271. If	x	=	y	=	z	, then
     	b + c		c + a		a + b

1. 1. x − y	=	y − z	=	z − x
      b − c		c − b		a − c

   
   
   

   2. x	=	y	=	z
      a		b		c

   
   
   

   3. x − y	=	y − z	=	z − x
      c		b		c

   
   
   

   4. None of the above is true

   
   
   

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1. View Hint View Answer Discuss in Forum

   	x	=	y
   	b + c		b + a

   
   

   =	x - y	=	x - y	;	y	=	z
   	b + c - c -a		b - a		c + a		a + b

   
   

   =	y - z	=	y - z	;	z	=	x
   	c + a - a - b		c - b		a + b		b + c

   
   

   =	z - x	=	z - x
   	a + b - b - c		a - c

   
   

   ∴	x - y	=	y - z	=	z - x
   	b - a		c - b		a - c

   Correct Option: A

   	x	=	y
   	b + c		b + a

   
   

   =	x - y	=	x - y	;	y	=	z
   	b + c - c -a		b - a		c + a		a + b

   
   

   =	y - z	=	y - z	;	z	=	x
   	c + a - a - b		c - b		a + b		b + c

   
   

   =	z - x	=	z - x
   	a + b - b - c		a - c

   
   

   ∴	x - y	=	y - z	=	z - x
   	b - a		c - b		a - c

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272. If   x = 3 + 2√2 and xy = 1, then the value of	x2 + 3xy + y2	is
     	x2 − 3xy + y2

1. 1. 30

      31

   
   
   

   2. 70

      31

   
   
   

   3. 35

      31

   
   
   

   4. 37

      31

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = 3 + 2√2
   ⇒ xy = 1
   

   ⇒ y =	1	=	1	×	3 - 2√2
   	3 + 2√2		3 + 2√2		3 - 2√2

   
   

   =	3 - 2√2	= 3 - 2√2
   	9 - 8

   
   ∴ x + y
   = 3 + 2√2 + 3 - 2√2 = 6
   

   ∴	x² + 3xy + y²	=	(x + y)² + xy
   	x² - 3xy + y²		(x - y)² - 5xy

   
   

   =	36 + 1	=	37
   	36 - 5		31

   Correct Option: D

   x = 3 + 2√2
   ⇒ xy = 1
   

   ⇒ y =	1	=	1	×	3 - 2√2
   	3 + 2√2		3 + 2√2		3 - 2√2

   
   

   =	3 - 2√2	= 3 - 2√2
   	9 - 8

   
   ∴ x + y
   = 3 + 2√2 + 3 - 2√2 = 6
   

   ∴	x² + 3xy + y²	=	(x + y)² + xy
   	x² - 3xy + y²		(x - y)² - 5xy

   
   

   =	36 + 1	=	37
   	36 - 5		31

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273. If   x2 + 5x + 6 = 0, then the value of	2x	is :
     	x2 − 7x + 6

1. 1. 1

      6

   
   
   

   2. 1

      3

   
   
   

   3. −	1
      	6

   
   
   

   4. −	1
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given,   x² + 5x + 6 = 0
   

   ∴  Expression =	2x
   	x2 − 7x + 6

   
   

   =	2x	=	2
   	x2 + 5x + 6 − 12x		−12

   
   

   =	−1
   	6

   Correct Option: C

   Given,   x² + 5x + 6 = 0
   

   ∴  Expression =	2x
   	x2 − 7x + 6

   
   

   =	2x	=	2
   	x2 + 5x + 6 − 12x		−12

   
   

   =	−1
   	6

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274. If	a	+	b	+	c	=	1	, then the value of
     	1 − 2a		1 − 2b		1 − 2c		2

     1	+	1	+	1	is :
     1 − 2a		1 − 2b		1 − 2c

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   a	+	b	+	c	=	1
   1 − 2a		1 − 2b		1 − 2c		2

   
   

   ⇒	2a	+	2b	+	2c	=	2	= 1
   	1 − 2a		1 − 2b		1 − 2c		2

   
   

   ⇒

   2a

   + 1

   +

   2b

   + 1

   +

   2c

   + 1

   = 4

   1 − 2a

   1 − 2b

   1 − 2c

   
   

   ⇒	2a + 1 − 2a	+	2b + 1 − 2b	+	2c + 1 − 2c	= 4
   	1 − 2a		1 − 2b		1 − 2c

   
   

   ⇒	1	+	1	+	1	= 4
   	1 − 2a		1 − 2b		1 − 2c

   Correct Option: D

   a	+	b	+	c	=	1
   1 − 2a		1 − 2b		1 − 2c		2

   
   

   ⇒	2a	+	2b	+	2c	=	2	= 1
   	1 − 2a		1 − 2b		1 − 2c		2

   
   

   ⇒

   2a

   + 1

   +

   2b

   + 1

   +

   2c

   + 1

   = 4

   1 − 2a

   1 − 2b

   1 − 2c

   
   

   ⇒	2a + 1 − 2a	+	2b + 1 − 2b	+	2c + 1 − 2c	= 4
   	1 − 2a		1 − 2b		1 − 2c

   
   

   ⇒	1	+	1	+	1	= 4
   	1 − 2a		1 − 2b		1 − 2c

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275. If		p2 +	1		= 47, the value of		p +	1		is :
     			p2					p

1. 1. 5

   
   
   

   2. 6

   
   
   

   3. 7

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   p2 +	1	= 47
   	p2

   
   

   ⇒		p +	1		2	– 2 = 47
   			p

   
   

   ⇒		p +	1		2	= 47 + 2 = 49
   			p

   
   

   ⇒  p +	1	= √49 = 7
   	p

   Correct Option: C

   p2 +	1	= 47
   	p2

   
   

   ⇒		p +	1		2	– 2 = 47
   			p

   
   

   ⇒		p +	1		2	= 47 + 2 = 49
   			p

   
   

   ⇒  p +	1	= √49 = 7
   	p

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