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# GATE 2024 Signals and Systems Rank Booster Quiz 26

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Question 1

Consider the LTI system whose impulse response is h(t)=e-atu(t), a=1, input to the system x(t)=e-btu(t), b=y(t) is the output obtained from the system then y’ (1) will be?

Question 2

Consider a signal y(t) which is related to two signals x1(t) and x2(t) by y(t)=x1(t-2) * x2(-t+3) where, x1(t)=e-2tu(t) and x2(t)=e-3tu(t)

Use the properties of the laplace transform to determine the laplace transform Y(s) of y(t).

Question 3

If X(s) = ln.then is __________

Question 4

For the given x(t), if the Laplace transform is X(s), then the value of X(2) is ________ . ( upto 3 decimal places)

Question 5

If Laplace transform of signal x(t) as shown in figure is , then value of k is

Question 6

Let the inverse Laplace transform of F(s) is f(t), the function f(t) at t = 6 will be, if

Question 7

Evaluate the Laplace transform of f(t) if f(t) = t2e–3t(cos 2t)
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