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ISRO 2023 Quiz 1

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Question 1

The state equation and the output equation of a control system is given as

, Y = [0 1] [X]

the state transition matrix of the system is given by

Question 2

What is simplified Boolean equation of a logic circuit? If the circuit output is 1 for following inputs?
ABCD = 0010
ABCD = 0110
ABCD = 1000
ABCD = 1100
And output is zero for all other inputs

Question 3

Find the relative permittivity of dielectric material used in parallel plate capacitor if electric flux density D = 15 µC/m2 and energy density is 20 J/m3.

Question 4

A box contains 2 blue, 3 black and 4 red balls. Balls are drawn from the box at random one at a time without replacement. The probability of drawing 2 blue balls first followed by 3 black balls and subsequently 4 red balls is

Question 5

Two signal x(t) and h(t) are given as x(t) = 3cos(2t+90°), h(t) = 5cos(2t+30°) another signal is formed by addition of these two signals, then the power of the new signal is
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