GATE AE 2007 Question Paper & Solutions

Quantitative Aptitude

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

Quantitative Aptitude

The damping of the system is given by

Quantitative Aptitude

An artificial satellite remains in orbit and does not fall to the earth because

Quantitative Aptitude

The number of natural frequencies of an elastic beam with cantilever boundary conditions is

Quantitative Aptitude

For maximum range of a glider, which of the following flight conditions is true?

Quantitative Aptitude

The longitudinal static stability of the airplane with low wing configuration will be

Quantitative Aptitude

For a fixed center of gravity location of an airplane, when the propeller is mounted on the nose of the fuselage

Quantitative Aptitude

A level and steady flight at a higher speed could be achieved by changing

Quantitative Aptitude

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

Quantitative Aptitude

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

Airfoil & Wing Theory

Mach number of an airfoil

Thermodynamic Cycles of Gas Turbines

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

Compressible Flow & Shocks

Across a normal shock

Airfoil & Wing Theory

The Joukowskii airfoil is studied in aerodynamics because

Airfoil & Wing Theory

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

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

Space Dynamics & Orbital Mechanics

The Earth's radius is $6.37 \times 10^6\text{ m}$ and the acceleration due to gravity on its surface is $9.81\text{ m/s}^2$. A satellite is in a circular orbit at an altitude of $6.30 \times 10^5\text{ m}$ above the Earth's surface. The minimum additional speed it needs to escape from the Earth's gravitational field is:

Basic Fluid Mechanics

Reynolds number, based on the pipe diameter, is

Airfoil & Wing Theory

The ratio of the minimum pressure coefficient of the larger airfoil to the minimum pressure coefficient of the smaller airfoil is

Compressible Flow & Shocks

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

Space Dynamics & Orbital Mechanics

The velocity change needed to make the orbit equatorial is:

Dynamic Stability

Power (BP) at the above flight condition will be

Space Dynamics & Orbital Mechanics

Dutch-roll mode will be

Static Stability & Control

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

Static Stability & Control

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

Linear Algebra

If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be

Linear Algebra

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

Calculus

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

Basic Fluid Mechanics

The thickness of the boundary layer at a point 0.8 m downstream of the leading edge will be

Static Stability & Control

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

Compressors and Turbines

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

Inlets, Combustors & Nozzles

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

Compressors and Turbines

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

Rocket Propulsion

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

If the combustion takes place with the fuel to air ratio 0.028, then the equivalence ratio of the fuel-oxidizer mixture is

Strength of Materials & Elasticity

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

Calculus

At a stationary point of a multi-variable function, which of the following is true?

Inlets, Combustors & Nozzles

If the nozzle expansion is optimum, then the thrust produced by the engine is

Inlets, Combustors & Nozzles

The pressure loss factor (stagnation pressure loss non-dimensionalized by the inlet dynamic pressure) of the combustor is

Inlets, Combustors & Nozzles

If the diffuser pressure recovery ratio is 0.92, then the isentropic efficiency of the diffuser is

Airfoil & Wing Theory

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

Inlets, Combustors & Nozzles

The purpose of a fuel injection system in the combustor is

Rocket Propulsion

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

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

Numerical Methods

The Newton-Raphson iteration formula to find the cube root of a positive number $c$ ($x = c^{1/3}$) is:

Thin-Walled Structures

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

Compressible Flow & Shocks

The flow system shown is designed such that the expansion generated at A is completely absorbed by wall B for p_1 = p_d. For p_1 > p_d, 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?

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?

Differential Equations

Let a dynamical system be described by the differential equation $\frac{d^2x}{dt^2} + \cos x = 0$. Which of the following differential equations describes this system in a close approximation sense for small perturbation $\Delta x$ about $x = \pi/4$?

Static Stability & Control

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

Atmospheric Flight Mechanics

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

Atmospheric Flight Mechanics

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?

Airfoil & Wing Theory

The lift curve slope of this wing is

Strength of Materials & Elasticity

The span efficiency factor of this wing is

Thin-Walled Structures

Let F(s) = (s + 10) / [(s + 2)(s + 20)]. The partial fraction expansion of F(s) is:

Thin-Walled Structures

The natural frequencies c of the fixed-free rod can then be obtained using

Compressors and Turbines

If the polytropic efficiency of the compressor is 0.89, then the isentropic efficiency of the compressor is

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?