GATE AE 2011 Question Paper & Solutions

Verbal Aptitude

Verbal Aptitude

Consider the standard principles of Verbal Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Quantitative Aptitude

Consider the standard principles of Quantitative Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Analytical & Spatial Aptitude

Consider the standard principles of Analytical & Spatial Aptitude. Evaluate the given statement or numerical relation and determine the correct option based on grammatical, quantitative, or spatial reasoning rules.

Analytical & Spatial Aptitude

(C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively,

Verbal Aptitude

Quantitative Aptitude

Quantitative Aptitude

(D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k

Verbal Aptitude

Analytical & Spatial Aptitude

Linear Algebra

Linear Algebra

(D) reaction jet control force Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies

Calculus

(C) propellant masses (D) control system masses In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as

Differential Equations

Numerical Methods

Basic Fluid Mechanics

In an aerospace engineering analysis of Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Airfoil & Wing Theory

(C) ahead of neutral point (D) aft of neutral point It is seen that the drag polar of a certain aerofoil is symmetric about the Cd axis. This drag polar could refer to

Compressible Flow & Shocks

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Wind Tunnel Testing & Instrumentation

In an aerospace engineering analysis of Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

Atmospheric Flight Mechanics

Static Stability & Control

(D) mass flow rate in that stage Thermodynamic cycle on which the jet engine operates can be Q.24

Dynamic Stability

In an aerospace engineering analysis of Dynamic Stability (Short Period & Phugoid Longitudinal Modes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

(D) inversely proportional to the thrust power and directly proportional to the air mass flow rate Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young's modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span (L/2) at the center of the cross-section. Unde r the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is

Thermodynamic Cycles of Gas Turbines

P L L/2 2011 AEROSPACE ENGINEERING - AE AE Consider a beam in bending with a solid circular cross-section of 1 mm2, which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm2) is

Thermodynamic Cycles of Gas Turbines

A simp ly supported slender column of square cross section (width=depth= d) has to be designed such that it buckles at the same instant as it yields. Length of the column is given to be 1.57 m and it is made of a material whose Young's modulus is 200 GPa and yield stress is 240 MPa. The width, d, of the column (in cm) should be

Inlets, Combustors & Nozzles

A turbojet powered aircraft is flying at Mach nu mber 0.8 at an altitude of 10 km. The inlet and exit areas of the engine are 0.7 m 2 and 0.4 m 2 respectively. The exhaust gases have velocity of 500 m/s and pressure of 60 kPa. The free stream pressure , density and speed of sound are 26.5 kPa, 0.413 kg/m3 and 299.5 m/s respectively. The thrust of the engine (in kN) is

Compressors and Turbines

A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1 m2. The static pressure difference between th e settling chamber and the test section is 40 cm of water column. Assume , and . The speed of air in the test section (in m/s) is 2m/s 81 . 9g 3kg/m 2 . 1air 3kg/m 1000water

Rocket Propulsion

Questions Q.31 to Q.55 are multiple choice type. Consider the function . The Newton-Raphson iteration formula to find the root of the function starting from an initial guess at iteration k is ) sin( ) (x x x f  ) 0 (x (A) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (B) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx  

Strength of Materials & Elasticity

(C) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   (D) ) ( ) ( ) ( ) 1 ( cos 1 cossin k kk k k x x x xx   Consider the matrix where a and b are real numbers. The two eigenvalues of this m atrix     2 2 b a 1 and 2 are real and distinct  2 1  when

Strength of Materials & Elasticity

Thin-Walled Structures

(C) 2 4 (2 ) te t (D) 2 1 52( 2 2 )tet t  2011 AEROSPACE ENGINEERING - AE 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. Th e 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,  = 1.4; 8rcp )

Structural Dynamics & Aeroelasticity

Aerospace Materials & Fatigue

Linear Algebra

(D) 0 , 0 , 002 . 0 , 001 . 0 , 001 . 0 , 0  yzxzxyyyxxzz  Which of the following Airy's stress functions could satisfy the given boundary conditions, assuming constant values of xx = P, yy = Q and xy = R, along the boundary? (A) RxyyQxP   2 2 22  (B) RxyxQyP   2 2 22 

Calculus

Differential Equations

Numerical Methods

(D) downward circular path with a speed of 25 m/s and radius of 254.8 m/s AE 2011 AEROSPACE ENGINEERING - AE 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 15o. The rate of climb and excess thrust available at the start of the climb respectively (assume g = 9.81 ms-2) are (A) 13.40 m/s and 13146.0 N (B) 12.94 m/s and 12694.1 N

Airfoil & Wing Theory

Basic Fluid Mechanics

Compressible Flow & Shocks

(C) 0.22 and 8300 km (D) 0.22 and 1900 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

Airfoil & Wing Theory

Compressible Flow & Shocks

Basic Fluid Mechanics

Airfoil & Wing Theory

Atmospheric Flight Mechanics

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Static Stability & Control

Dynamic Stability

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

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

Inlets, Combustors & Nozzles

(C) a quadratic function of  (D) a cubic function of  AE 2011 AEROSPACE ENGINEERING - AE General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each.

Compressors and Turbines

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

Inlets, Combustors & Nozzles

Choose the most appropriate word(s) from the opt ions given below to complete the following sentence. We lost confidence in him because he never __________ the grandiose promises he had made.

Rocket Propulsion

Choose the word or phrase that best completes the sentence below. ______________ in the frozen wastes of Arctic takes special equipment.

Compressors and Turbines

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

Structural Dynamics & Aeroelasticity

Aerospace Materials & Fatigue

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 recei ves 10 points for hitting the bulls' eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle. AE Outer circle 1 point Inner circle 5 points Bull's eye 10 points The final scores received by the play ers during the tournament are listed in the table below. Round P Q R S 1 5 1 10 1 5 10 10 1 2 1 1 1 5 3 10 10 1 1 4 1 5 5 10 5 10 5 1 1 6 5 10 1 1 7 The most accurate and the most consistent players during the tournament are respectively

Aerospace Materials & Fatigue

It can be inferred from the passage that