The diameters of two circles are the side of a square and the dia

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 Multiple Choice QuestionsMultiple Choice Questions

101.

Two angles of a triangle are 1 half space radian and 1 third space radian. The measure of the third angle in degree open parentheses taking space straight pi space equals space 22 over 7 close parentheses is

  • 132 fraction numerator 2 degree over denominator 11 end fraction

  • 132 fraction numerator 3 degree over denominator 11 end fraction

  • 132 degree

  • 132 fraction numerator 3 degree over denominator 11 end fraction

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102.

The diameter of garden roller is 1.4 m and it is 2 m long. The area covered by the roller in 5 revolution is

  • 4.4 m2

  • 44 m2

  • 16.8 m2

  • 8.8 m2

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103.

ABCD is a trapezium, such that AB = CD and AD || BC. AD = 5 cm,  BC = 9 cm. If area of ABCD is 35 sq cm, then CD is

  • 5 cm

  • 6 cm

  • square root of 21 space cm

  • square root of 29 space cm

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104.

The diameters of two circles are the side of a square and the diagonal of the square. The ratio of the areas of the smaller circle and the larger circle is

  • 1 : 4

  • square root of 2 space colon space square root of 3

  • 1 space colon space square root of 2

  • 1 : 2


D.

1 : 2

For first circle,
Diameter of a circle  = Side of a square
⟹       2r = a
⟹         r = a/2

For second circle,
Diameter of a circle = Diagonal of a square
rightwards double arrow space space 2 straight r space equals space square root of 2 straight a
rightwards double arrow space space straight r space equals space fraction numerator square root of 2 straight a over denominator 2 end fraction
∴   Required ratio of the areas of the smaller circle and the larger circle is:
  equals space πr subscript 1 squared over πr subscript 2 squared
equals space fraction numerator straight pi space cross times space open parentheses begin display style straight a over 2 end style close parentheses squared over denominator straight pi space cross times space open parentheses begin display style fraction numerator square root of 2 straight a over denominator 2 end fraction end style close parentheses squared end fraction space equals space 1 half space equals space 1 space colon space 2






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105.

Three sides of a triangular field are of length 15 m, 20 m and 25 m long, respectively.

  • 750

  • 150

  • 300

  • 600

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106.

If the median drawn on the base of a triangle is half its base, then the triangle will be

  • obtuse angled

  • equilateral

  • right angled

  • acute angled

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107.

A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, then the radius of the circular ground is open parentheses take space straight pi space equals space 22 over 7 close parentheses

  • 10.5 m

  • 3.5 m

  • 5.5 m

  • 7.5 m

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108.

If the perimeter of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1 : 2, then the ratio of area of the rectangle and that of the square is

  • 1 : 1

  • 1 : 2

  • 2 : 3

  • 8 : 9

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109.

If the arcs of square length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is

  • 3 : 4

  • 4 : 5

  • 5 : 4

  • 3 : 5

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110.

A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope stretched and describes 88 m when it has traced out 72° at the centre at the length of the rope is 

  • 70 m

  • 75 m

  • 80 m

  • 65 m

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