146. Match list-I with List-II and select the correct answer using the codes given below the list—
     
     
     

1. 1. A B C D
      1 2 3 4

   
   
   

   2. A B C D
      3 4 1 2

   
   
   

   3. A B C D
      4 3 2 1

   
   
   

   4. A B C D
      4 3 1 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   	V(t) = u(t – 1) – u(t – 3)
   	V(t) = δ(t – 1), a → 0
   	V(t) = u(t + 1)
   	V(t) = u(t – 1) – 2u(t – 1) + 2u(t – 2) – 2u(t – 3) + ....

   
   Hence, alternative (B) is the correct choice.

   Correct Option: B

   	V(t) = u(t – 1) – u(t – 3)
   	V(t) = δ(t – 1), a → 0
   	V(t) = u(t + 1)
   	V(t) = u(t – 1) – 2u(t – 1) + 2u(t – 2) – 2u(t – 3) + ....

   
   Hence, alternative (B) is the correct choice.

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147. Which of the following periodic wave forms will have only odd harmonics of sinusoidal wave forms?

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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148. Which one of the following is the Fourier transform of the signal given in figure (B) if the Fourier transform of the signal in figure (A) is given
     

     2	sin ωT1
     	ω

     
     
     

1. 1. 2	sin ωT1	e+ jωT1
      	ω

   
   
   

   2. 2	sin ωT1	e– jωT1
      	ω

   
   
   

   3. 	sin ωT1	e– jωT1
      	ω

   
   
   

   4. 	sin ωT1	e+ jω(T1 – 2)
      	ω

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   F.T[f(t)] =		∞	f(t) e– jωt dω
   		– ∞

   
   

   =		T1	1e– jωt dt
   		– T1

   
   

   =		– 1e– jωt		T1
   		jω		– T1

   
   

   F(jω) =	2	sin ωT1
   	ω

   
   Now, since the required waveform is shifted with T₁ .
   

   F[f(t – T1 )] →	2	sin ωT1 .e– jωT1
   	ω

   
   
   Hence, alternative (B) is the correct choice.

   Correct Option: B

   
   

   F.T[f(t)] =		∞	f(t) e– jωt dω
   		– ∞

   
   

   =		T1	1e– jωt dt
   		– T1

   
   

   =		– 1e– jωt		T1
   		jω		– T1

   
   

   F(jω) =	2	sin ωT1
   	ω

   
   Now, since the required waveform is shifted with T₁ .
   

   F[f(t – T1 )] →	2	sin ωT1 .e– jωT1
   	ω

   
   
   Hence, alternative (B) is the correct choice.

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149. Let u(t) be the unit step function. Which of the wave forms in fig. corresponds to the convolution of u(t) – u(t – 1) with u(t) – u(t – 2)?

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given x₁(t) = u(t) – u(t – 1)
   x₂(t) = u(t) – u(t – 2)
   
   x(t) = x₁(t) * x₂(t)
   
   

   or x(t) =		∞	x1(τ) x2(t – τ )dτ
   		– ∞

   
   
   Hence, alternative (B) is the correct choice.

   Correct Option: B

   Given x₁(t) = u(t) – u(t – 1)
   x₂(t) = u(t) – u(t – 2)
   
   x(t) = x₁(t) * x₂(t)
   
   

   or x(t) =		∞	x1(τ) x2(t – τ )dτ
   		– ∞

   
   
   Hence, alternative (B) is the correct choice.

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150. Figure-I and figure-II show respectively the input x(t) to a linear time-invariant system and the impulse response h(t) of the system.
     
     The output of the system is zero every where except for the time interval—

1. 1. 0 < t < 4

   
   
   

   2. 0 < t < 5

   
   
   

   3. 1 < t < 5

   
   
   

   4. 1 < t < 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given x(t) and h(t) y(t) = x(t) * h(t)
   

   y(t) =		∞	x(τ) h(t – τ)dτ
   		– ∞

   
   
   Thus, we conclude that the output of the system is zero everywhere except for the time interval.
   1 < t < 5

   Correct Option: C

   Given x(t) and h(t) y(t) = x(t) * h(t)
   

   y(t) =		∞	x(τ) h(t – τ)dτ
   		– ∞

   
   
   Thus, we conclude that the output of the system is zero everywhere except for the time interval.
   1 < t < 5

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