GATE AE exam:gate PYQs & Answers — Page 59

Questions 581–590 of 650. Imported answers require independent review unless marked reviewed.

A cantilever beam having a rectangular cross-section of width 60 mm and depth 100 mm, is made of aluminum alloy. The material mechanical properties are: Young’s modulus, E = 73 GPa and ultimate stress,

= 480 MPa. Assuming a factor of safety of 4, the maximum bending moment (in kN-m) that can be applied on the beam is ______ (accurate to one decimal place).

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The components of stress in a body under plane stress condition, in the absence of body forces, is given by:

;

and

. The coefficient, A, such that the body is under equilibrium is ____ (accurate to one decimal place).

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An axial compressor rotor with 50 % degree of reaction, operates with an axial velocity of 200 m/s. The absolute flow angle at the inlet of the rotor is 22° with reference to the axial direction. If the axial velocity is assumed to remain constant through the rotor, the magnitude of the relative velocity (in m/s) at the rotor exit is __________ (accurate to one decimal place).

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The relative velocity of air leaving a straight radial impeller of a centrifugal compressor is 100 m/s. If the impeller tip speed is 200 m/s, for a slip free operation, the absolute velocity (in m/s) at the impeller exit is ________ (accurate to one decimal place).

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An aircraft wind tunnel model, having a pitch axis mass moment of inertia (

) of 0.014 kg-m

, is mounted in such a manner that it has pure pitch motion about its centre of gravity, where it is supported through a frictionless hinge. If the pitching moment (M) derivative with respect to angle of attack (

), denoted by

, is −0.504 N-m/rad and the pitching moment (M) derivative with respect to pitch rate (q), denoted by

, is −0.036 N-m/(rad/s), the damping ratio of the resulting motion due to an initial disturbance in pitch angle is approximately ________ (accurate to three decimal places).

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Given the vectors

;

, the vector

that is perpendicular to both

and

is given by:

Your answerChoose one option.

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The value of the integral

, with C the boundary of the square

, is __________

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Let

be a unit vector that is a function of the parameter

. Then

__________

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The eigenvalues

and eigenfunctions

of the Sturm-Liouville problem

are given by:

Your answerChoose one option.

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3-point Gaussian integration formula is given by:

with

;

. This formula exactly integrates

Your answerChoose one option.

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GATE AE exam:gate PYQs

Question 51

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Question 54

Question 55

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Question 5