366. 	4	11	+	15		2	−		4	11	−	15		2	is equal to :
     		15		71						15		71

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using (v) of Basic Formulae
   

   Let 4	11	= a and	15	= b.
   	15		71

   
   ∴  Expression
   = (a + b)² – (a – b)²
   = (a² + b² + 2ab) – (a² + b² – 2ab) = 4ab
   

   = 4 × 4	11	×	15	= 4 ×	71	×	15	= 4
   	15		71		15		71

   Correct Option: D

   Using (v) of Basic Formulae
   

   Let 4	11	= a and	15	= b.
   	15		71

   
   ∴  Expression
   = (a + b)² – (a – b)²
   = (a² + b² + 2ab) – (a² + b² – 2ab) = 4ab
   

   = 4 × 4	11	×	15	= 4 ×	71	×	15	= 4
   	15		71		15		71

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367. 17	×	17	+	2	×	2	−	17	×	4	is equal to
     15		15		15		15		15		15

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 10

   
   
   

   4. 11

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression
   

   17	×	17	+	2	×	2	− 2 ×	17	×	2
   15		15		15		15		15		15

   
   

   =		17	−	2		2
   		15		15

   
   

   =		17 − 2		2	=		15		2	= 1
   		15					15

   Correct Option: B

   Expression
   

   17	×	17	+	2	×	2	− 2 ×	17	×	2
   15		15		15		15		15		15

   
   

   =		17	−	2		2
   		15		15

   
   

   =		17 − 2		2	=		15		2	= 1
   		15					15

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368. (4.53 − 3.07)2	+	(3.07 − 2.15)2	+	(2.15 − 4.53)2	is simplified to
     (3.07 − 2.15)(2.15 − 4.53)		(2.15 − 4.53)(4.53 − 3.07)		(4.53 − 3.07)(4.53 − 2.15)

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let (4.53 – 3.07) = a
   (3.07 – 2.15) = b and
   (2.15 – 4.53) = c ∴  a + b + c = 0
   ∴  Expression
   

   =	a2	+	b2	+	c2
   	bc		ac		ab

   
   

   =	a3 + b3 + c3	=	3abc	= 3
   	abc		abc

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

   Correct Option: D

   Let (4.53 – 3.07) = a
   (3.07 – 2.15) = b and
   (2.15 – 4.53) = c ∴  a + b + c = 0
   ∴  Expression
   

   =	a2	+	b2	+	c2
   	bc		ac		ab

   
   

   =	a3 + b3 + c3	=	3abc	= 3
   	abc		abc

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

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369. The simplification of (0.63 + 0.37 + 0.80 yields the result

1. 1. 1.80

   
   
   

   2. 1.81

   
   
   

   3. 1.79

   
   
   

   4. 1.80

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression
   = 0.63 + 0.37 + 0.80
   

   =	63	+	37	+	80
   	99		99		99

   
   

   =	63 + 37 + 80	=	180
   	99		99

   
   

   = 1	81	= 1.81
   	99

   Correct Option: B

   Expression
   = 0.63 + 0.37 + 0.80
   

   =	63	+	37	+	80
   	99		99		99

   
   

   =	63 + 37 + 80	=	180
   	99		99

   
   

   = 1	81	= 1.81
   	99

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370. −	1	−	2	+	4	−	1	+	1	+	3
     	2		3		5		3		5		4
     1	+	2	−	4	+	1	−	1	−	4
     2		3		3		3		5		5

     
     is simplified to

1. 1. −	10
      	3

   
   
   

   2. −	3
      	10

   
   
   

   3. 1

   
   
   

   4. –2

   
   
   

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   Expression
   

   =	− 30 − 40 + 48 − 20 + 12 + 45
   	60
   	30 + 40 − 80 + 20 − 12 − 48
   	60

   
   

   =	105 − 90	= −	15	= −	3
   	90 − 140		50		10

   Correct Option: B

   Expression
   

   =	− 30 − 40 + 48 − 20 + 12 + 45
   	60
   	30 + 40 − 80 + 20 − 12 − 48
   	60

   
   

   =	105 − 90	= −	15	= −	3
   	90 − 140		50		10

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