86. The value of		1	+	1	+	1		is
    		(p − n)(n − q)		(n − q)(q − p)		(q − p)(p − n)

1. 1. 1

   
   
   

   2. 0

   
   
   

   3. p + q + n

   
   
   

   4. 2n

      p + q

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	+	1	+	1
   (p − n)(n − q)		(n − q)(q − p)		(q − p)(p − n)

   
   

   =	(q − p) + (p − n) + (n − q)
   	(p − n)(n − q)(q − p)

   
   

   =	0	= 0
   	(p − n)(n − q)(q − p)

   Correct Option: B

   1	+	1	+	1
   (p − n)(n − q)		(n − q)(q − p)		(q − p)(p − n)

   
   

   =	(q − p) + (p − n) + (n − q)
   	(p − n)(n − q)(q − p)

   
   

   =	0	= 0
   	(p − n)(n − q)(q − p)

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87. If 4x² – 12x + k is a perfect square, then the value of k is

1. 1. 2

   
   
   

   2. 9

   
   
   

   3. 12

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   (a – b)² = a² – 2ab + b²
   ∴  4x² – 12x + k = (2x)² – 2 × 2x × 3 + k
   ∴  k = (3)² = 9

   Correct Option: B

   (a – b)² = a² – 2ab + b²
   ∴  4x² – 12x + k = (2x)² – 2 × 2x × 3 + k
   ∴  k = (3)² = 9

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88. If x² + y² = 29 and xy = 10, where x > 0, y > 0, x > y

    then the value of	x + y	is
    	x − y

1. 1. −7

      3

   
   
   

   2. 7

      3

   
   
   

   3. 3

      7

   
   
   

   4. −3

      7

   
   
   

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1. View Hint View Answer Discuss in Forum

   x² + y² = 29;
   xy = 10
   ∴  (x + y)² = x² + y² + 2xy
   = 29 + 2 × 10 = 49
   ⇒  x + y = ±7
   Again, (x – y)² = x² + y² – 2xy
   = 29 – 2 × 10 = 9
   ∴  x – y = ±3
   

   ∴	x + y	=	±7	=	7
   	x – y		±3		3

   Correct Option: B

   x² + y² = 29;
   xy = 10
   ∴  (x + y)² = x² + y² + 2xy
   = 29 + 2 × 10 = 49
   ⇒  x + y = ±7
   Again, (x – y)² = x² + y² – 2xy
   = 29 – 2 × 10 = 9
   ∴  x – y = ±3
   

   ∴	x + y	=	±7	=	7
   	x – y		±3		3

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89. If	x	+ 1 =	x	+	a − b	, then x is equal to
    	a + b		a − b		a + b

1. 1. 2a – b

   
   
   

   2. a + b

   
   
   

   3. a – b

   
   
   

   4. 2a + b

   
   
   

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1. View Hint View Answer Discuss in Forum

   x	+ 1 =	x	+	a − b
   a + b		a − b		a + b

   
   

   ⇒	x	−	a − b	=	x	− 1
   	a + b		a + b		a − b

   
   

   ⇒	x − a + b	=	x − a + b
   	a + b		a − b

   
   

   ⇒  (x − a + b)		1	−	1		= 0
   		a + b		a − b

   
   ⇒  x − a + b = 0
   ⇒  x = a – b

   Correct Option: C

   x	+ 1 =	x	+	a − b
   a + b		a − b		a + b

   
   

   ⇒	x	−	a − b	=	x	− 1
   	a + b		a + b		a − b

   
   

   ⇒	x − a + b	=	x − a + b
   	a + b		a − b

   
   

   ⇒  (x − a + b)		1	−	1		= 0
   		a + b		a − b

   
   ⇒  x − a + b = 0
   ⇒  x = a – b

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90. If p = 99, then the value of p(p² + 3p + 3) will be

1. 1. 999999

   
   
   

   2. 1000000

   
   
   

   3. 1000001

   
   
   

   4. 999998

   
   
   

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1. View Hint View Answer Discuss in Forum

   p(p² + 3p + 3)
   = p³ + 3p² + 3p
   = p³ + 3p² + 3p + 1 – 1
   = (p + 1)³ – 1
   = (99 + 1)³ – 1
   = (100)³ – 1 = 1000000 – 1
   = 999999

   Correct Option: A

   p(p² + 3p + 3)
   = p³ + 3p² + 3p
   = p³ + 3p² + 3p + 1 – 1
   = (p + 1)³ – 1
   = (99 + 1)³ – 1
   = (100)³ – 1 = 1000000 – 1
   = 999999

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