6. A linear system has the transfer functi on
   

   H(jω) =	1
   	(jω + 1)

   
   When it is subjected to an input white noise process with a constant spectral density A, the spectral density of the output will be

1. 1. A
      (jω + 1)

   
   
   

   2. A
      (jω + 1)²

   
   
   

   3. A
      (ω² + 1)

   
   
   

   4. A
      √(ω² + 1)

   
   
   

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   NA

   Correct Option: B

   NA

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7. The period of the function cos π/4 (t– 1) is

1. 1. 1	s
      8

   
   
   

   2. 8 s

   
   
   

   3. 4 s

   
   
   

   4. 1	s
      4

   
   
   

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   2π	=	π	,
   T		4

   
   ⇒ T = 8 sec

   Correct Option: B

   2π	=	π	,
   T		4

   
   ⇒ T = 8 sec

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8. The Fourier series representation of a periodic current is
   [2 + 6 √2 cos ωt + √48sin 2ωt]A.
   The effective value of the current is

1. 1. (2 + 6 + √24)A

   
   
   

   2. 8A

   
   
   

   3. 6A

   
   
   

   4. 2A

   
   
   

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   NA

   Correct Option: B

   NA

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9. Which of the following cannot be the Fourier series expansion of a periodic signal?

1. 1. x(t) = 2cos t + 3 cos 3t

   
   
   

   2. x(t) = 2cos πt + 7 cos t

   
   
   

   3. x(t) = cos t + 0.5

   
   
   

   4. x(t) = 2cos 1.5πt + sin 3.5πt

   
   
   

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   x(t) = 2cos πt + 7 cost, does not satisfy the Dirichlet condition, therefore, it can't be expanded as Fourier series.

   Correct Option: B

   x(t) = 2cos πt + 7 cost, does not satisfy the Dirichlet condition, therefore, it can't be expanded as Fourier series.

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10. Consider the voltage waveform shown in the figure. The equation for V(t) is
    

1. 1. u (t – 1) + u (t – 2) + u (t – 3)

   
   
   

   2. u (t – 1) + 2u (t – 2) + 3u (t – 3)

   
   
   

   3. u (t) + u (t – 1) + u (t – 2) + u (t – 4)

   
   
   

   4. u (t– 1) + u (t – 2) + u (t – 3) – 3u (t – 4)

   
   
   

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   NA

   Correct Option: D

   NA

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