351. If ²√0.014 × 0.14x = 0.014 × 0.14²√y, find the value of x/y .

1. 1. 0.000196

   
   
   

   2. 0.00196

   
   
   

   3. 0.0196

   
   
   

   4. 0.196

   
   
   

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   ²√0.014 × 0.14x
   = 0.014 × 0.14  ²√y
   On squaring both sides,
   0.014 × 0.14x
   = (0.014)² × (0.14)² × y
   

   ∴	x	= 0.014 × 0.14 = 0.00196
   	y

   Correct Option: B

   ²√0.014 × 0.14x
   = 0.014 × 0.14  ²√y
   On squaring both sides,
   0.014 × 0.14x
   = (0.014)² × (0.14)² × y
   

   ∴	x	= 0.014 × 0.14 = 0.00196
   	y

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352. The least fraction to be subtracted from the expression
     

     to make it an integer.

     
     

1. 1. 1

      2

   
   
   

   2. 5

      6

   
   
   

   3. 1

      4

   
   
   

   4. 3

      10

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   =	31	×	30	=	31	= 15	1
   	12		5		2		2

   
   

   ∴  Required answer = 15	1	− 15 =	1
   	2		2

   Correct Option: A

   
   

   =	31	×	30	=	31	= 15	1
   	12		5		2		2

   
   

   ∴  Required answer = 15	1	− 15 =	1
   	2		2

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353. The value of	(2.697 − 0.498)2 + (2.697 + 0.498)2	is
     	2.697 × 2.697 + 0.498 × 0.498

1. 1. 4

   
   
   

   2. 2

   
   
   

   3. 2.199

   
   
   

   4. 3.195

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let 2.697 =a and 0.498 = b
   

   ∴  Expression =	(a − b)2 + (a + b)2
   	a2 + b2

   
   

   =	2(a2 + b2)	= 2
   	a2 + b2

   Correct Option: B

   Let 2.697 =a and 0.498 = b
   

   ∴  Expression =	(a − b)2 + (a + b)2
   	a2 + b2

   
   

   =	2(a2 + b2)	= 2
   	a2 + b2

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354. 8(3.75)3 + 1	is equal to
     (7.5)2 − 6.5

1. 1. 2.75

   
   
   

   2. 9

      5

   
   
   

   3. 4.75

   
   
   

   4. 8.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	8(3.75)3 + 1
   	(7.5)2 − 6.5

   
   

   =	(2 × 3.75)3 + 1
   	(7.5)2 − 7.5 × 1 + 12

   
   

   =	(7.5)3 + 1
   	(7.5)2 − 7.5 × 1 + 12

   
   [a³ + b³ = (a + b)(a² − ab + b² )]
   = 7.5 + 1 = 8.5

   Correct Option: D

   Expression =	8(3.75)3 + 1
   	(7.5)2 − 6.5

   
   

   =	(2 × 3.75)3 + 1
   	(7.5)2 − 7.5 × 1 + 12

   
   

   =	(7.5)3 + 1
   	(7.5)2 − 7.5 × 1 + 12

   
   [a³ + b³ = (a + b)(a² − ab + b² )]
   = 7.5 + 1 = 8.5

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355. The value of	0.125 + 0.027	is
     	0.25 − 0.15 + 0.09

1. 1. 0.2

   
   
   

   2. 0.25

   
   
   

   3. 0.3

   
   
   

   4. 0.8

   
   
   

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   =	(0.5)3 + (0.3)3
   	(0.5)2 − 0.5 × 0.3 + (0.3)2

   
   Let 0.5 = a ,and 0.3 = b
   

   ∴  Expression =	a3 + b3
   	a2 − ab + b2

   
   

   =	(a + b)(a2 − ab + b2)
   	a2 − ab + b2

   
   = a + b = 0.5 + 0.3 = 0.8

   Correct Option: D

   =	(0.5)3 + (0.3)3
   	(0.5)2 − 0.5 × 0.3 + (0.3)2

   
   Let 0.5 = a ,and 0.3 = b
   

   ∴  Expression =	a3 + b3
   	a2 − ab + b2

   
   

   =	(a + b)(a2 − ab + b2)
   	a2 − ab + b2

   
   = a + b = 0.5 + 0.3 = 0.8

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