41. If   x = √3 + √2, then the value of		x +	1		is :
    			x

1. 1. 2√2

   
   
   

   2. 2√3

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = √3 + √2
   

   ∴	1	=	1
   	x		√3 + √2

   
   

   =	√3 - √2
   	(√3 + √2)(√3 - √2)

   
   = √3 - √2
   

   ∴ x +	1
   	x

   
   = √3 + √2 + √3 - √2 = 2√3

   Correct Option: B

   x = √3 + √2
   

   ∴	1	=	1
   	x		√3 + √2

   
   

   =	√3 - √2
   	(√3 + √2)(√3 - √2)

   
   = √3 - √2
   

   ∴ x +	1
   	x

   
   = √3 + √2 + √3 - √2 = 2√3

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42. If   x −	1	= 5, then x2 +	1	is
    	x		x2

1. 1. 5

   
   
   

   2. 25

   
   
   

   3. 27

   
   
   

   4. 23

   
   
   

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1. View Hint View Answer Discuss in Forum

   x −	1	= 5
   	x

   
   On squaring both sides,
   

   x2 +	1	− 2 = 25
   	x2

   
   

   ⇒  x2 +	1	= 27
   	x2

   
   Second Method :
   

   Here,   x −	1	= 5
   	x

   
   We know that
   

   x2 +	1	=		x −	1		2	+ 2
   	x2				x

   
   = 5² + 2 = 27

   Correct Option: C

   x −	1	= 5
   	x

   
   On squaring both sides,
   

   x2 +	1	− 2 = 25
   	x2

   
   

   ⇒  x2 +	1	= 27
   	x2

   
   Second Method :
   

   Here,   x −	1	= 5
   	x

   
   We know that
   

   x2 +	1	=		x −	1		2	+ 2
   	x2				x

   
   = 5² + 2 = 27

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43. One of the factors of the expression 4√3x² + 5x − 2√3 is :

1. 1. 4x + √3

   
   
   

   2. 4x + 3

   
   
   

   3. 4x – 3

   
   
   

   4. 4x – √3

   
   
   

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1. View Hint View Answer Discuss in Forum

   4√3x² + 5x – 2√3
   = 4√3 x² + 8x – 3x – 2√3
   = 4x (√3x + 2) - √3( √3x + 2)
   = (4x - √3) (√3 + 2) ⇒ factors

   Correct Option: D

   4√3x² + 5x – 2√3
   = 4√3 x² + 8x – 3x – 2√3
   = 4x (√3x + 2) - √3( √3x + 2)
   = (4x - √3) (√3 + 2) ⇒ factors

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44. If   a2 – 4a – 1 = 0, then value of   a2 +	1	+ 3a –	3	is
    	a2		a

1. 1. 25

   
   
   

   2. 30

   
   
   

   3. 35

   
   
   

   4. 40

   
   
   

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1. View Hint View Answer Discuss in Forum

   a² – 4a – 1 = 0
   ⇒ a² – 1 = 4a
   On dividing by a, we have
   

   a -	1	= 4
   	a

   
   

   ∴ a² +	1	+ 3		a -	1
   	a²				a

   
   

   =		a -	1		²	+ 2 + 3		a -	1
   			a						a

   
   = 16 + 2 + 3 (4) = 30

   Correct Option: B

   a² – 4a – 1 = 0
   ⇒ a² – 1 = 4a
   On dividing by a, we have
   

   a -	1	= 4
   	a

   
   

   ∴ a² +	1	+ 3		a -	1
   	a²				a

   
   

   =		a -	1		²	+ 2 + 3		a -	1
   			a						a

   
   = 16 + 2 + 3 (4) = 30

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