2022 · Paper 1

Complete GATE ECE 2022 Paper 1 overview, original pages and practice · Timed previous-paper practice

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

Question 10

Open question

GAMCQ2 marksNeeds review

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.



Let X, Y and Z represent the following operations:

X: rotation of the square by 180 degree with respect to the S-Q axis.

Y: rotation of the square by 180 degree with respect to the P-R axis.

Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZ (2) XY (3) ZZZ

Which one of the following statements is correct as per the information provided above?

Your answerChoose one option.

A.

The sequence of operations (1) and (2) are equivalent

B.

The sequence of operations (1) and (3) are equivalent

C.

The sequence of operations (2) and (3) are equivalent

D.

The sequence of operations (1), (2) and (3) are equivalent

Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Question 11

Open question

ECMCQ1 markNeeds review

Consider the two-dimensional vector field



, where



and



denote the unit vectors along the



-axis and the



-axis, respectively. A contour



in the



-



plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral



is ________.



Your answerChoose one option.

A.



B.



C.



D.



Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Question 12

Open question

ECMCQ1 markNeeds review

Consider a system of linear equations



, where



This system of equations admits ________.

Your answerChoose one option.

A.

a unique solution for



B.

infinitely many solutions for



C.

no solutions for



D.

exactly two solutions for



Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer