GATE ME format:mcq PYQs & Answers — Page 18

Questions 171–180 of 599. Imported answers require independent review unless marked reviewed.

Given below are three conclusions drawn based on the following three statements.

Statement 1: All teachers are professors.

Statement 2: No professor is a male.

Statement 3: Some males are engineers.

Conclusion I: No engineer is a professor.

Conclusion II: Some engineers are professors.

Conclusion III: No male is a teacher.

Which one of the following options can be logically inferred?

Your answerChoose one option.

Only conclusion III is correct

Only conclusion I and conclusion II are correct

Only conclusion II and conclusion III are correct

Only conclusion I and conclusion III are correct

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Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.

If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?

Diagram for Mechanical Engineering question 9

Your answerChoose one option.

6 hours 30 minutes

3 hours 45 minutes

4 hours 30 minutes

5 hours 15 minutes

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In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

Your answerChoose one option.

144

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Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

Diagram for Mechanical Engineering question 10

Your answerChoose one option.

2 : 3

1 : 1

3 : 2

2 : 1

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The limit

has a finite value for a real

. The value of

and the corresponding limit

are

Your answerChoose one option.

, and

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is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before change. What is the constant term in the Fourier series expansion of

Diagram for Mechanical Engineering question 11

Your answerChoose one option.

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Solution of

in a square domain

with boundary conditions:

Your answerChoose one option.

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Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point

. The surface integral

of a vector field

over the entire surface

of the cube is _____.

Your answerChoose one option.

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Given a function

in three-dimensional Cartesian space, the value of the surface integral

where

is the surface of a sphere of unit radius and

is the outward unit normal vector on

, is

Your answerChoose one option.

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Consider the definite integral

Let

be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is

. The percentage error is defined as

. The value of

Your answerChoose one option.

2.5

3.5

1.2

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GATE ME format:mcq PYQs

Question 9

Question 9

Question 10

Question 10

Question 11

Question 11

Question 12

Question 12

Question 13

Question 13