# GATE Electrical Engineering Higher Questions and Answers Paper 2013 Part 3

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17. (Topic: Signals and Systems)

(Subtopic: Representation of continuous and discrete‐time signals)

(Sub-Subtopic: Sampling frequency)

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is

(A) 5

(B) 12

(C) 15

(D) 20

18. (Topic: Electric Circuits)

(Subtopic: KCL, KVL, Node and Mesh analysis)

(Sub-Subtopic: Delta and star connection)

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

(A)

(B)

(C)

(D)

19. (Topic: Electric Circuits)

(Subtopic: Ideal current and voltage sources)

(Sub-Subtopic: Voltmeter)

Three moving iron type voltmeters are connected as shown below. Voltmeter readings are, and , as indicated. The correct relation among the voltmeter readings is

(A)

(B)

(C)

(D)

20. (Topic: Engineering Mathematics)

(Subtopic: Linear Algebra)

(Sub-Subtopic: Euler’s formula)

Square roots of , where , are

(A)

(B)

(C)

(D)

21. (Topic: Engineering Mathematics)

(Subtopic: Calculus)

(Sub-Subtopic: Line integral)

Given a vector field , the line integral evaluated along a segment on the x-axis from to is

(A)

(B)

(C)

(D)

22. (Topic: Engineering Mathematics)

(Subtopic: Linear Algebra)

(Sub-Subtopic: Solution of homogeneous equation)

The equation has

(A) No solution

(B) Only one solution

(C) Non-zero unique solution

(D) Multiple solutions

23. (Topic: Analog and Digital Electronics)

(Subtopic: Simple diode circuits)

(Sub-Subtopic: Zener diode)

In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V across, the minimum value of in and the minimum power rating of the Zener diode in mW respectively are

(A) 125 and 125

(B) 125 and 250

(C) 250 and 125

(D) 250 and 250

24. (Topic: Control Systems)

(Subtopic: Transient and Steady‐state analysis of linear time invariant systems)

(Sub-Subtopic: First order system)

The open-loop transfer function of a dc motor is given as. When connected in feedback as shown below, the approximate value of that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is