96. If (a – b) = 3 and (a² + b²) = 25, then the value of (ab) is

1. 1. 16

   
   
   

   2. 8

   
   
   

   3. 10

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   a – b = 3
   On squaring both sides,
   (a – b)² = 9
   ⇒  a² + b² – 2ab = 9
   ⇒  25 – 2ab = 9
   ⇒  2ab = 25 – 9 = 16
   

   ⇒  ab =	16	= 8
   	2

   Correct Option: B

   a – b = 3
   On squaring both sides,
   (a – b)² = 9
   ⇒  a² + b² – 2ab = 9
   ⇒  25 – 2ab = 9
   ⇒  2ab = 25 – 9 = 16
   

   ⇒  ab =	16	= 8
   	2

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97. If	2p	=	1	, then the value of p +	1	will be
    	p2 − 2p + 1		4		p

1. 1. 8

   
   
   

   2. 10

   
   
   

   3. 12

   
   
   

   4. None of these

   
   
   

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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		p		p

   
   

   ⇒  p +	1	= 8 + 2 = 10
   	p

   Correct Option: B

   2p	=	1
   p2 − 2p + 1		4

   
   

   p2 − 2p + 1	= 4
   2p

   
   

   ⇒	p2	−	2p	+	1	= 8
   	p		p		p

   
   

   ⇒  p +	1	= 8 + 2 = 10
   	p

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98. If x = 99, then the value of 2(x² + 3x + 3 ) is equal to

1. 1. 1000001

   
   
   

   2. 1000000

   
   
   

   3. 999999

   
   
   

   4. 9999999

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   x² + 3x + 3
   = x² + 2x + 1 + x + 2
   = (x + 1)² + x + 2
   = (99 + 1)² + 99 + 2
   = (100)² + 101
   = 10000 + 101 = 10101
   ∴  2(x² + 3x + 3 ) = 2 × 10101 = 20202

   Correct Option: E

   x² + 3x + 3
   = x² + 2x + 1 + x + 2
   = (x + 1)² + x + 2
   = (99 + 1)² + 99 + 2
   = (100)² + 101
   = 10000 + 101 = 10101
   ∴  2(x² + 3x + 3 ) = 2 × 10101 = 20202

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99. If   p2 + q2 = 7 pq, then the value of	p	+	q	is equal to
    	q		p

1. 1. 9

   
   
   

   2. 5

   
   
   

   3. 7

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   p² + q² = 7 pq
   

   ⇒	p2 + q2	= 7
   	pq

   
   

   ⇒	p2	+	q2	= 7
   	pq		pq

   
   

   ⇒	p	+	q	= 7
   	q		p

   Correct Option: C

   p² + q² = 7 pq
   

   ⇒	p2 + q2	= 7
   	pq

   
   

   ⇒	p2	+	q2	= 7
   	pq		pq

   
   

   ⇒	p	+	q	= 7
   	q		p

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100. If 9x² + 16y² = 60 and 3x + 4y = 6, then the value of xy is

1. 1. –1

   
   
   

   2. 1

   
   
   

   3. –2

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   9x² + 16y² = 60
   and 3x + 4y = 6
   On squaring,
   9x² + 16y² + 2 × 3x × 4y = 36
   ⇒  60 + 24xy = 36
   ⇒  24xy = 36 – 60 = –24
   

   ⇒  xy = −	24	= – 1
   	24

   Correct Option: A

   9x² + 16y² = 60
   and 3x + 4y = 6
   On squaring,
   9x² + 16y² + 2 × 3x × 4y = 36
   ⇒  60 + 24xy = 36
   ⇒  24xy = 36 – 60 = –24
   

   ⇒  xy = −	24	= – 1
   	24

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