461. If	√7 − 2	= a√7 + b,   then the value of a is
     	√7 + 2

1. 1. 11

      3

   
   
   

   2. −	4
      	3

   
   
   

   3. 4

      3

   
   
   

   4. −	4√7
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   √7 − 2	=	√7 − 2	×	√7 − 2
   √7 + 2		√7 + 2		√7 − 2

   (Rationalising the denominator)
   

   =	(√7 − 2)2	=	7 + 4 − 4√7
   	7 − 4		3

   
   

   =	11	−	4√7
   	3		3

   
   

   ∴	√7 − 2	= a√7 + b
   	√7 + 2

   
   

   =	11	−	4	√7 = a√7 + b
   	3		3

   
   Clearly,
   

   a = −	4	and b =	11
   	3		3

   Correct Option: B

   √7 − 2	=	√7 − 2	×	√7 − 2
   √7 + 2		√7 + 2		√7 − 2

   (Rationalising the denominator)
   

   =	(√7 − 2)2	=	7 + 4 − 4√7
   	7 − 4		3

   
   

   =	11	−	4√7
   	3		3

   
   

   ∴	√7 − 2	= a√7 + b
   	√7 + 2

   
   

   =	11	−	4	√7 = a√7 + b
   	3		3

   
   Clearly,
   

   a = −	4	and b =	11
   	3		3

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462. If (125)^x = 3125, then the value of x is

1. 1. 1

      5

   
   
   

   2. 3

      5

   
   
   

   3. 5

      3

   
   
   

   4. 5

      7

   
   
   

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1. View Hint View Answer Discuss in Forum

   (125)^x = 3125
   ⇒  (5³)^x = 5⁵ ⇒ 5^3x = 5⁵
   ⇒  3x = 5
   

   ⇒  x =	5
   	3

   Correct Option: C

   (125)^x = 3125
   ⇒  (5³)^x = 5⁵ ⇒ 5^3x = 5⁵
   ⇒  3x = 5
   

   ⇒  x =	5
   	3

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463. If (125)^x = 3125, then the value of x is

1. 1. 1

      5

   
   
   

   2. 3

      5

   
   
   

   3. 5

      3

   
   
   

   4. 5

      7

   
   
   

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1. View Hint View Answer Discuss in Forum

   (125)^x = 3125
   ⇒  (5³)^x = 5⁵ ⇒ 5^3x = 5⁵
   ⇒  3x = 5
   

   ⇒  x =	5
   	3

   Correct Option: C

   (125)^x = 3125
   ⇒  (5³)^x = 5⁵ ⇒ 5^3x = 5⁵
   ⇒  3x = 5
   

   ⇒  x =	5
   	3

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464. If   x2 – 3x + 1 = 0, then the vaule of   x +	1	is
     	x

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x² – 3x + 1 = 0
   ⇒  x² + 1 = 3x
   

   ⇒	x2 + 1	=	3x
   	x		x

   
   

   ⇒  x +	1	= 3
   	x

   Correct Option: D

   x² – 3x + 1 = 0
   ⇒  x² + 1 = 3x
   

   ⇒	x2 + 1	=	3x
   	x		x

   
   

   ⇒  x +	1	= 3
   	x

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465. If		3		3		3		−6	=		3		2x − 1	, then x is equal to
     		5				5					5

1. 1. –2

   
   
   

   2. 2

   
   
   

   3. –1

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   	3		3		3		−6	=		3		2x − 1
   	5				5					5

   
   

   ⇒		3		3		3		−3		3		−3	=		3		2x − 1
   		5				5				5					5

   
   

   ⇒		3		0		3		−3	=		3		2x − 1
   		5				5					5

   
   ⇒  2x – 1 = – 3
   ⇒  2x = – 3 + 1 = – 2
   ⇒  x = –1
   Method : 2
   

   	3		3		3		−6	=		3		2x − 1
   	5				5					5

   
   

   ⇒		3		−6 + 3	=		3		2x − 1
   		5					5

   
   ⇒  –3 = 2x –1
   ⇒  –2 = 2x
   ⇒  x = –1

   Correct Option: C

   	3		3		3		−6	=		3		2x − 1
   	5				5					5

   
   

   ⇒		3		3		3		−3		3		−3	=		3		2x − 1
   		5				5				5					5

   
   

   ⇒		3		0		3		−3	=		3		2x − 1
   		5				5					5

   
   ⇒  2x – 1 = – 3
   ⇒  2x = – 3 + 1 = – 2
   ⇒  x = –1
   Method : 2
   

   	3		3		3		−6	=		3		2x − 1
   	5				5					5

   
   

   ⇒		3		−6 + 3	=		3		2x − 1
   		5					5

   
   ⇒  –3 = 2x –1
   ⇒  –2 = 2x
   ⇒  x = –1

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