GATE ME format:mcq PYQs & Answers — Page 29

Questions 281–290 of 599. Imported answers require independent review unless marked reviewed.

Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents

Diagram for Mechanical Engineering question 19

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direct shear stress in the coil wire cross-section

torsional shear stress in the coil wire cross-section

combined direct shear and torsional shear stress in the coil wire cross-section

combined direct shear and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section

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Value of

, where

, is equal to

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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

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Direction of

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The value of

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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

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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

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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

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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

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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:

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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

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and

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GATE ME format:mcq PYQs

Question 19

Question 19

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29