286. The diagonals of a rhombus are 12 cm and 16 cm respectively. The length of one side is
     

1. 1. 8 cm
      

   
   
   

   2. 6 cm
      

   
   
   

   3. 10 cm
      

   
   
   

   4. 12 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Side of rhombus = √		d1		²	+		√	d2		²
   		2						2

   
   = √6² + 8² = 10 cm

   Correct Option: C

   Side of rhombus = √		d1		²	+		√	d2		²
   		2						2

   
   = √6² + 8² = 10 cm

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287. Each interior angle of a regular polygon is 18° more than eight times an exterior angle. The number of sides of the polygon is
     

1. 1. 10
      

   
   
   

   2. 15
      

   
   
   

   3. 20
      

   
   
   

   4. 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of sides of the regular polygon be n, then
   

   ∴		2n - 4		× 90
   		n

   
   

   = 8 ×	4 × 90°	+ 18
   	n

   
   

   ⇒		2n - 4		× 5 =	160	+ 1
   		n			n

   
   ⇒ 10 = n – 20 = 160 + n
   ⇒ 10n – n = 180
   ⇒ 9n = 180
   ⇒ n = 20

   Correct Option: C

   Let the number of sides of the regular polygon be n, then
   

   ∴		2n - 4		× 90
   		n

   
   

   = 8 ×	4 × 90°	+ 18
   	n

   
   

   ⇒		2n - 4		× 5 =	160	+ 1
   		n			n

   
   ⇒ 10 = n – 20 = 160 + n
   ⇒ 10n – n = 180
   ⇒ 9n = 180
   ⇒ n = 20

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288. An exterior angle of a regular polygon is 72°. The sum of all the interior angles is
     

1. 1. 360°
      

   
   
   

   2. 480°
      

   
   
   

   3. 520°
      

   
   
   

   4. 540°

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of sides of polygon =	360	= 5
   	72

   
   ∴ Sum of interior angles = (2n – 4) × 90°
   = (2 × 5 – 4) × 90° = 540°

   Correct Option: D

   Number of sides of polygon =	360	= 5
   	72

   
   ∴ Sum of interior angles = (2n – 4) × 90°
   = (2 × 5 – 4) × 90° = 540°

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289. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by : (use π = 22/7)
     

1. 1. 10	1	cm.
      	2

      
      

   
   
   

   2. 12	6	cm.
      	7

   
   
   

   3. 14 cm.
      

   
   
   

   4. 11	3	cm.
      	7

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of water drawn from cylinder
   

   = πr²h =	22	×	35	×	35	× h
   	7		2		2

   
   

   ∴	22	×	35	×	35	× h = 110000 cm³
   	7		2		2

   
   

   ∴ h =	11000 × 7 × 2 × 2
   	22 × 35 × 35

   
   

   =	80	= 11	3	cm.
   	7		7

   Correct Option: D

   Volume of water drawn from cylinder
   

   = πr²h =	22	×	35	×	35	× h
   	7		2		2

   
   

   ∴	22	×	35	×	35	× h = 110000 cm³
   	7		2		2

   
   

   ∴ h =	11000 × 7 × 2 × 2
   	22 × 35 × 35

   
   

   =	80	= 11	3	cm.
   	7		7

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290. A right circular cylinder is formed by rolling a rectangular paper 12 cm long and 3 cm wide along its length. The radius of the base of the cylinder will be
     

1. 1. 3	cm.
      2π

      
      

   
   
   

   2. 6	cm.
      π

      
      

   
   
   

   3. 9	cm.
      2π

      
      

   
   
   

   4. 2π cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   When a right circular cylinder is formed by rolling a rectangular paper along its length, the circumference of base is equal to length of paper.
   

   ∴ 2πr = 12 ⇒ r =	12	=	6	cm.
   	2π		π

   Correct Option: B

   When a right circular cylinder is formed by rolling a rectangular paper along its length, the circumference of base is equal to length of paper.
   

   ∴ 2πr = 12 ⇒ r =	12	=	6	cm.
   	2π		π

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