What is exp(ja) equal to, where j is the square root of unity?

cos a + jsin a

sin a + jcos a

cos ja + jsin a

cos j + a sin j

Correct Answer : Option (A) : cos a + jsin a

Explanation : This is the corollary of DeMoivre/Euler’s Theorem.

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For a Gaussian process, auto-correlation sequence also implies that

ergodic process

statistical dependence

statistical independence

All of the above

Correct Answer : statistical dependence

Consider the following statements

1. If ensemble and time averages of a random process are identical, the process is ergodic.
2. If ensemble and time average of a random process are not identical, the process is ergodic.
3. An ergodic process is stationary.
4. A stationary process is necessarily ergodic.

Which of the above statements are correct?

1 only

1 and 3 only

1 and 4 only

1, 3 and 4 only

Correct Answer : 1 and 3 only

In RLC circuits the state variables generally selected are

voltages across capacitors

currents through resistances and capacitances

currents through inductances and voltages across capacitances

currents through resistances and voltages across capacitors

Correct Answer : currents through inductances and voltages across capacitances