GATE ME topic:mechanical-engineering PYQs & Answers — Page 86

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Questions 851–860 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 86 of 104

Let

be two independent normal random variables with means

and standard deviations

, respectively. Consider

;

. Then,

Your answerChoose one option.

Y is normally distributed with mean 0 and variance 1

Y is normally distributed with mean 0 and variance 5

Y has mean 0 and variance 5, but is NOT normally distributed

Y has mean 0 and variance 1, but is NOT normally distributed

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Let

be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin,

the value of A is

Your answerChoose one option.

2/5

1/2

4/5

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The value of the integral

over the closed surface S bounding a volume V, where

is the position vector and

is the normal to the surface S, is

Your answerChoose one option.

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Let

and

be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then

Your answerChoose one option.

exponentially distributed with mean 1/6

exponentially distributed with mean 2

normally distributed with mean 3/4

normally distributed with mean 1/6

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A point mass is shot vertically up from ground level with a velocity of 4 m/s at time,

. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s

and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

Your answerChoose one option.

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For a position vector

the norm of the vector can be defined as

. Given a function

, its gradient

Your answerChoose one option.

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The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress

(in kPa) is

Diagram for Mechanical Engineering question 29

Your answerChoose one option.

9.45

18.88

37.78

75.50

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In a rigid body in plane motion, the point R is accelerating with respect to point P at

m/s

. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s

) of point R is

Your answerChoose one option.

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An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

Diagram for Mechanical Engineering question 30

Your answerChoose one option.

240

−240

375

−375

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A rigid rod of length 1 m is resting at an angle

as shown in the figure. The end P is dragged with a velocity of U = 5 m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is

Your answerChoose one option.

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GATE ME topic:mechanical-engineering PYQs

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29

Question 30

Question 30