76. If   5x +	1	= 10, then x2 +	1	is equal to
    	x		25x2

1. 1. 2	1
      	5

   
   
   

   2. 3	1
      	5

   
   
   

   3. 3	3
      	5

   
   
   

   4. 2	3
      	5

   
   
   

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1. View Hint View Answer Discuss in Forum

   5x +	1	= 10
   	x

   
   On dividing by 5,
   

   x +	1	= 2
   	5x

   
   On squaring both sides,
   

   	x +	1		2	= 4
   		5x

   
   

   ⇒  x2 +	1	+ 2x ×	1	= 4
   	25x2		5x

   
   

   ⇒  x2 +	1	= 4 −	2
   	25x2		5

   
   

   =	20 − 2	=	18
   	5		5

   
   

   = 3	3
   	5

   Correct Option: C

   5x +	1	= 10
   	x

   
   On dividing by 5,
   

   x +	1	= 2
   	5x

   
   On squaring both sides,
   

   	x +	1		2	= 4
   		5x

   
   

   ⇒  x2 +	1	+ 2x ×	1	= 4
   	25x2		5x

   
   

   ⇒  x2 +	1	= 4 −	2
   	25x2		5

   
   

   =	20 − 2	=	18
   	5		5

   
   

   = 3	3
   	5

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77. If		x +	1		= 2 then		x2 +	1		is equal to
    			x					x2

1. 1. 0

   
   
   

   2. 2

   
   
   

   3. 4

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   x +	1	= 2
   	x

   
   On squaring both sides,
   

   	x +	1		2	= 4
   		x

   
   

   ⇒  x2 +	1	+ 2 = 4
   	x2

   
   

   ⇒  x2 +	1	= 4 − 2 = 2
   	x2

   Correct Option: B

   x +	1	= 2
   	x

   
   On squaring both sides,
   

   	x +	1		2	= 4
   		x

   
   

   ⇒  x2 +	1	+ 2 = 4
   	x2

   
   

   ⇒  x2 +	1	= 4 − 2 = 2
   	x2

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78. If	3a + 4b	=	3a − 4b	, then
    	3c + 4d		3c − 4d

1. 1. ab = cd

   
   
   

   2. ad = bc

   
   
   

   3. ac = bd

   
   
   

   4. a = b = c ≠ d

   
   
   

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1. View Hint View Answer Discuss in Forum

   3a + 4b	=	3a − 4b
   3c + 4d		3c − 4d

   
   

   ⇒	3a + 4b	=	3c + 4d
   	3a − 4b		3c − 4d

   
   By componendo and dividendo,
   

   3a + 4b + 3a − 4b	=	3c + 4d + 3c − 4d
   3a + 4b − 3a + 4b		3c + 4d − 3c + 4d

   
   

   ⇒	6a	=	6c
   	8b		8d

   
   

   ⇒	a	=	c
   	b		d

   
   ⇒  ad = bc

   Correct Option: B

   3a + 4b	=	3a − 4b
   3c + 4d		3c − 4d

   
   

   ⇒	3a + 4b	=	3c + 4d
   	3a − 4b		3c − 4d

   
   By componendo and dividendo,
   

   3a + 4b + 3a − 4b	=	3c + 4d + 3c − 4d
   3a + 4b − 3a + 4b		3c + 4d − 3c + 4d

   
   

   ⇒	6a	=	6c
   	8b		8d

   
   

   ⇒	a	=	c
   	b		d

   
   ⇒  ad = bc

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79. If	a	=	b	=	c	, find the value of (pa + qb + rc).
    	q − r		r − p		p − q

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. –1

   
   
   

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1. View Hint View Answer Discuss in Forum

   a	=	b	=	c	= k (let)
   q − r		r − p		p − q

   
   ⇒  a = k (q – r);
   b = k (r – p);
   c = k (p – q)
   ∴  pa + qb + rc
   = k [p (q – r) + q (r – p) + r (p – q)]
   = k (pq – pr + qr – pq + rp – qr)
   = k × 0 = 0

   Correct Option: A

   a	=	b	=	c	= k (let)
   q − r		r − p		p − q

   
   ⇒  a = k (q – r);
   b = k (r – p);
   c = k (p – q)
   ∴  pa + qb + rc
   = k [p (q – r) + q (r – p) + r (p – q)]
   = k (pq – pr + qr – pq + rp – qr)
   = k × 0 = 0

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80. If

    x −

    1

    =

    1

    , the value of 3

    x −

    1

    is

    3x

    3

    3x

1. 1. –1

   
   
   

   2. 1

   
   
   

   3. –2

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   x –	1	=	1
   	3x		3

   
   

   ∴  3		x –	1		= 0
   			3x

   
   

   = 3 ×	1	= 1
   	3

   Correct Option: B

   x –	1	=	1
   	3x		3

   
   

   ∴  3		x –	1		= 0
   			3x

   
   

   = 3 ×	1	= 1
   	3

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