GATE IN kind:question PYQs & Answers — Page 50

Questions 491–500 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 50 of 65

The curve

is such that the tangent to the curve at every point

has a Y-axis intercept

, given by

. Then,

is proportional to

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The function

is given by

where A and

are constants with

and

for

. For

to be a probability density function, the value of A should be equal to

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The dynamics of the state

of a system is governed by the differential equation

Given that the initial state is

, the steady state value of

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A complex function

and its complex conjugate

are both analytic in the entire complex plane, where

and

. The function

is then given by

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In a control system with unity gain feedback, the plant has the transfer function

. Assuming that a controller of the form

is used, where K is a positive constant, the value of p for which the root-locus of the closed-loop system passes through the points

where

, is

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The forward path transfer function

of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance

is given by

where

, the steady-state amplitude of the output

Diagram for Instrumentation Engineering question 31

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In the control system shown in the figure below, a reference signal

is applied at time

. The control system employs a PID controller

and the plant has a transfer function

. If

and

, the steady state value of e is

Diagram for Instrumentation Engineering question 32

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A voltage amplifier is constructed using enhancement mode MOSFETs labeled M1, M2, M3 and M4 in the figure below. M1, M2 and M4 are n-channel MOSFETs and M3 is a p-channel MOSFET. All MOSFETs operate in saturation mode and channel length modulation can be ignored. The low frequency, small signal input and output voltages are

and

respectively and the dc power supply voltage is

. All n-channel MOSFETs have identical transconductance

while the p-channel MOSFET has transconductance

. The expressions for the low frequency small signal voltage gain

Diagram for Instrumentation Engineering question 33

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In the circuit shown below, assume that the comparators are ideal and all components have zero propagation delay. In one period of the input signal

, the fraction of the time for which the output OUT is in logic state HIGH is

Diagram for Instrumentation Engineering question 34

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and

are 2-bit binary numbers. The Boolean function S that satisfies the condition “If X > Y, then S = 1”, in its minimized form, is

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