GATE IN format:mcq PYQs & Answers — Page 11

Questions 101–110 of 360. Imported answers require independent review unless marked reviewed.

Topic practice 360 questionsPage 11 of 36

A discrete-time sequence is given by

for

. The zero lag auto-correlation value of

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Match the following measuring devices with their principle of measurement.

Measuring Device	Principle of Measurement
(P) Optical pyrometer	(I) Variation in mutual inductance
(Q) Thermocouple	(II) Change in resistance
(R) Strain gauge	(III) Wavelength of radiated energy
(S) Linear variable differential transformer	(IV) Electromotive force generated by two dissimilar metals

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(P) – (III), (Q) – (IV), (R) – (II), (S) – (I)

(P) – (IV), (Q) – (III), (R) – (II), (S) – (I)

(P) – (III), (Q) – (I), (R) – (IV), (S) – (II)

(P) – (II), (Q) – (IV), (R) – (I), (S) – (III)

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The capacitor shown in the figure has parallel plates, with each plate having an area

. The thickness of the dielectric materials are

and

and their relative permittivities are

and

, respectively. Assume that the fringing field effects are negligible and

is the permittivity of free space.

Diagram for Instrumentation Engineering question 15

is decreased by

, the resultant capacitance becomes

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Among the given options, the simplified form of the Boolean function

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Consider the state-space representation of a system

where

is the state vector,

is the input,

is the system matrix and

is the input matrix. Choose the matrix

from the following options such that the system has a pole at the origin.

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The sinusoidal transfer function corresponding to the pole plot shown in the figure, for

, is

Diagram for Instrumentation Engineering question 18

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A matrix

is constructed by stacking three column vectors

Choose the set of vectors from the following options such that

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The capacitance formed between two concentric spherical metal shells having radii

and

with

Note:

is the permittivity of the medium between the shells.

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A wire of circular cross section with radius

is shown in the figure. The current density is given by

, where

is a constant,

is the radial distance from the axis and

. The total current

in the wire is

Diagram for Instrumentation Engineering question 36

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The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the maximum error (in flow units), respectively are

Diagram for Instrumentation Engineering question 37

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0.12 and 0.14

0.01 and 0.10

0.10 and 0.14

0.04 and 0.12

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