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Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Test  >  GATE Mock Test Series 2027  >  Test: The State Variable Analysis - 3 - Electrical Engineering (EE) MCQ

GATE Electrical Engineering (EE) Test: The State Variable Analysis - 3


MCQ Practice Test & Solutions: Test: The State Variable Analysis - 3 (20 Questions)

You can prepare effectively for Electrical Engineering (EE) GATE Electrical Engineering (EE) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: The State Variable Analysis - 3". These 20 questions have been designed by the experts with the latest curriculum of Electrical Engineering (EE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 60 minutes
  • - Number of Questions: 20

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Test: The State Variable Analysis - 3 - Question 1
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The state-space representation for a system is

The transfer function Y(s) /U(s) is ​ ​ ​

Detailed Solution: Question 1





Substituting the values,

Test: The State Variable Analysis - 3 - Question 2
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Determine the state-space representation for the transfer function given in question. Choose the state variable as follows

Q.   ​ ​ ​

Detailed Solution: Question 2


(s3 + a2s2 + a1s + a0)C(s) = b0R(s)
Taking the inverse Laplace transform assuming zero initial conditions 



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Test: The State Variable Analysis - 3 - Question 3
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Determine the state-space representation for the transfer function given in question. Choose the state variable as follows

Q. 

Detailed Solution: Question 3

Fourth order hence four state variable

Test: The State Variable Analysis - 3 - Question 4
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A state-space representation of a system is given by

The time response of this system will be​ ​ ​ ​

Detailed Solution: Question 4




Test: The State Variable Analysis - 3 - Question 5
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Detailed Solution: Question 5





Test: The State Variable Analysis - 3 - Question 6
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Detailed Solution: Question 6



Test: The State Variable Analysis - 3 - Question 7
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Consider the system shown in fig.

The controllability matrix is

Detailed Solution: Question 7



Test: The State Variable Analysis - 3 - Question 8
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Consider the system shown in fig.

The observability matrix is

Detailed Solution: Question 8


Test: The State Variable Analysis - 3 - Question 9
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Consider the system shown in fig.

The system is

Detailed Solution: Question 9

det CM = 0. Hence system is not controllable. det OM = 1. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 10
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Consider the system shown in fig.

Q. The controllability matrix for this system is

Detailed Solution: Question 10




Test: The State Variable Analysis - 3 - Question 11
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Consider the system shown in fig.

The observability matrix is

Detailed Solution: Question 11




Test: The State Variable Analysis - 3 - Question 12
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Consider the system shown in fig.

Q. The system is

Detailed Solution: Question 12

Since the determinant is not zero, the 3 x 3 matrix is nonsingular and system is controllable


The rank of OM is 3. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 13
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A state flow graph is shown in fig.

​ ​ ​

Q.The state and output equation for this system is

Detailed Solution: Question 13

Test: The State Variable Analysis - 3 - Question 14
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A state flow graph is shown in fig.

The system is

Detailed Solution: Question 14

det OM = 0. Thus system is not observable

det CM = -1. Thus system is controllable.

Test: The State Variable Analysis - 3 - Question 15
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Consider the network shown in fig. The state-space representation for this network is

Detailed Solution: Question 15


vc and iL are state variable.

Hence equation are 

Test: The State Variable Analysis - 3 - Question 16
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For the network shown in fig. The output is

iR(t). The state space representation is

Detailed Solution: Question 16


Hence v1 and i3 are state variable.



Test: The State Variable Analysis - 3 - Question 17
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Consider the network shown in fig. This system may be represented in state space representation 

Q. The state variable may be

Detailed Solution: Question 17

Energy storage elements are capacitor and inductor. vC and iL are available in differential form and linearly independent. Hence vC and iL are suitable for state-variable.

Test: The State Variable Analysis - 3 - Question 18
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Consider the network shown in fig. This system may be represented in state space representation  

Q. If state variable are chosen as in previous question, then the matrix A is  

Detailed Solution: Question 18




.....(i)
.....(ii)
Solving equation (i) and (ii)

Test: The State Variable Analysis - 3 - Question 19
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Consider the network shown in fig. This system may be represented in state space representation  

Q. The matrix B is  

Detailed Solution: Question 19

Test: The State Variable Analysis - 3 - Question 20
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Consider the network shown in fig.

Q. The state variable may be

Detailed Solution: Question 20

There are three energy storage elements, hence 3 variable. i2 ,i4 and vo are available in differentiated form hence these are state variable.

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About this Electrical Engineering (EE) Practice Test

This test contains 20 MCQs on The State Variable Analysis - 3 with detailed solutions for each question. It is part of the GATE Electrical Engineering (EE) Mock Test Series 2027 course on EduRev, designed to align with the current Electrical Engineering (EE) syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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If you found this The State Variable Analysis - 3 MCQ Test helpful, you can further enhance your Electrical Engineering (EE) preparation with in-depth courses on EduRev, for all the subjects and topics available in GATE Electrical Engineering (EE) Mock Test Series 2027 course. The course offers:
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