36. If m4 +	1	= 119 , then m -		1	= ?
    	m4			m

    
    

1. 1. ± 3
      

   
   
   

   2. 4
      

   
   
   

   3. ± 2
      

   
   
   

   4. ± 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   m4 +	1	= 119
   	m4

   
   

   ⇒		m2 +	1		2	- 2 = 119
   			m2

   
   

   ⇒		m2 +	1		2	= 119 + 2 = 121
   			m2

   
   

   ⇒ m2 +	1	= 11
   	m2

   
   

   ⇒		m -	1		2	+ 2 = 11
   			m

   
   

   ⇒		m -	1		2	= 11 – 2 = 9
   			m

   
   

   ⇒ m -	1	= ± 3
   	m

   Correct Option: A

   m4 +	1	= 119
   	m4

   
   

   ⇒		m2 +	1		2	- 2 = 119
   			m2

   
   

   ⇒		m2 +	1		2	= 119 + 2 = 121
   			m2

   
   

   ⇒ m2 +	1	= 11
   	m2

   
   

   ⇒		m -	1		2	+ 2 = 11
   			m

   
   

   ⇒		m -	1		2	= 11 – 2 = 9
   			m

   
   

   ⇒ m -	1	= ± 3
   	m

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37. If x -	1	= 3 , then the value of x3 -		1	is
    	x			x3

    
    

1. 1. 32
      

   
   
   

   2. 36
      

   
   
   

   3. 40
      

   
   
   

   4. 49

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 9,
   

   x -	1	= 3
   	x

   
   On cubing both sides,
   

   ⇒		x -	1		3	= 27
   			x

   
   

   ⇒ x3 -	1	- 3		x -	1		= 27
   	x3				x

   
   

   ⇒ x3 -	1	- 3 × 3 = 27
   	x3

   
   

   ⇒ x3 -	1	= 27 + 9 = 36
   	x3

   Correct Option: B

   Using Rule 9,
   

   x -	1	= 3
   	x

   
   On cubing both sides,
   

   ⇒		x -	1		3	= 27
   			x

   
   

   ⇒ x3 -	1	- 3		x -	1		= 27
   	x3				x

   
   

   ⇒ x3 -	1	- 3 × 3 = 27
   	x3

   
   

   ⇒ x3 -	1	= 27 + 9 = 36
   	x3

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38. If x +	1	= 3 , then the value of x5 +		1	is
    	x			x5

    
    

1. 1. 322
      

   
   
   

   2. 126
      

   
   
   

   3. 123
      

   
   
   

   4. 113

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1 and 8,
   

   	x +	1		2	= x2 +	1	+ 2
   		x				x2

   
   

   ⇒ x2 +	1	= 9 - 2 = 7
   	x2

   
   Again ,
   

   	x +	1		3	= x3 +	1	+ 3		x +	1
   		x				x3				x

   
   

   ⇒ 27 = x3 +	1	+ 3 × 3
   	x3

   
   

   ⇒ x3 +	1	= 18
   	x3

   
   

   ∴		x2 +	1			x3 +	1		= 7 × 18 = 126
   			x2				x3

   
   

   ⇒ x5 +		x +	1		+	1	= 126
   			x			x5

   
   

   ⇒ x5 +	1	= 126 – 3 = 123
   	x5

   Correct Option: C

   Using Rule 1 and 8,
   

   	x +	1		2	= x2 +	1	+ 2
   		x				x2

   
   

   ⇒ x2 +	1	= 9 - 2 = 7
   	x2

   
   Again ,
   

   	x +	1		3	= x3 +	1	+ 3		x +	1
   		x				x3				x

   
   

   ⇒ 27 = x3 +	1	+ 3 × 3
   	x3

   
   

   ⇒ x3 +	1	= 18
   	x3

   
   

   ∴		x2 +	1			x3 +	1		= 7 × 18 = 126
   			x2				x3

   
   

   ⇒ x5 +		x +	1		+	1	= 126
   			x			x5

   
   

   ⇒ x5 +	1	= 126 – 3 = 123
   	x5

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39. If x is real, x +	1	≠ 0 and x3 +		1	= 0 , then the value of		x +	1		4	is
    	x			x3				x

1. 1. 4
      

   
   
   

   2. 9
      

   
   
   

   3. 16
      

   
   
   

   4. 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 8
   

   	x +	1		3	= x3 +	1	+ 3		x +	1
   		x				x3				x

   
   

   = 3		x +	1
   			x

   
   

   ⇒		x +	1		2	= 3
   			x

   
   

   ∴		x +	1		4	= 3 × 3 = 9
   			x

   Correct Option: B

   Using Rule 8
   

   	x +	1		3	= x3 +	1	+ 3		x +	1
   		x				x3				x

   
   

   = 3		x +	1
   			x

   
   

   ⇒		x +	1		2	= 3
   			x

   
   

   ∴		x +	1		4	= 3 × 3 = 9
   			x

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40. If x +	1	= 5 , then the value of		x4 + 3x3 + 5x2 + 3x + 1
    	x			x4 + 1

1. 1. 	43
      	23

   
   
   

   2. 	47
      	21

   
   
   

   3. 	41
      	23

   
   
   

   4. 	45
      	21

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule1 and 8,
   

   ⇒ x +	1	= 5
   	x

   
   On squaring both sides,
   

   ⇒ x2 +	1	+ 2 = 25
   	x2

   
   

   ⇒ x2 +	1	= 25 - 2 = 23 ...(i)
   	x2

   
   Expression
   

   =	x4 + 3x3 + 5x2 + 3x + 1
   	x4 + 1

   
   

   =	x4 + 1 + 3x3 + 3x + 5x2
   	x4 + 1

   
   
   

   =	23 + 3 × 5 + 5	=		43
   	23			23

   
   

   Correct Option: A

   Using Rule1 and 8,
   

   ⇒ x +	1	= 5
   	x

   
   On squaring both sides,
   

   ⇒ x2 +	1	+ 2 = 25
   	x2

   
   

   ⇒ x2 +	1	= 25 - 2 = 23 ...(i)
   	x2

   
   Expression
   

   =	x4 + 3x3 + 5x2 + 3x + 1
   	x4 + 1

   
   

   =	x4 + 1 + 3x3 + 3x + 5x2
   	x4 + 1

   
   
   

   =	23 + 3 × 5 + 5	=		43
   	23			23

   
   

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