411. If x = 0.5 and y = 0.2, then value of √0.6 × (3y)^x is equal to

1. 1. 1.0

   
   
   

   2. 0.5

   
   
   

   3. 0.6

   
   
   

   4. 1.1

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = 0.5 and y = 0.2 (Given)
   ∴  √0.6 × (3y)^x
   = √0.6 × (3 × 0.2)^0.5
   = √0.6 × (0.6)^1/2
   = √0.6 × 0.6 = 0.6

   Correct Option: C

   x = 0.5 and y = 0.2 (Given)
   ∴  √0.6 × (3y)^x
   = √0.6 × (3 × 0.2)^0.5
   = √0.6 × (0.6)^1/2
   = √0.6 × 0.6 = 0.6

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412. The value of	(243)n/5.32n + 1	is
     	9n.3n − 1

1. 1. 1

   
   
   

   2. 9

   
   
   

   3. 3

   
   
   

   4. 3n

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	(243)n/5.32n + 1
   	9n.3n − 1

   
   

   =	(35)n/5×32n + 1
   	(32)n × 3n − 1

   
   

   =	3n × 32n + 1
   	32n × 3n − 1

   
   

   =	3n + 2n + 1	=	33n + 1
   	32n + n − 1		33n − 1

   
   = 3^{3n + 1 − 3n + 1} = 3² = 9

   Correct Option: B

   Expression =	(243)n/5.32n + 1
   	9n.3n − 1

   
   

   =	(35)n/5×32n + 1
   	(32)n × 3n − 1

   
   

   =	3n × 32n + 1
   	32n × 3n − 1

   
   

   =	3n + 2n + 1	=	33n + 1
   	32n + n − 1		33n − 1

   
   = 3^{3n + 1 − 3n + 1} = 3² = 9

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413. If	1	×	2	×	3	×	4	×	5	×.....×	31	×	1	, the value of x is
     	4		6		8		10		12		64		2x

1. 1. 31

   
   
   

   2. 32

   
   
   

   3. 36

   
   
   

   4. 37

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	×	2	×	3	×	4	×	5	×.....×	31	=	1
   4		6		8		10		12		64		2x

   
   

   ⇒	1	×	1	×	1	×.....to 30 terms ×	1	=	1
   	2		2		2		64		2x

   
   

   ⇒	1	×	1	=	1
   	230		26		2x

   
   

   ⇒	1	=	1	⇒ x = 36
   	236		2x

   Correct Option: C

   1	×	2	×	3	×	4	×	5	×.....×	31	=	1
   4		6		8		10		12		64		2x

   
   

   ⇒	1	×	1	×	1	×.....to 30 terms ×	1	=	1
   	2		2		2		64		2x

   
   

   ⇒	1	×	1	=	1
   	230		26		2x

   
   

   ⇒	1	=	1	⇒ x = 36
   	236		2x

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414. If 3^{x + 3} + 7 = 250, then x is equal to

1. 1. 5

   
   
   

   2. 3

   
   
   

   3. 2

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   3^{x + 3} = 250
   ⇒  3^{x + 3} = 243 ⇒ 3^{x + 3} = 3⁵
   ⇒  x + 3 = 5 ⇒ x = 2

   Correct Option: C

   3^{x + 3} = 250
   ⇒  3^{x + 3} = 243 ⇒ 3^{x + 3} = 3⁵
   ⇒  x + 3 = 5 ⇒ x = 2

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415. If	2p	=	1	, p ≠ 0, then the value of p +	1	is
     	p2 − 2p + 1		4		p

1. 1. 4

   
   
   

   2. 5

   
   
   

   3. 10

   
   
   

   4. 12

   
   
   

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1. View Hint View Answer Discuss in Forum

   2p	=	1
   p2 − 2p + 1		4

   
   

   ⇒	p2 − 2p + 1	= 4
   	2p

   
   

   ⇒	p2 − 2p + 1	= 8
   	p

   
   

   ⇒	p2	−	2p	+	1	= 8
   	p		p		p

   
   

   ⇒  p +	1	= 8 + 2 = 10
   	p

   Correct Option: C

   2p	=	1
   p2 − 2p + 1		4

   
   

   ⇒	p2 − 2p + 1	= 4
   	2p

   
   

   ⇒	p2 − 2p + 1	= 8
   	p

   
   

   ⇒	p2	−	2p	+	1	= 8
   	p		p		p

   
   

   ⇒  p +	1	= 8 + 2 = 10
   	p

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