GATE EE kind:question PYQs & Answers — Page 55

Questions 541–550 of 715. Imported answers require independent review unless marked reviewed.

Topic practice 715 questionsPage 55 of 72

Let f be a real-valued function of a real variable defined as

for

, and

for

. Which one of the following statements is true?

Your answerChoose one option.

f(x) is discontinuous at x = 0.

f(x) is continuous but not differentiable at x = 0.

f(x) is differentiable but its first derivative is not continuous at x = 0.

f(x) is differentiable but its first derivative is not differentiable at x = 0.

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The value of the directional derivative of the function

at the point (2, −1, 1) in the direction of the vector

Your answerChoose one option.

0.95

0.93

0.9

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The value of the integral

in counter clockwise direction around a circle C of radius 1 with center at the point

Your answerChoose one option.

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In the logic circuit shown in the figure, Y is given by

Diagram for Electrical Engineering question 14

Your answerChoose one option.

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The op-amp shown in the figure is ideal. The input impedance

is given by

Diagram for Electrical Engineering question 15

Your answerChoose one option.

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A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

Your answerChoose one option.

k x(t), where k is an eigenvalue

, where k is an eigenvalue and

is a complex exponential signal

, where

is a complex exponential signal

k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system

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Consider a non-singular 2×2 square matrix A. If trace(A)=4 and trace(

)=5, the determinant of the matrix A is ______ (up to 1 decimal place).

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Let f be a real-valued function of a real variable defined as

, where [x] denotes the largest integer less than or equal to x. The value of

is ______ (up to 2 decimal places).

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In the two-port network shown, the

parameter (where,

, when

) in ohms is __________ (up to 2 decimal places).

Diagram for Electrical Engineering question 19

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The series impedance matrix of a short three-phase transmission line in phase coordinates is

. If the positive sequence impedance is (1 + j 10) Ω, and the zero sequence is (4 + j 31) Ω, then the imaginary part of

(in Ω) is _____ (up to 2 decimal places).

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GATE EE kind:question PYQs

Question 11

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Question 14

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Question 19

Question 20