91. If a + b = 17 and a – b = 9, then the value of (4a² + 4b²) is :

1. 1. 710

   
   
   

   2. 720

   
   
   

   3. 730

   
   
   

   4. 740

   
   
   

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1. View Hint View Answer Discuss in Forum

   a + b = 17
   a – b = 9
   ∴  (a + b)² + (a – b)² = 17² + 9²
   ⇒  2 (a² + b²) = 289 + 81 = 370
   ⇒  4 (a² + b²) = 2 × 370 = 740

   Correct Option: D

   a + b = 17
   a – b = 9
   ∴  (a + b)² + (a – b)² = 17² + 9²
   ⇒  2 (a² + b²) = 289 + 81 = 370
   ⇒  4 (a² + b²) = 2 × 370 = 740

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92. If

    a2

    =

    b2

    =

    c2

    = 1 then find the value of

    2

    +

    2

    +

    2

    .

    b + c

    c + a

    a + b

    1 + a

    1 + b

    1 + c

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   a2	=	b2	=	c2	= 1
   b + c		c + a		a + b

   
   

   ⇒	a2	= 1 ⇒ a2 = b + c
   	b + c

   
   ⇒  a² + a = a + b + c
   ⇒  a (a + 1) = a + b + c
   

   ⇒  a + 1 =	a + b + c
   	a

   
   

   ⇒	1	=	a
   	a + 1		a + b + c

   
   Similarly,
   

   b2	= 1
   c + a

   
   

   ⇒	1	=	b
   	b + 1		a + b + c

   
   

   and,	c2	= 1
   	a + b

   
   

   ⇒	1	=	c
   	c + 1		a + b + c

   
   

   ∴	2	+	2	+	2
   	1 + a		1 + b		1 + c

   
   

   = 2		a	+	b	+	c
   		a + b + c		a + b + c		a + b + c

   
   

   = 2		a + b + c		= 2
   		a + b + c

   Correct Option: C

   a2	=	b2	=	c2	= 1
   b + c		c + a		a + b

   
   

   ⇒	a2	= 1 ⇒ a2 = b + c
   	b + c

   
   ⇒  a² + a = a + b + c
   ⇒  a (a + 1) = a + b + c
   

   ⇒  a + 1 =	a + b + c
   	a

   
   

   ⇒	1	=	a
   	a + 1		a + b + c

   
   Similarly,
   

   b2	= 1
   c + a

   
   

   ⇒	1	=	b
   	b + 1		a + b + c

   
   

   and,	c2	= 1
   	a + b

   
   

   ⇒	1	=	c
   	c + 1		a + b + c

   
   

   ∴	2	+	2	+	2
   	1 + a		1 + b		1 + c

   
   

   = 2		a	+	b	+	c
   		a + b + c		a + b + c		a + b + c

   
   

   = 2		a + b + c		= 2
   		a + b + c

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93. If   x +	1	= 5, then the value of	x	is
    	x		1 + x + x2

1. 1. 1

      5

   
   
   

   2. 1

      6

   
   
   

   3. 5

   
   
   

   4. 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   = x +	1	= 5  (Given)
   	x

   
   

   ∴	x	=	x
   	1 + x + x2		x		1	+ 1+ x
   					x

   
   

   =	1						=	1
   	x +	1	+ 1						5 + 1
   		x

   
   

   =	1
   	6

   Correct Option: B

   = x +	1	= 5  (Given)
   	x

   
   

   ∴	x	=	x
   	1 + x + x2		x		1	+ 1+ x
   					x

   
   

   =	1						=	1
   	x +	1	+ 1						5 + 1
   		x

   
   

   =	1
   	6

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94. If   x −	1	= 2, then what is the value of x2 +	1	?
    	x		x2

1. 1. 4

   
   
   

   2. 5

   
   
   

   3. 3

   
   
   

   4. 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   x −	1	= 2
   	x

   
   On squaring both sides,
   

   x2 +	1	– 2 = 4
   	x2

   
   

   ⇒  x2 +	1	= 6
   	x2

   Correct Option: D

   x −	1	= 2
   	x

   
   On squaring both sides,
   

   x2 +	1	– 2 = 4
   	x2

   
   

   ⇒  x2 +	1	= 6
   	x2

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95. If   a +	1	= 1, then the value of	a2 − a + 1	is (a ≠ 0)
    	a		a2 + a + 1

1. 1. 1

   
   
   

   2. –1

   
   
   

   3. 0

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   ⇒  a +	1	= 1
   	a

   
   ⇒  a² + 1 = a ⇒ a² – a + 1 = 0
   

   ∴	a2 − a + 1	=	0	= 0
   	a2 + a + 1		a2 + a + 1

   Correct Option: C

   ⇒  a +	1	= 1
   	a

   
   ⇒  a² + 1 = a ⇒ a² – a + 1 = 0
   

   ∴	a2 − a + 1	=	0	= 0
   	a2 + a + 1		a2 + a + 1

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