161. Given Z-transform,
     

     X(z) =	1	, |z| <	1
     	1 - 4z-2		4

     
     The time signal x(t) will be

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   Correct Option: C

   
   

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162. Given Z-transform,
     

     X(z) =	3z² -	1	z	, |z| > 4
     		4
     	z² - 16

     
     The time signal x(t) will be

1. 1. 	49	(-4)n +	47	(-4)n		u[n]
      	32		32

   
   
   

   2. 	49	4n +	47	4n		u[n]
      	32		32

   
   
   

   3. 49	(-4)n u[-n] +	47	4n u[n]
      32		32

   
   
   

   4. 49	4n u[n] +	47	(-4)n u[-n]
      32		32

   
   
   

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1. View Hint View Answer Discuss in Forum

   X(z) =	3z² -	1	z-1		=	49			=	47
   		4				32				32
   	z² - 16					1 + 4z-1				1 - 4z-1

   
   

   ⇒ x[n] =		49	(-4)n +	47	4n		u[n]
   		32		32

   Correct Option: A

   X(z) =	3z² -	1	z-1		=	49			=	47
   		4				32				32
   	z² - 16					1 + 4z-1				1 - 4z-1

   
   

   ⇒ x[n] =		49	(-4)n +	47	4n		u[n]
   		32		32

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163. Given Z-transform,
     

     X(z) =	z² - 3z			,	1			< |z| < 2
     	z²	3	z-1		2
     		2

     
     The time signal x(t) will be

1. 1. -	1	u[n] - 2n+1 u[-n-1]
      	2n

   
   
   

   2. -	1	u[n] - 2n+1 u[n+1]
      	2n

   
   
   

   3. 	1	u[n] + 2n+1 u[n+1]
      	2n

   
   
   

   4. 	1	u[n] - 2n-1 u[-n-1]
      	2n

   
   
   

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1. View Hint View Answer Discuss in Forum

   X(z) =	z² - 3z					=		1 - 3z-1
   	z² +	3	z-1				1 +	3	z-1 - z-1
   		2						2

   
   

   =	2	=	1			, ROC :	1	< |z| < 2
   	1 + 2z-1		1 -	1	z-1		2
   				2

   
   ⇒ x[n] = – 2(2)ⁿ u[– n – 1] – 1/2ⁿ u[n]

   Correct Option: A

   X(z) =	z² - 3z					=		1 - 3z-1
   	z² +	3	z-1				1 +	3	z-1 - z-1
   		2						2

   
   

   =	2	=	1			, ROC :	1	< |z| < 2
   	1 + 2z-1		1 -	1	z-1		2
   				2

   
   ⇒ x[n] = – 2(2)ⁿ u[– n – 1] – 1/2ⁿ u[n]

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164. Z-transform of x[n] = cos		π	n		u[n] will be .
     		3

1. 1. z	(2z - 1)	, 0 < |z| < 1
      2	(z² - z + 2)

   
   
   

   2. z	(2z - 1)	|z| > 1
      2	(z² - z + 2)

   
   
   

   3. z	(1 - 2z)	, 0 < |z| < 1
      2	(z² - z + 2)

   
   
   

   4. z	(1 - 2z)	|z| > 1
      2	(z² - z + 2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   Correct Option: B

   
   

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165. The Z-transform of
     

     x[n] =		2		|n|	will be .
     		3

1. 1. - 5z	, -	3	< z < -	3
      (2z - 3)(3z - 2)		2		3

   
   
   

   2. - 5z	,	2	< |z| <	3
      (2z - 3)(3z - 2)		3		2

   
   
   

   3. 5z	,	2	< |z| <	3
      (2z - 3)(3z - 2)		2		2

   
   
   

   4. 5z	, -	3	< |z| < -	2
      (2z - 3)(3z - 2)		2		3

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   Correct Option: B

   
   

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