GATE IN format:nat PYQs & Answers — Page 3

Questions 21–30 of 270. Imported answers require independent review unless marked reviewed.

Topic practice 270 questionsPage 3 of 27

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In the circuit shown, the galvanometer (G) has an internal resistance of 100 Ω. The galvanometer current

is ______ μA (rounded off to the nearest integer).

Diagram for Instrumentation Engineering question 61

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A series RLC circuit resonates at 750 rad/s for inductance L = 20 mH and resistance R = 10

. The uncertainties in the measurement of L and R are 0.8 mH and 0.3

, respectively. The percentage uncertainty in the measurement of quality factor is ______% (rounded off to one decimal place).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In the circuit shown, the switch is opened at

s. The current

ms is ____________ mA (rounded off to two decimal places).

Diagram for Instrumentation Engineering question 63

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE IN format:nat PYQs

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60

Question 61

Question 62

Question 63