GATE IN year:2019 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 2 of 7

are three orthogonal vectors. Given that

and

, the vector

is parallel to

Your answerChoose one option.

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The vector function

is given by

, where

is a scalar function. Then

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-1

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A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is

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4/15

7/16

1/2

8/15

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In the Figures (a) and (b) shown below, the transformers are identical and ideal, except that the transformer in Figure (b) is centre-tapped. Assuming ideal diodes, the ratio of the root-mean-square (RMS) voltage across the resistor

in Figure (a) to that in Figure (b) is

Diagram for Instrumentation Engineering question 4

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The output

of a system is related to its input

where,

and

for

. The transfer function of the system is

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The input

and output

of a discrete-time system are related as

. The condition on

for which the system is Bounded-Input Bounded-Output (BIBO) stable is

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In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time constant

. Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time-constant

. The desired relationship between

and

in a well-designed control system is

Your answerChoose one option.

is much less than

is equal to

is much greater than

is independent of

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The loop-gain function

of a control system with unity feedback is given to be

, where

. If the gain cross-over frequency of the loop-gain function is less than its phase cross-over frequency, the closed-loop system is

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unstable

marginally stable

conditionally stable

stable

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If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit would

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reduce by a factor

reduce by a factor 2

increase by a factor

increase by a factor 2

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In the circuit shown below, the input voltage

is positive. The current (

) - voltage (

) characteristics of the diode can be assumed to be

under the forward bias condition, where

is the thermal voltage and

is the reverse saturation current. Assuming an ideal op-amp, the output voltage

of the circuit is proportional to

Diagram for Instrumentation Engineering question 10

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GATE IN year:2019 PYQs

Question 1

Question 2

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Question 4

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Question 6

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Question 8

Question 9

Question 10