GATE AE branch:ae PYQs & Answers — Page 62

Questions 611–620 of 650. Imported answers require independent review unless marked reviewed.

Matrix

and vector

are given. If vector

is the solution to the system of equations

, which of the following is true for

Your answerChoose one option.

Solution does not exist

Infinite solutions exist

Unique solution exists

Five possible solutions exist

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Let matrix

. Then for any non-trivial vector

, which of the following is true for the value of

Your answerChoose one option.

K is always less than zero

K is always greater than zero

K is non-negative

K can be anything

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Consider the initial value problem:

and

are the Laplace transforms of

and

respectively, then

is given by:

Your answerChoose one option.

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Let

denote the displacement of a point on a rod. The displacement satisfies the following equation of motion:

with

;

. The value of

is ________ (in three decimal places).

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The equation

has a solution

that is:

Your answerChoose one option.

A polynomial in

Finite series in terms of non-integer fractional powers of

Consists of negative integer powers of

and logarithmic function of

Consists of exponential functions of

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Consider a straight wing with rectangular planform of aspect ratio 10 and with a NACA 0012 airfoil. The span effectiveness factor for this wing is 0.95. Assume the flow to be incompressible and governed by thin airfoil theory. The lift coefficient of this wing, at an angle of attack of 6 deg, is _________ (in three decimal places).

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Consider an incompressible flow over a flat plate with the following approximation to the velocity profile:

where

is the boundary layer thickness and

the free-stream speed. The normalized momentum thickness

for this profile is ____________ (in three decimal places).

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An idealized velocity field is given by

. At point (-1,1,0) and at t = 1, the magnitude of the material acceleration vector of the fluid element is _______________

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A trace from the schlieren photograph of the flow around a corner reveals the edges of the expansion fan as shown below. The leading and trailing edges of the expansion fan make the angles as shown. Assuming

, the angle of the expansion fan (in degrees) is _________ (in two decimal places)

Prandtl Meyer function is given by

Diagram for Aerospace Engineering question 34

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A strong normal shock wave, with a pressure ratio of 29 across it, is travelling into stationary air (

) at T = 280 K in a straight duct (see figure). The magnitude of the velocity of the air induced behind the shock wave is ____________ m/s. (round to nearest integer)

(Gas constant = 287 J/kg.K; Shock wave relations: Pressure ratio:

; Density ratio:

)

Diagram for Aerospace Engineering question 35

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GATE AE branch:ae PYQs

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35