GATE IN year:2025 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

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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Consider an AC bridge shown in the figure with

, and a detector

. The source voltage is

. At the bridge balance condition, the frequency of the excitation source

is ________ kHz (rounded off to two decimal places).

Diagram for Instrumentation Engineering question 56

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An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is 100 μm × 100 μm. The distance between the plates

μm when both the capacitor charge and spring restoring force are zero as shown in Figure (a). A linear spring of constant k = 0.01 N/m is connected to the movable plate. When charge is supplied to the capacitor using a current source, the top plate moves as shown in Figure (b). The magnitude of minimum charge (Q) required to momentarily close the gap between the plates is ______×

C (rounded off to two decimal places).

Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is

F/m and relative permittivity of air (

) is 1.

Diagram for Instrumentation Engineering question 57

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The resistance of a thermistor is measured to be 2.25 kΩ at 30 °C and 1.17 kΩ at 60 °C. Its material constant

is __________ K (rounded off to two decimal places).

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A feedback control system is shown in the figure.

Diagram for Instrumentation Engineering question 59

The maximum allowable value of

such that the output

, due to any step disturbance signal

, becomes zero at steady-state, is ________ (in integer).

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The circuit given in the figure is driven by a voltage source

V. The system is operating at a frequency of 50 Hz. The transformers are assumed to be ideal. The average power dissipated, in W, in the 50 kΩ resistance is ______ (rounded off to two decimal places).

Diagram for Instrumentation Engineering question 60

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GATE IN year:2025 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60