Let a dynamical system be described by the differential equation - + cos x = 0. Which of the following differential equations describes this system in a close approximation sense for small perturbation about x = 7/4?

Thermodynamic Cycles of Gas Turbines

0.35 c (B) 0.25 c D) 0.52 c The most aft location of the airplane center of gravity permitted to fulfill designer's requirement on longitudinal static stability is

Inlets, Combustors & Nozzles

The center of gravity location to have dõe dC, = 0 is

Compressors and Turbines

The system shows the following type of coordinate coupling

Inlets, Combustors & Nozzles

V (True air speed) The maximum rate of climb achievable by this airplane at 5 km altitude will be

Rocket Propulsion

1.65 m/s (B) 0.51 m/s (C) 1.43 m/s (D) 3.65 m/s If during the maximum rate of climb at 5 km altitude, the airplane was flying at an angle of attack of 4 degrees and attitude (pitch) angle of 5 degrees, what was equivalent airspeed of the airplane?

Compressors and Turbines

The lift curve slope of this wing is

Strength of Materials & Elasticity

The span efficiency factor of this wing is

Thin-Walled Structures

2 (C) - +| s + 2 s + 20 20 s + 20 The inverse Laplace transform of F(s) is

Thin-Walled Structures

(x =l) = 0 ди ди (D) - (x = 0) = 0, - (x =l) = 0 дх The natural frequencies c of the fixed-free rod can then be obtained using

Structural Dynamics & Aeroelasticity

0.22 (B) 0.28 (C) 3.50 • (D) 3.90 If the polytropic efficiency of the compressor is 0.89, then the isentropic efficiency of the compressor is

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?