26. ³√(333)³ + (333)³ + (334)³ − 3 × 333 × 333 × 334 is equal to

1. 1. 12

   
   
   

   2. 11

   
   
   

   3. 10

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that
   a³ + b³ + c³ – 3abc
   = (a+b+c ) (a² + b² + c² – ab – bc – ca)
   

   =	1	(a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]
   	2

   
   ∴ ³√(333)³ + (333)³ + (334)³ − 3 × 333 × 333 × 334
   =   ³√(1/2)(333 + 333 + 334) [(333 − 333)² + (333 − 334)² + (334 − 333)²]
   =   ³√(1/2) × 1000 × 2
   =   ³√1000
   =   ³√10 × 10 × 10
   =   10

   Correct Option: C

   We know that
   a³ + b³ + c³ – 3abc
   = (a+b+c ) (a² + b² + c² – ab – bc – ca)
   

   =	1	(a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]
   	2

   
   ∴ ³√(333)³ + (333)³ + (334)³ − 3 × 333 × 333 × 334
   =   ³√(1/2)(333 + 333 + 334) [(333 − 333)² + (333 − 334)² + (334 − 333)²]
   =   ³√(1/2) × 1000 × 2
   =   ³√1000
   =   ³√10 × 10 × 10
   =   10

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27. The value of	4 − √0.04	is close to
    	4 + √0.4

1. 1. 0.4

   
   
   

   2. 0.8

   
   
   

   3. 1.0

   
   
   

   4. 1.4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	4 − √0.04
   	4 + √0.4

   
   

   =	4 − 0.02
   	4 + 0.6

   
   

   =	3.8	=	38	=	19
   	4.6		46		23

   
   ≈ 0.83 ≈ 0.8

   Correct Option: A

   Expression =	4 − √0.04
   	4 + √0.4

   
   

   =	4 − 0.02
   	4 + 0.6

   
   

   =	3.8	=	38	=	19
   	4.6		46		23

   
   ≈ 0.83 ≈ 0.8

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28. √	0.25	×	√	0.09	is equal to :
    	0.0009			0.36

1. 1. 5

      6

   
   
   

   2. 7	1
      	6

   
   
   

   3. 7	1
      	3

   
   
   

   4. 8	1
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   =	√	(0.25 × 0.09)
   		0.0009 × 0.36

   
   
   

   =	√	25 × 9 × 1000000
   		9 × 36 × 10000

   
   

   =	5 × 10	=	25	= 8	1
   	6		3		3

   Correct Option: D

   =	√	(0.25 × 0.09)
   		0.0009 × 0.36

   
   
   

   =	√	25 × 9 × 1000000
   		9 × 36 × 10000

   
   

   =	5 × 10	=	25	= 8	1
   	6		3		3

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29. The simplified value of	4	of	5	× 6 + 15 – 10 is
    	15		8

1. 1. 6

   
   
   

   2. 3

   
   
   

   3. 5

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	4	of	5	× 6 + 15 – 10
   	15		8

   
   = 1 + 15 – 10 = 16 – 10 = 6

   Correct Option: A

   Expression =	4	of	5	× 6 + 15 – 10
   	15		8

   
   = 1 + 15 – 10 = 16 – 10 = 6

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30. 

1. 1. 1

   
   
   

   2. 1.5

   
   
   

   3. 2

   
   
   

   4. 2.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   =	79
   	14
   	5 +	9
   		14

   
   

   =	79
   	14
   	5 +	70 + 9
   		14

   
   

   =	79	×	14	= 1
   	14		79

   Correct Option: A

   
   

   =	79
   	14
   	5 +	9
   		14

   
   

   =	79
   	14
   	5 +	70 + 9
   		14

   
   

   =	79	×	14	= 1
   	14		79

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