76. If	a	=	7	,	b	=	3	, then the value of a : b : c is
    	b		9		c		5

    
    

1. 1. 7 : 9 : 15
      

   
   
   

   2. 7 : 9 : 5
      

   
   
   

   3. 21 : 35 : 45
      

   
   
   

   4. 7 : 3 : 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   a : b = 7 : 9
   b : c = 3 : 5 = 9 : 15
   ∴ a : b : c
   = 7 : 9 : 15

   Correct Option: A

   a : b = 7 : 9
   b : c = 3 : 5 = 9 : 15
   ∴ a : b : c
   = 7 : 9 : 15

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77. If x : y = 7 : 3, then the value of	xy + y²	is
    	x² + y²

1. 1. 3

      4

   
   
   

   2. 4

      3

   
   
   

   3. 3

      7

   
   
   

   4. 7

      3

   
   
   

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1. View Hint View Answer Discuss in Forum

   =	x	=	7	(Given)
   	y		3

   
   Now,
   

   =	xy + y²	=	y (x + y)
   	x² - y²		(x + y)(x - y)

   
   

   =	y	=	1			=	1			=	1			=	3
   	x - y		x	- 1			7	- 1			7 - 3				4
   			y				3				3

   Correct Option: A

   =	x	=	7	(Given)
   	y		3

   
   Now,
   

   =	xy + y²	=	y (x + y)
   	x² - y²		(x + y)(x - y)

   
   

   =	y	=	1			=	1			=	1			=	3
   	x - y		x	- 1			7	- 1			7 - 3				4
   			y				3				3

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78. Find the equation of a line which passes through the point of intersection of lines x + 2y = 5 and x – 3y = 7 and also passes through the point (0, –1)

1. 1. 3x – 29y + 1 = 0

   
   
   

   2. 3 x – 29y – 29 = 0

   
   
   

   3. 3x + 4y – 6 = 0

   
   
   

   4. –3x + 29y + 7 = 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the equation of line be
   (x + 2y – 5) + l(x – 3y – 7) = 0
   As it passes through (0, –1)
   ∴ 0 – 2 – 5 + l (0 + 3 – 7) = 0 –7 – 4λ = 0
   

   λ =	- 7
   	4

   
   ∴ Equation of line is
   

   ( x + 2y - 5)	- 7	( x - 3y - 7) = 0
   	4

   
   ⇒ 4x + 8y – 20 – 7x + 21y + 49 = 0
   –3x + 29y + 29 = 0 3x – 29y – 29 = 0

   Correct Option: B

   Let the equation of line be
   (x + 2y – 5) + l(x – 3y – 7) = 0
   As it passes through (0, –1)
   ∴ 0 – 2 – 5 + l (0 + 3 – 7) = 0 –7 – 4λ = 0
   

   λ =	- 7
   	4

   
   ∴ Equation of line is
   

   ( x + 2y - 5)	- 7	( x - 3y - 7) = 0
   	4

   
   ⇒ 4x + 8y – 20 – 7x + 21y + 49 = 0
   –3x + 29y + 29 = 0 3x – 29y – 29 = 0

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79. For what value of k, the following pair of lines –kx + 2y + 3 = 0 and 2x + 4y + 7 = 0 are perpendicular ?

1. 1. k = 2

   
   
   

   2. k = 4

   
   
   

   3. k = –1

   
   
   

   4. k = 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   When two lines are perpendicular than the product of their slopes is –1.
   i.e m₁ × m₂ = –1
   For equation
   – kx + 2y + 3 = 0
   

   m2 =	k
   	2

   
   k 1 2 = For equation 2x + 4y + 7 = 0
   

   m2 = -	2
   	4

   
   

   m2 = -	1
   	2

   
   As lines are perpendicular
   m₁ × m₂ = –1
   

   k	× -	1	= - 1
   2		2

   
   k = 4

   Correct Option: B

   When two lines are perpendicular than the product of their slopes is –1.
   i.e m₁ × m₂ = –1
   For equation
   – kx + 2y + 3 = 0
   

   m2 =	k
   	2

   
   k 1 2 = For equation 2x + 4y + 7 = 0
   

   m2 = -	2
   	4

   
   

   m2 = -	1
   	2

   
   As lines are perpendicular
   m₁ × m₂ = –1
   

   k	× -	1	= - 1
   2		2

   
   k = 4

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80. What will be the equation of a line passing through the point (–4, 3) and having slope 1/2 ?

1. 1. x – 2y + 5 = 0

   
   
   

   2. – x + 2y + 10 = 0

   
   
   

   3. x – 2y + 6 = 0

   
   
   

   4. x – 2y + 10 = 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the equation of line bey – y₁ = m(x – x₁)
   Here,
   

   m =	1
   	2

   
   and x₁ = – 4, y₁ = 3
   ⇒ Equation of line be
   

   y - 3 =	1	(x + 4)
   	2

   
   2 y – 6 = x + 4
   x – 2y + 10 = 0

   Correct Option: D

   Let the equation of line bey – y₁ = m(x – x₁)
   Here,
   

   m =	1
   	2

   
   and x₁ = – 4, y₁ = 3
   ⇒ Equation of line be
   

   y - 3 =	1	(x + 4)
   	2

   
   2 y – 6 = x + 4
   x – 2y + 10 = 0

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