391. If x = y = z, then	(x + y + z)2	is equal to
     	x2 + y2 + z2

     
     

1. 1. 4
      

   
   
   

   2. 2
      

   
   
   

   3. 3
      

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = y = z
   

   ∴ Expression =	(x + y + z)2
   	x2 + y2 + z2

   
   

   Expression =	(x + x + x)2
   	x2 + x2 + x2

   
   

   Expression =	9x2	= 3
   	3x2

   
   

   Correct Option: C

   x = y = z
   

   ∴ Expression =	(x + y + z)2
   	x2 + y2 + z2

   
   

   Expression =	(x + x + x)2
   	x2 + x2 + x2

   
   

   Expression =	9x2	= 3
   	3x2

   
   

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392. If x = y = z, then	(x + y + z)2	is equal to
     	x2 + y2 + z2

     
     

1. 1. 4
      

   
   
   

   2. 2
      

   
   
   

   3. 3
      

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = y = z
   

   ∴ Expression =	(x + y + z)2
   	x2 + y2 + z2

   
   

   Expression =	(x + x + x)2
   	x2 + x2 + x2

   
   

   Expression =	9x2	= 3
   	3x2

   
   

   Correct Option: C

   x = y = z
   

   ∴ Expression =	(x + y + z)2
   	x2 + y2 + z2

   
   

   Expression =	(x + x + x)2
   	x2 + x2 + x2

   
   

   Expression =	9x2	= 3
   	3x2

   
   

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393. If x = a (b – c), y = b (c – a), z = c (a – b), then the value of

     x

     3

     +

     y

     3

     +

     z

     3

     is :

     a

     b

     c

     
     

1. 1. 	2xyz
      	abc

      
      

   
   
   

   2. 	xyz
      	abc

      
      

   
   
   

   3. 0
      

   
   
   

   4. 	3xyz
      	abc

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = a (b – c)
   

   ⇒	x	= b – c
   	a

   
   Similarly, y = b (c – a)
   

   ⇒	y	= c – a
   	b

   
   

   and	z	= a – b
   	c

   
   

   ∴	x	+	y	+	z	= b – c + c – a + a – b = 0
   	a		b		c

   
   

   ∴

   x

   3

   +

   y

   3

   +

   z

   3

   = 3 ×

   x

   ×

   y

   ×

   z

   =

   3xyz

   a

   b

   c

   a

   b

   c

   abc

   
   [If a + b + c = 0, a³ + b³ + c³ = 3 abc]
   

   Correct Option: D

   x = a (b – c)
   

   ⇒	x	= b – c
   	a

   
   Similarly, y = b (c – a)
   

   ⇒	y	= c – a
   	b

   
   

   and	z	= a – b
   	c

   
   

   ∴	x	+	y	+	z	= b – c + c – a + a – b = 0
   	a		b		c

   
   

   ∴

   x

   3

   +

   y

   3

   +

   z

   3

   = 3 ×

   x

   ×

   y

   ×

   z

   =

   3xyz

   a

   b

   c

   a

   b

   c

   abc

   
   [If a + b + c = 0, a³ + b³ + c³ = 3 abc]
   

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394. If a² + a + 1 = 0 , then the value of a⁵ + a⁴ + 1 is :
     

1. 1. a²
      

   
   
   

   2. 1
      

   
   
   

   3. 0
      

   
   
   

   4. a + 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   a² + a + 1 = 0
   

   ⇒	a2 + a + 1	= 0
   	a

   
   

   ⇒ a + 1 +	1	= 0 ....(i)
   	a

   
   Expression = a⁵ + a⁴ + 1 = a⁴(a + 1) + 1
   

   Expression = a4		-	1		+ 1
   			a

   
   Expression = -a³ + 1 = 1 - a³
   Expression = (1 – a) (1 + a + a²)
   Expression = (1 – a) × 0 = 0

   Correct Option: C

   a² + a + 1 = 0
   

   ⇒	a2 + a + 1	= 0
   	a

   
   

   ⇒ a + 1 +	1	= 0 ....(i)
   	a

   
   Expression = a⁵ + a⁴ + 1 = a⁴(a + 1) + 1
   

   Expression = a4		-	1		+ 1
   			a

   
   Expression = -a³ + 1 = 1 - a³
   Expression = (1 – a) (1 + a + a²)
   Expression = (1 – a) × 0 = 0

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395. If x -	1	= 2 , then the value of x3 -	1	is :
     	x		x3

     
     

1. 1. 15
      

   
   
   

   2. 2
      

   
   
   

   3. 14
      

   
   
   

   4. 11

   
   
   

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1. View Hint View Answer Discuss in Forum

   x -	1	= 2
   	x

   
   On cubing both sides,
   

   ⇒		x +	1		3	= 23
   			x

   
   

   ⇒ x3 -	1	- 3		x -	1		= 8
   	x3				x

   
   

   ⇒ x3 -	1	= 3 × 2 = 8
   	x3

   
   

   ⇒ x3 -	1	= 8 + 6 = 14
   	x3

   
   

   Correct Option: C

   x -	1	= 2
   	x

   
   On cubing both sides,
   

   ⇒		x +	1		3	= 23
   			x

   
   

   ⇒ x3 -	1	- 3		x -	1		= 8
   	x3				x

   
   

   ⇒ x3 -	1	= 3 × 2 = 8
   	x3

   
   

   ⇒ x3 -	1	= 8 + 6 = 14
   	x3

   
   

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