11. Determine final value of x(t), if laplace transform of x(t) is given
    

    = X(s) =	2s² + 3
    	s² + 5s + 1

1. 1. 0

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. does not exist

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: A

   

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12. A signal x(t) is given by
    
    Which among the following gives the fundamental Fourier term of x(t)?

1. 1. 4	cos		πt	-	π
      π			T		4

   
   
   

   2. 4	cos		πt	+	π
      π			2T		4

   
   
   

   3. 4	sin		πt	-	π
      π			T		4

   
   
   

   4. 4	sin		πt	+	π
      π			2T		4

   
   
   

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1. View Hint View Answer Discuss in Forum

   By property of symmetry of Fourier term of x (t).

   Correct Option: C

   By property of symmetry of Fourier term of x (t).

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13. If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t) * r(t) their convolution, then the function u(t+1) * r(t– 2) is given by

1. 1. 1/2 (t – 1) (t – 2)

   
   
   

   2. 1/2 (t – 1) (t – 2)

   
   
   

   3. 1/2 (t – 1)² u(t – 1)

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: C

   

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14. A random variable X has probability density function f(x) as given below.
    

    ƒ(x) =		a + bx,		0 ≤ x < 1
    		0		otherwise

    
    If the expected value E[X] = 2/3, then Pr[X < 0.5] is _______.

1. 1. 0.125

   
   
   

   2. 0.304

   
   
   

   3. 0.25

   
   
   

   4. 0.259

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: C

   

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15. What is the Laplace transform of x (t) = – e^2t u(t)^* (tu(t)) ?

1. 1. - 1
      s²(s + 2)

   
   
   

   2. - 1
      s²(s - 2)

   
   
   

   3. 1
      s²(s - 2)

   
   
   

   4. - 1
      s(s - 2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   X(s) = L[- e^-2t u(t)] . L[tu(t)]
   Using l[x₁(t) * X₂(t)] = X₁(s). X₂(s), we get
   

   X(s) =	- 1	.	1	= -	1
   	(s - 2)		s²		s²(s - 2)

   Correct Option: B

   X(s) = L[- e^-2t u(t)] . L[tu(t)]
   Using l[x₁(t) * X₂(t)] = X₁(s). X₂(s), we get
   

   X(s) =	- 1	.	1	= -	1
   	(s - 2)		s²		s²(s - 2)

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