726. A gear 12 cm in diameter is turning a gear 18 cm in diameter. When the smaller gear has 42 revolutions, how many has the larger one made ?
     

1. 1. 28
      

   
   
   

   2. 20
      

   
   
   

   3. 15
      

   
   
   

   4. 24

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of revolutions =	12 × 42	= 28
   	18

   
   

   Correct Option: A

   Number of revolutions =	12 × 42	= 28
   	18

   
   

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727. If the perimeter of circle A is equal to perimeter of semi circle B, what is the ratio of their areas ?
     

1. 1. (π + 2)² : 2π²
      

   
   
   

   2. 2π² : (π + 2)²
      

   
   
   

   3. (π + 2)² : 4π²
      

   
   
   

   4. 4π² : (π + 2)²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let radius of circle A be r₁ units.
   Radius of semi-circle = r₂ units.
   According to the question, 2πr₁ = πr₂ + 2r₂
   ⇒ 2πr₁ = r₂ (π + 2)
   

   ⇒	r1/center>	=	π + 2
   	r2		2π

   
   

   ∴ Ratio of their areas =	πr1²	=	(π + 2)²	= (π + 2)² : 4πr²
   	πr2²		(2π)²

   Correct Option: C

   Let radius of circle A be r₁ units.
   Radius of semi-circle = r₂ units.
   According to the question, 2πr₁ = πr₂ + 2r₂
   ⇒ 2πr₁ = r₂ (π + 2)
   

   ⇒	r1/center>	=	π + 2
   	r2		2π

   
   

   ∴ Ratio of their areas =	πr1²	=	(π + 2)²	= (π + 2)² : 4πr²
   	πr2²		(2π)²

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728. A circular road runs around a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 metres, the width of the road is:(Take π = 22/7)
     

1. 1. 10.5 metres
      

   
   
   

   2. 7 metres
      

   
   
   

   3. 5.25 metres
      

   
   
   

   4. 21 metres

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Breadth of road = r₂ – r₁
   ∴ 2πr₂ - 2πr₁ = 66
   → 2π(r₂ - r₁) = 66
   

   r2 - r1 =	66	=	66 × 7
   	2π		2 × 22

   
   = 10.5 metres

   Correct Option: A

   
   Breadth of road = r₂ – r₁
   ∴ 2πr₂ - 2πr₁ = 66
   → 2π(r₂ - r₁) = 66
   

   r2 - r1 =	66	=	66 × 7
   	2π		2 × 22

   
   = 10.5 metres

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729. A person observed that he required 30 seconds less time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30 m/minute, then the radius of the circular ground is (Take π = 22/7) :
     

1. 1. 5.5 m
      

   
   
   

   2. 7.5 m
      

   
   
   

   3. 10.5 m
      

   
   
   

   4. 3.5 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of circular field be r metre, then
   

   	2πr	-	2r	=	30
   	30		30		60

   
   

   ⇒	πr	-	r	=	1
   	15		15		2

   
   

   ⇒ πr - r =	15
   	2

   
   

   ⇒ r(π - 1) =	15
   	2

   
   

   ⇒ r		22	- 1		=	15
   		7				2

   
   

   ⇒ r ×	15	=	15
   	7		2

   
   

   ⇒ r =	7	= 3.5 metre
   	2

   Correct Option: D

   Let the radius of circular field be r metre, then
   

   	2πr	-	2r	=	30
   	30		30		60

   
   

   ⇒	πr	-	r	=	1
   	15		15		2

   
   

   ⇒ πr - r =	15
   	2

   
   

   ⇒ r(π - 1) =	15
   	2

   
   

   ⇒ r		22	- 1		=	15
   		7				2

   
   

   ⇒ r ×	15	=	15
   	7		2

   
   

   ⇒ r =	7	= 3.5 metre
   	2

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730. The difference of perimeter and diameter of a circle is X unit. The diameter of the circle is
     

1. 1. X	unit
      π - 1

   
   
   

   2. X	unit
      π + 1

      
      

   
   
   

   3. X	unit
      π

   
   
   

   4. 	X	- 1		units
      	π - 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the diameter of the circle be d units, then
   π d – d = X
   ⇒ d(π – 1) = X
   

   ⇒ d =	X	units
   	π - 1

   Correct Option: A

   If the diameter of the circle be d units, then
   π d – d = X
   ⇒ d(π – 1) = X
   

   ⇒ d =	X	units
   	π - 1

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