Q. Consider the following as regards cumulative disribution function F(x):

1. 0 ≤ F(x) ≤ 1
2. F(- ∞) = 0
3. F(∞) = 1
4. F(x1) ≤ F(x2)

If x1 < x2, Out of above which are correct?

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Q. Assertion (A): Fourier series can also be written in exponential form.

Reason (R): sin (n ωt) and cos (n ωt) can be expressed as sum or difference of exponentials.

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Q. A number of impulses spaced fron one another form an impulse train.

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Q. In a complex wave, the negative half of the wave is a reproduction of the positive half wave. Then

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Q. Which one is correct option about ROC?

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Q. Assertion (A): The scalling theroem in Laplace transform relates the scale changes in s domain to the consequent changes in t domain.Reason (R): If

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Q. The integral of a unit impulse is unit step function.

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Q. If X(z) = (1 - αz¯¹)¯¹ and |a| < |z|, the initial value x₀ = 0

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Q. ROC of sequence x[n] = δ[n] is

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Q. The output of a linear system for any input can be computed in which of the following ways?

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Q. For a second order system, damping ratio ζ is such that 0 < ζ <. Then the roots of characteristic equation are

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Q. If f(t)↔ F(jω), and f(t) is real, then F(- jω)

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Q. Fourier transform of the function f(t) = 1 is

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Q. The inverse response of a system h(n) = aⁿ∪(n) what is the condition for the system to be BIBO stable?

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Q. A system has poles at 0.01 Hz, 1 Hz and 80 Hz, zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

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Q. Fourier transform of sgn (t) is

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Q. If the number of ways an event may result ins analysed into m successes and n failures, each equally likely to occur, the probability of success in a single trial is m( m + n)

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Q. If X(z) = (1 - a)z¯¹/[(1 - z¯¹)(1 - az¯¹)] and 1 < |z|, the final value of xk is

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Q. Final value theorem is used to find

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Q. Which one of following is correct condition to check the stability of sysytem in terms of impulse response?

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