81. d²y(t)	+ 2	dy(t)	+ 5y(t)	dx(t)	, y(0-) = 2,	dy(t)			=, x(t) = u(t)
    dt²		dt		dt		dt		t-0

1. 1. 1	e-t sin t u(t)
      2

   
   
   

   2. 2e^{– t} cos t u(t)

   
   
   

   3. 2e– t cost u(t) +	1	e-t sin t u(t)
      	2

   
   
   

   4. 1	e-t cos t u(t - 1) + 2e-t sin t u(t - 1)
      2

   
   
   

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1. View Hint View Answer Discuss in Forum

   s²Y(s) – 2s + 2sY(s) – 2 + 5Y(s) = 1
   ∴ (s² + 2s + 5) Y(s) = 3 + 2s
   

   ⇒ Y(s) =	2s + 3
   	s² + 2s + 5

   
   

   =	2(s + 1)	+	1
   	(s + 1)² + 2²		(s + 1)² + 2²

   
   Inverse Laplace transform given,
   

   ⇒ 2e– t cost u(t) +	1	e-t sin t u(t)
   	2

   Correct Option: C

   s²Y(s) – 2s + 2sY(s) – 2 + 5Y(s) = 1
   ∴ (s² + 2s + 5) Y(s) = 3 + 2s
   

   ⇒ Y(s) =	2s + 3
   	s² + 2s + 5

   
   

   =	2(s + 1)	+	1
   	(s + 1)² + 2²		(s + 1)² + 2²

   
   Inverse Laplace transform given,
   

   ⇒ 2e– t cost u(t) +	1	e-t sin t u(t)
   	2

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82. For the signal ƒ(t) = 3 sin 8πt + 6 sin 12πt + sin 14πt, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is __________.

1. 1. 10 sample/sec

   
   
   

   2. 1.4 sample/sec

   
   
   

   3. 14 sample/sec

   
   
   

   4. 2.4 sample/sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   Maximum frequency content in 7Hz
   ⇒ Nyquist rate = 2 × 7 = 14 sample/sec
   

   Correct Option: C

   Maximum frequency content in 7Hz
   ⇒ Nyquist rate = 2 × 7 = 14 sample/sec
   

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83. A movi ng aver age function is given by If input u is sinusoidal signal of frequency 1/2T Hz then in steady state the output y will lag u (in degrees) by _______.

1. 1. 30°

   
   
   

   2. 90°

   
   
   

   3. 45°

   
   
   

   4. 180°

   
   
   

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1. View Hint View Answer Discuss in Forum

   u(τ) = sin (ωτ)
   

   τ = 2πƒ = 2π.	1	=	π
   	2T		T

   
   ωT = π
   
   

   =	1	[cos ω(t - T) - cosω t]
   	π

   
   

   =	1	[cosωt cos ωT + sinωt sinωT - cosωt]
   	π

   
   

   y(t) = -	1	=	π
   	2T		T

   
   

   y(t) = -	2	cosωt =	2	sinω(90 + ωt)
   	π		π

   
   x(t) = sin ωt
   φ = 90°

   Correct Option: B

   u(τ) = sin (ωτ)
   

   τ = 2πƒ = 2π.	1	=	π
   	2T		T

   
   ωT = π
   
   

   =	1	[cos ω(t - T) - cosω t]
   	π

   
   

   =	1	[cosωt cos ωT + sinωt sinωT - cosωt]
   	π

   
   

   y(t) = -	1	=	π
   	2T		T

   
   

   y(t) = -	2	cosωt =	2	sinω(90 + ωt)
   	π		π

   
   x(t) = sin ωt
   φ =

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84. y[n] denotes output and x [n] denotes input of a discrete-time system given by the difference equation
    y [n] – 0.8 y [n – 1] = x[n] + 1.25 x [n + 1]. Its right- sided impulse response is

1. 1. causal

   
   
   

   2. unbounded

   
   
   

   3. periodic

   
   
   

   4. non-negative

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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85. The discrete-time signal
    
    where ↔ denotes a transform-pair relationship, is orthogonal to the signal

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. y₄ [n] ↔ Y₄(z) = 2z^–4 + 3z^–2 + 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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