GATE EE format:mcq PYQs & Answers — Page 15

Questions 141–150 of 437. Imported answers require independent review unless marked reviewed.

A continuous-time system that is initially at rest is described by

, where

is the input voltage and

is the output voltage. The impulse response of the system is

Your answerChoose one option.

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The Fourier transform

of the signal

is given by

Which one of the following statements is true?

Your answerChoose one option.

tends to be an impulse as

decreases as

increases.

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The Z-transform of a discrete signal

Which one of the following statements is true?

Your answerChoose one option.

Discrete-time Fourier transform of

converges if

Discrete-time Fourier transform of

converges if

Discrete-time Fourier transform of

converges if

is such that

is a left-sided sequence

Discrete-time Fourier transform of

converges if

is such that

is a right-sided sequence

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For the three-bus power system shown in the figure, the trip signals to the circuit breakers B₁ to B₉ are provided by overcurrent relays R₁ to R₉, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R-L loads with isolation of minimum portion of the network using minimum number of directional relays is

Diagram for Electrical Engineering question 20

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R₃ and R₄ are directional overcurrent relays blocking faults towards bus 2

R₃ and R₄ are directional overcurrent relays blocking faults towards bus 2 and R₇ is directional overcurrent relay blocking faults towards bus 3

R₃ and R₄ are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively, R₇ is directional overcurrent relay blocking faults towards Line 3 and R₅ is directional overcurrent relay blocking faults towards bus 2

R₃ and R₄ are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively.

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The expressions of fuel cost of two thermal generation units as a function of the respective power generation

and

are given as

where a is a constant. For a given value of a, optimal dispatch requires the total load of 290 MW to be shared as

and

. With the load remaining unchanged, the value of a is increased by 10% and optimal dispatch is carried out. The changes in

and the total cost of generation, F (= F₁ + F₂) in Rs/hour will be as follows

Your answerChoose one option.

will decrease and F will increase

Both

and F will increase

will increase and F will decrease

Both

and F will decrease

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The four stator conductors (A, A′, B and B′) of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils a-a′ and b-b′ are formed by connecting the back ends of conductors ‘a’ and ‘a′’ and ‘b’ and ‘b′’, respectively, as shown in figure (ii). The e.m.f. induced in coil a-a′ and coil b-b′ are denoted by Eₐ₋ₐ′ and Eᵦ₋ᆼ′, respectively. If the rotor is rotated at uniform angular speed ω rad/s in the clockwise direction then which of the following correctly describes the Eₐ₋ₐ′ and Eᵦ₋ᆼ′?

Diagram for Electrical Engineering question 22

Your answerChoose one option.

Eₐ₋ₐ′ and Eᵦ₋ᆼ′ have finite magnitudes and are in the same phase

Eₐ₋ₐ′ and Eᵦ₋ᆼ′ have finite magnitudes with Eᵦ₋ᆼ′ lead Eₐ₋ₐ′

Eₐ₋ₐ′ and Eᵦ₋ᆼ′ have finite magnitudes with Eₐ₋ₐ′ lead Eᵦ₋ᆼ′

Eₐ₋ₐ′ = Eᵦ₋ᆼ′ = 0

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The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is 100 kHz. All the components can be assumed to be ideal. The gate signals of switches S₁ and S₂ are shown in figure (ii). Average voltage across the 5 A current source is

Diagram for Electrical Engineering question 23

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10 V

6 V

12 V

20 V

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In the figure, the vectors u and v are related as: Au = v by a transformation matrix A. The correct choice of A is

Diagram for Electrical Engineering question 24

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One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation

. The

is estimated by randomly drawing out 10,000 numbers of samples (

). The estimates

are computed in the following two ways.

Which of the following statements is true?

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The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

Diagram for Electrical Engineering question 36

Your answerChoose one option.

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GATE EE format:mcq PYQs

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 36