111. Let y[n] denote the convolution of h[n] and g[n], where
     

     h[n] =		1		n	u[n]
     		2

     
     and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

1. 1. 0

   
   
   

   2. 1/2

   
   
   

   3. 1

   
   
   

   4. 3/2

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Eqⁿ (B) – Eqⁿ (A) × (1/2) gives,
   ⇒ 1/2 g[1] = 0
   ⇒ g[1] = 0

   Correct Option: A

   
   Eqⁿ (B) – Eqⁿ (A) × (1/2) gives,
   ⇒ 1/2 g[1] = 0
   ⇒ g[1] = 0

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112. If x[n] =		1		|n|	-		1		|n|	u[n],
     		3					2

     
     then the region of conver gence (ROC) of its Z-transform in the Z-plane will be

1. 1. 1	< |z| < 3
      3

   
   
   

   2. 1	< |z| <	1
      3		2

   
   
   

   3. 1	< |z| > 3
      2

   
   
   

   4. 1	< |z|
      3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x(n) =		1		|n|	-		1		n	+ u[n]
   		3					2

   
   

   =		1		n	u(n) +		1		-n	u(-n) -		1		n	u(n)
   		3					3					2

   
   

   =		1		n	u(n) + (3)n u(-n) -		1		n	u(n)
   		3					2

   
   

   ROC : |z| >	1	|z| < 3
   	3

   
   

   |z| >	1
   	2

   
   

   Common ROC :	1	< |z| < 3
   	2

   
   

   Correct Option: C

   x(n) =		1		|n|	-		1		n	+ u[n]
   		3					2

   
   

   =		1		n	u(n) +		1		-n	u(-n) -		1		n	u(n)
   		3					3					2

   
   

   =		1		n	u(n) + (3)n u(-n) -		1		n	u(n)
   		3					2

   
   

   ROC : |z| >	1	|z| < 3
   	3

   
   

   |z| >	1
   	2

   
   

   Common ROC :	1	< |z| < 3
   	2

   
   

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113. Given f(z) =	1	-	2
     	z + 1		z + 3

     
     If C is a counterclockwise path in the z-plane such the |z + 1| = 1, the value of 1/2 ∮_C ƒ(z)dz is

1. 1. – 2

   
   
   

   2. – 1

   
   
   

   3. 1

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: C

   

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114. For a periodic signal v(t) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π/4), the fundamental frequency in rad/s is

1. 1. 100

   
   
   

   2. 300

   
   
   

   3. 500

   
   
   

   4. 1500

   
   
   

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1. View Hint View Answer Discuss in Forum

   LCM of T1, T2, T3 will be: =	LCM of numerator	=	2π
   	HCF of denominator.		100

   
   

   ∴ Overall time period =	2π	sec.
   	100

   
   Harmonic frequency = 100 rad/sec.

   Correct Option: A

   LCM of T1, T2, T3 will be: =	LCM of numerator	=	2π
   	HCF of denominator.		100

   
   

   ∴ Overall time period =	2π	sec.
   	100

   
   Harmonic frequency = 100 rad/sec.

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115. A differentiable non-constant even function x(t) has a derivative y(t), and their respective Fourier Transforms ar e X(ω) and Y(ω). Which of the following statements is TRUE?

1. 1. X(ω) and Y(ω) are both real.

   
   
   

   2. X(ω) is real and Y(ω) is imaginary.

   
   
   

   3. X(ω) and Y(ω) are both imaginary.

   
   
   

   4. X(ω) is imaginary and Y(ω) is real.

   
   
   

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1. View Hint View Answer Discuss in Forum

   y(t) =	d	x(t)
   	dt

   
   Y(ω) = jω × (ω)
   ⇒ if X(ω) is real, Y(ω) is imaginary

   Correct Option: B

   y(t) =	d	x(t)
   	dt

   
   Y(ω) = jω × (ω)
   ⇒ if X(ω) is real, Y(ω) is imaginary

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