196. If   x +	1	= 2, then the value of   x2 +	1	is equal to ?
     	x		x6

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x +	1	= 2
   	x

   
   ⇒  x² + 1 = 2x ⇒ x² – 2x + 1 = 0
   ⇒  (x – 1)² = 0 ⇒ x – 1 = 0
   ⇒  x = 1
   

   ∴  x2 +	1	= 1 +	2	= 1 + 2 = 3
   	x6		1

   Correct Option: D

   x +	1	= 2
   	x

   
   ⇒  x² + 1 = 2x ⇒ x² – 2x + 1 = 0
   ⇒  (x – 1)² = 0 ⇒ x – 1 = 0
   ⇒  x = 1
   

   ∴  x2 +	1	= 1 +	2	= 1 + 2 = 3
   	x6		1

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197. If a + b = 3, then the value of a³ + b³ + 9ab – 27 is

1. 1. 24

   
   
   

   2. 25

   
   
   

   3. 0

   
   
   

   4. 27

   
   
   

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1. View Hint View Answer Discuss in Forum

   a + b = 3
   On cubing both sides,
   (a + b)³ = 3³
   ⇒  a³ + b³ + 3ab (a + b) = 27
   ⇒  a³ + b³ + 3ab × 3 = 27
   ⇒  a³ + b³ + 9ab – 27 = 0

   Correct Option: C

   a + b = 3
   On cubing both sides,
   (a + b)³ = 3³
   ⇒  a³ + b³ + 3ab (a + b) = 27
   ⇒  a³ + b³ + 3ab × 3 = 27
   ⇒  a³ + b³ + 9ab – 27 = 0

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198. If p = 3 +	1	, the value of		p4 +	1		is :
     	p				p4

1. 1. 81

   
   
   

   2. 27

   
   
   

   3. 120

   
   
   

   4. 119

   
   
   

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1. View Hint View Answer Discuss in Forum

   p = 3 +	1	(Given)
   	p

   
   

   ∴ p -	1	= 3
   	p

   
   On squaring both sides,
   

   ⇒		p -	1		2	= (3)2 = 9
   			p

   
   

   ⇒ p2 +	1	- 2 = 9
   	p2

   
   

   ⇒ p2 +	1	= 9 + 2 = 11
   	p2

   
   On squaring again,
   

   ⇒		p2 +	1		2	= (11)2 = 121
   			p2

   
   

   ⇒ p4 +	1	+ 2 = 121
   	p4

   
   

   ⇒ p4 +	1	= 121 - 2 = 119
   	p4

   Correct Option: D

   p = 3 +	1	(Given)
   	p

   
   

   ∴ p -	1	= 3
   	p

   
   On squaring both sides,
   

   ⇒		p -	1		2	= (3)2 = 9
   			p

   
   

   ⇒ p2 +	1	- 2 = 9
   	p2

   
   

   ⇒ p2 +	1	= 9 + 2 = 11
   	p2

   
   On squaring again,
   

   ⇒		p2 +	1		2	= (11)2 = 121
   			p2

   
   

   ⇒ p4 +	1	+ 2 = 121
   	p4

   
   

   ⇒ p4 +	1	= 121 - 2 = 119
   	p4

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199. If x = 12 and y = 4, then the value of (x + y)^x/y is

1. 1. 48

   
   
   

   2. 1792

   
   
   

   3. 4096

   
   
   

   4. 570

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = 12 and y = 4
   ∴  (x + y)^x/y = (12 + 4)^12/4 = (16)³
   = 16 × 16 × 16 = 4096

   Correct Option: C

   x = 12 and y = 4
   ∴  (x + y)^x/y = (12 + 4)^12/4 = (16)³
   = 16 × 16 × 16 = 4096

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200. If  x = ³√28 , y = ³√27, then the value of x + y –	1	is
     	x2 + xy + y2

1. 1. 8

   
   
   

   2. 7

   
   
   

   3. 6

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = ³√28
   ∴  x³ = (³√28)³ = 28
   Again, y = ³√27
   ∴  y³ = (³√27)³ = 27
   

   ∴  Expression = (x + y) –	1
   	x2 + xy + y2

   
   

   = (x + y) –	(x – y)
   	(x – y)(x2 + xy + y2)

   
   

   = (x + y) –	(x – y)
   	x3 – y3

   
   

   = (x + y) –	(x – y)
   	28 – 27

   
   = x + y – x + y
   = 2y = 2 × ³√27 = 2 × 3 = 6

   Correct Option: C

   x = ³√28
   ∴  x³ = (³√28)³ = 28
   Again, y = ³√27
   ∴  y³ = (³√27)³ = 27
   

   ∴  Expression = (x + y) –	1
   	x2 + xy + y2

   
   

   = (x + y) –	(x – y)
   	(x – y)(x2 + xy + y2)

   
   

   = (x + y) –	(x – y)
   	x3 – y3

   
   

   = (x + y) –	(x – y)
   	28 – 27

   
   = x + y – x + y
   = 2y = 2 × ³√27 = 2 × 3 = 6

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