GATE IN year:2018 PYQs & Answers — Page 2

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

Topic practice 65 questionsPage 2 of 7

Let

be a 3 by 3 matrix with real number entries. The matrix

is such that

. The eigen values of N are

Your answerChoose one option.

0, 0, 0

0, 0, 1

0, 1, 1

1, 1, 1

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Let

and

be two complex variable functions. Here

is the complex conjugate of z. Choose the correct answer.

Your answerChoose one option.

Both

and

are analytic

Only

is analytic

Only

is analytic

Both

and

are not analytic

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and

are two independent random variables with variances 1 and 2, respectively. Let

. The variance of Z is

Your answerChoose one option.

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Consider two functions

and

, where

is real. The smallest value of

for which

is _____.

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Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is

Your answerChoose one option.

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A series R-C circuit is excited by a

V sinusoidal ac voltage source. The locus diagram of the phasor current

A, when C is varied, while keeping R fixed, is

Your answerChoose one option.

Diagram for Instrumentation Engineering question 6

Diagram for Instrumentation Engineering question 6 (figure 2)

Diagram for Instrumentation Engineering question 6 (figure 3)

Diagram for Instrumentation Engineering question 6 (figure 4)

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Thevenin equivalent circuit representation across terminals p-q of the circuit shown in the figure is a

Diagram for Instrumentation Engineering question 7

Your answerChoose one option.

1 V source in series with 150 kΩ

1 V source in parallel with 100 kΩ

2 V source in series with 150 kΩ

2 V source in parallel with 200 kΩ

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A coil having an impedance of

is connected in parallel to a variable capacitor as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor is changed so that parallel resonance occurs. The impedance across terminals p-q at resonance (in

) is _____.

Diagram for Instrumentation Engineering question 8

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Two periodic signals

and

have the same fundamental period of 3 seconds. Consider the signal

. The fundamental period of

in seconds is

Your answerChoose one option.

1.5

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Consider signal

. Let

denote the unit impulse (Dirac-delta) function. The value of the integral

Your answerChoose one option.

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GATE IN year:2018 PYQs

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10