Complete GATE ME 2022 Paper 2 overview, original pages and practice · Timed previous-paper practice

Questions 10–12 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 4 of 22

Question 10

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GAMCQ2 marksNeeds review
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

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Question 11

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MEMCQ1 markNeeds review

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

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Question 12

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MEMCQ1 markNeeds review
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 _____.
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