GATE ECE discipline:electrical-electronics-and-instrumentation PYQs & Answers — Page 65

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Questions 641–650 of 715. Imported answers require independent review unless marked reviewed.

Topic practice 715 questionsPage 65 of 72

If the vector function

is irrotational, then the values of the constants

and

, respectively, are

Your answerChoose one option.

0.3, −2.5, 0.5

0.0, 3.0, 2.0

0.3, 0.33, 0.5

4.0, 3.0, 2.0

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Which one of the following is the general solution of the first order differential equation

, where

are real?

Your answerChoose one option.

, where

is a constant.

, where

is a constant.

, where

is a constant.

, where

is a constant.

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Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is ________.

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Starting with

, the solution of the equation

, after two iterations of Newton-Raphson’s method (up to two decimal places) is __________.

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The minimum value of the function

in the interval

occurs at

________.

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Let

be a continuous time periodic signal with fundamental period

seconds. Let

be the complex Fourier series coefficients of

, where

is integer valued. Consider the following statements about

I. The complex Fourier series coefficients of

are

where

is integer valued II. The complex Fourier series coefficients of

are

where

is integer valued III. The fundamental angular frequency of

rad/s

For the three statements above, which one of the following is correct?

Your answerChoose one option.

only II and III are true

only I and III are true

only III is true

only I is true

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The switch in the circuit, shown in the figure, was open for a long time and is closed at

Diagram for Electronics and Communication Engineering question 31

The current

(in ampere) at

seconds is ________.

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Two discrete-time signals

and

are both non-zero only for

, and are zero otherwise. It is given that

Let

be the linear convolution of

and

. Given that

and

, the value of the expression

is __________.

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Consider the circuit shown in the figure.

Diagram for Electronics and Communication Engineering question 32

The Thevenin equivalent resistance (in

) across P-Q is ________.

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Let

be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by

Let

be the discrete-time Fourier transform (DTFT) of

, where

is the normalized angular frequency in radians. Given that

and

, the value of

(in radians) is equal to __________.

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GATE ECE discipline:electrical-electronics-and-instrumentation PYQs

Question 28

Question 29

Question 29

Question 30

Question 30

Question 31

Question 31

Question 32

Question 32

Question 33