GATE EE exam:gate PYQs & Answers — Page 6

Questions 51–60 of 715. Imported answers require independent review unless marked reviewed.

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas

and

within the loop are subjected to magnetic fields

, and

, respectively.

Diagram for Electrical Engineering question 51

What is the expression for the induced rms voltage in loop A?

Your answerChoose one option.

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A system is characterized by the following state equation and output equation (

: input,

: state vector,

: output)

What are the values of

and

for which the poles of the transfer function are at

and

Your answerChoose one option.

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A system is represented in state-space form as follows: (

: input,

: state vector,

: output)

Consider the new state vector

What is the state-space representation of the system in terms of the new state vector

Your answerChoose one option.

;

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For the balanced 3-phase transmission line shown, consider the following cases:

Case-1:

and

Case-2:

and

Diagram for Electrical Engineering question 54

Which of the following statements is/are correct about real power loss and reactive power loss in the line?

Your answerSelect all correct options. You can choose more than one.

Real power loss in Case-1 is more than that in Case-2

Real power loss in Case-2 is more than that in Case-1

Reactive power loss in Case-1 is more than that in Case-2

Reactive power loss in Case-2 is more than that in Case-1

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Consider an

orthogonal matrix

with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

The value of the determinant of

is either +1 or −1

The eigenvalues of

have modulus 1

, for all

, where

denotes the Euclidean norm of

, and

, for all distinct

, for all

, where

denotes the Euclidean norm of

, and

, for all

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Consider the system of linear equations:

, where

is an

matrix, and

and

are n-dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

exists

The system of equations

also has a unique solution for

, for

, where

denotes the augmented matrix.

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The resistance values of the Wheatstone bridge shown are: P = 200 Ω, Q = 500 Ω, R = 300 Ω. The battery voltage E = 50 V. The battery has an internal resistance of 1 Ω and the Galvanometer (G) has a resistance of 50 Ω.

Diagram for Electrical Engineering question 57

The value of the resistance S for balanced condition is ______ Ω (Answer in integer)

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A system with two generators G1 and G2 (without generator limits) is shown.

Diagram for Electrical Engineering question 58

The total load on the system is 1184 MW. The expressions for the cost of generation (C₁ and C₂) and real power loss (Pₗₒₛ) are as follows:

C₁(P_G₁) = 1000 + 50P_G₁ + 0.01(P_G₁)² Rs/MWh

C₂(P_G₂) = 2000 + 50P_G₂ + 0.001(P_G₂)² Rs/MWh

Pₗₒₛ = 0.001(P_G₂ − 50)² MW

When the generators are operating at their optimal generation, meeting the total load requirement, the real power loss in the system is ______ MW (Round off to one decimal place)

Consider the Lagrange multiplier λ = 70.25 for optimal generation.

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A balanced three-phase supply is given to a 30 kW, 4-pole, 400 V, 50 Hz, wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted sliprings, the machine runs at 1476 rpm.

When an external non-inductive resistance of 0.27 Ω per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance is ___ Ω

(Round off to two decimal places)

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Consider the two-port network shown. For maximum power transfer to the resistive load (R_L), the value of R_L should be _________ Ω (Round off to two decimal places)

Diagram for Electrical Engineering question 60

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GATE EE exam:gate PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60