GATE IN kind:question PYQs & Answers — Page 12

Questions 111–120 of 650. Imported answers require independent review unless marked reviewed.

A 2-pole, 50 Hz, 3-phase induction motor supplies power to a certain load at 2970 rpm. The torque-speed curve of this machine follows a linear relationship between synchronous speed and 95 % of synchronous speed. Assume mechanical and stray losses to be zero. If the load torque of the motor is doubled, the new operating speed of the motor, in rpm, is

Your answerChoose one option.

2940

2812

2970

2850

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The figure shows a closed-loop system with a plant

and a lead compensator

. The compensator is designed to place the dominant closed-loop poles at

. From the following options, choose the phase lead that the compensator needs to contribute.

Diagram for Instrumentation Engineering question 47

Your answerChoose one option.

30°

60°

90°

120°

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Let

and

represent continuous-time real-valued signals. If

denotes cross-correlation between

and

, its continuous-time Fourier transform

equals

Note:

and

denote the continuous-time Fourier transforms of

and

, respectively.

Your answerChoose one option.

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Choose the correct statement(s) from the following options, regarding Cauchy’s theorem on complex integration

where C is a simple closed path in a simply connected domain D.

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

Cauchy’s theorem cannot be directly applied to conclude that

when

, and C is the unit circle

is analytic in D, then it can be concluded that

for any simple closed path C in D

The function

must be analytic in D to conclude

for any simple closed path C in D

when

, since the function is not analytic at

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The plant in the feedback control system shown in the figure is

, where

and

. The type(s) of controller

that CANNOT stabilize the plant is/are

Diagram for Instrumentation Engineering question 50

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

proportional (P) controller

integral (I) controller

proportional-integral (PI) controller

proportional-derivative (PD) controller

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Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.

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

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The probability of a student missing a class is 0.1. In a total number of 10 classes, the probability that the student will not miss more than one class is ___ (rounded off to two decimal places).

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A metallic strain-gage (SG) with resistance

is connected as shown in the figure, where

represent the lead wire resistances. The SG has a gauge factor of 2 and nominal resistance

. When the SG is subjected to a tensile strain of

, the resulting change in

. The

value is measured as

. The

and

are the equivalent resistances measured between the terminals 1 and 2, and terminals 2 and 3, respectively.

, and

, the measured value of tensile strain is ___

(rounded off to two decimal places).

Diagram for Instrumentation Engineering question 53

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Let

represent the discrete time Fourier transform of a 4-length sequence

, where

, and

is sampled at

to generate a periodic sequence in

with period 3, where

represents an integer. Let

represent another sequence such that its discrete Fourier transform

is given as

for

. The value of

is_____ (in integer).

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A schematic of a Michelson interferometer, used for the measurement of refractive index of gas, is shown in the figure. The transparent chamber is filled with a gas of refractive index

, where

, at atmospheric pressure. If a 532 nm laser beam produces 30 interference fringes on the screen, then the number of fringes produced by a 632.8 nm laser beam will be ____ (rounded off to one decimal place).

Note: Assume that the effect of beamsplitter width is negligible. The setup is placed in air medium with refractive index equal to 1.

Diagram for Instrumentation Engineering question 55

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GATE IN kind:question PYQs

Question 46

Question 47

Question 48

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54

Question 55