GATE ME year:2021 PYQs & Answers — Page 8

Questions 71–80 of 130. Imported answers require independent review unless marked reviewed.

Consider a vector

in 2-dimensional space. Let its direction (counter-clockwise angle with the positive

-axis) be

. Let

be an eigenvector of a

matrix

with corresponding eigenvalue

. If we denote the magnitude of a vector

, identify the VALID statement regarding

, where

Your answerChoose one option.

Direction of

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The value of

Your answerChoose one option.

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Let

represent the unit circle centered at origin in the complex plane, and complex variable,

. The value of the contour integral

(where integration is taken counter clockwise) is

Your answerChoose one option.

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Let the superscript

represent the transpose operation. Consider the function

, where

and

are

vectors and

is a symmetric

matrix. The stationary point of

Your answerChoose one option.

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A set of jobs A, B, C, D, E, F, G, H arrive at time

for processing on turning and grinding machines. Each job needs to be processed in sequence – first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below.

Job	A	B	C	D	E	F	G	H
Turning (minutes)	2	4	8	9	7	6	5	10
Grinding (minutes)	6	1	3	7	9	5	2	4

If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is

Your answerChoose one option.

A-E-D-F-H-C-G-B

A-D-E-F-H-C-G-B

G-E-D-F-H-C-A-B

B-G-C-H-F-D-E-A

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Consider the following differential equation

The solution of the equation that satisfies the condition

Your answerChoose one option.

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The fundamental thermodynamic relation for a rubber band is given by

, where

is the absolute temperature,

is the entropy,

is the tension in the rubber band, and

is the length of the rubber band. Which one of the following relations is CORRECT:

Your answerChoose one option.

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A factory produces

(

) products, each of which requires processing on

(

) workstations. Let

be the amount of processing time that one unit of the

product requires on the

workstation. Let the revenue from selling one unit of the

product be

and

be the holding cost per unit per time period for the

product. The planning horizon consists of

(

) time periods. The minimum demand that must be satisfied in time period

and the capacity of the

workstation in time period

. Consider the aggregate planning formulation below, with decision variables

(amount of product

sold in time period

(amount of product

manufactured in time period

) and

(amount of product

held in inventory at the end of time period

The capacity constraints and inventory balance constraints for this formulation are

Your answerChoose one option.

and

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Consider a two degree of freedom system as shown in the figure, where

is a rigid uniform rod of length,

and mass,

Diagram for Mechanical Engineering question 30

Assume that the spring deflects only horizontally and force

is applied horizontally at

. For this system, the Lagrangian,

Your answerChoose one option.

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Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is ______ g/kg of dry air.

Your answerChoose one option.

21.4

35.1

21.9

13.6

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GATE ME year:2021 PYQs

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29

Question 30

Question 30