96. Simplify :   999	998	× 999 + 999
    	999

1. 1. 999997

   
   
   

   2. 999998

   
   
   

   3. 99998

   
   
   

   4. 999994

   
   
   

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1. View Hint View Answer Discuss in Forum

   	999 +	998		999 + 999
   		999

   
   = (999)² + 998 + 999
   = (1000 – 1)² + 998 + 999
   = 1000000 +1–2000+998+ 999
   = 999998

   Correct Option: B

   	999 +	998		999 + 999
   		999

   
   = (999)² + 998 + 999
   = (1000 – 1)² + 998 + 999
   = 1000000 +1–2000+998+ 999
   = 999998

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97. Simplify :

1. 1. 3

      4

   
   
   

   2. 1

      2

   
   
   

   3. 3

      5

   
   
   

   4. 3

      7

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   =	3					=	3
   	4 +	5 × 8					4 +	8
   		55						11

   
   

   =	3
   	44 + 8
   	11

   
   

   =	3 × 11	=	33
   	52		52

   
   

   ∴  Expression =	33	−	3	÷	1	of 1	1	+ 1	3
   	52		5		2		5		26

   
   

   =	33	−	3	÷	1	×	6	+	29
   	52		5		2		5		26

   
   

   =	33	−	3	×	5	+	29
   	52		5		3		26

   
   

   =	33	− 1 +	29
   	52		26

   
   

   =	33 − 52 + 58	=	39	=	3
   	52		52		4

   Correct Option: A

   
   

   =	3					=	3
   	4 +	5 × 8					4 +	8
   		55						11

   
   

   =	3
   	44 + 8
   	11

   
   

   =	3 × 11	=	33
   	52		52

   
   

   ∴  Expression =	33	−	3	÷	1	of 1	1	+ 1	3
   	52		5		2		5		26

   
   

   =	33	−	3	÷	1	×	6	+	29
   	52		5		2		5		26

   
   

   =	33	−	3	×	5	+	29
   	52		5		3		26

   
   

   =	33	− 1 +	29
   	52		26

   
   

   =	33 − 52 + 58	=	39	=	3
   	52		52		4

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98. Simplify :

1. 1. 0.9

   
   
   

   2. 0.95

   
   
   

   3. 0.095

   
   
   

   4. 0.082

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =
   
   

   = 3.5 ×		1
   	3 +	2
   		3

   
   

   = 3.5 ×	1
   	9 + 2
   	3

   
   

   =	3.5 × 3	=	10.5	= 0.95
   	11		11

   Correct Option: B

   Expression =
   
   

   = 3.5 ×		1
   	3 +	2
   		3

   
   

   = 3.5 ×	1
   	9 + 2
   	3

   
   

   =	3.5 × 3	=	10.5	= 0.95
   	11		11

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99. The simplified value of	(0.0539 − 0.002) × 0.4 + 0.56 × 0.07	= ?
    	0.04 × 0.25

1. 1. 59.96

   
   
   

   2. 0.5996

   
   
   

   3. 5.996

   
   
   

   4. 599.6

   
   
   

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1. View Hint View Answer Discuss in Forum

   ? =	(0.0539 − 0.002) × 0.4 + 0.56 × 0.07
   	0.04 × 0.25

   
   

   =	0.0519 × 0.4 + 0.0392
   	0.01

   
   

   =	0.2076 + 0.0392
   	0.01

   
   

   =	0.05996	= 5.996
   	0.01

   Correct Option: C

   ? =	(0.0539 − 0.002) × 0.4 + 0.56 × 0.07
   	0.04 × 0.25

   
   

   =	0.0519 × 0.4 + 0.0392
   	0.01

   
   

   =	0.2076 + 0.0392
   	0.01

   
   

   =	0.05996	= 5.996
   	0.01

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100. The sum of the cubes of two numbers in the ratio 3 : 4 is 5824. The sum of the numbers is :

1. 1. (5824)^1/3

   
   
   

   2. 28

   
   
   

   3. 24

   
   
   

   4. 14

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 3x and 4x.
   According to the question,
   (3x)³ + (4x)³ = 5824
   ⇒  27x³ + 64x³ = 5824
   ⇒  91x³ = 5824
   

   ⇒  x3 =	5824	= 64
   	91

   
   ⇒  x = ³√64 = 4
   ∴  Sum of numbers
   = 3x + 4x = 7x
   = 7 × 4 = 28

   Correct Option: B

   Let the numbers be 3x and 4x.
   According to the question,
   (3x)³ + (4x)³ = 5824
   ⇒  27x³ + 64x³ = 5824
   ⇒  91x³ = 5824
   

   ⇒  x3 =	5824	= 64
   	91

   
   ⇒  x = ³√64 = 4
   ∴  Sum of numbers
   = 3x + 4x = 7x
   = 7 × 4 = 28

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