A copper wire is bent in the shape of a square of area 81 cm2. If

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91.

A copper wire is bent in the shape of a square of area 81 cm2. If the same wire is bent in the form of a semicircle, the radius (in cm) of the semicircle is open parentheses take space straight pi space equals space 22 over 7 close parentheses

  • 16

  • 14

  • 10

  • 7


D.

7

Let the side of a square be x cm
∴                    x2 = 81 cm
⟹                  straight x space equals space square root of 81 space equals space 9 space cm
∴                 Perimeter of a square = 9 x 4 = 36 cm
Now, 
Perimeter of semi-circle = Perimeter of square
therefore space space space space space space πr space plus space 2 straight r space equals space space 36 space
rightwards double arrow space space space space space space straight r open parentheses straight pi space plus 2 close parentheses space equals space 36
rightwards double arrow space space space space space straight r open parentheses 22 over 7 space plus space 2 close parentheses space equals space 36
rightwards double arrow space space space space straight r space cross times space 36 over 7 space equals space 36 space space rightwards double arrow space space space straight r space equals space 7 space cm
     

                   

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92.

The perimeter of a triangle is 40 cm and its area is 60 cm2. If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is

  • 4

  • 6

  • 8

  • 15

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93.

A bicycle wheel makes 5000 revolutions in moving 11 km. The diameter of the wheel (in cm) is

  • 35

  • 55

  • 65

  • 70

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94.

If a wire is bent into the shape of a square, then the area of the square so formed 81 cm2. When the wire is rebent into semicircular shape, then the area (in cm2) of the semi-circle will be open parentheses Use space straight pi space equals space 22 over 7 close parentheses

  • 22

  • 44

  • 77

  • 154

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95.

At each corner of the triangular filed of sides 26 m, 28 m and 30 m, a cow is tethered by a rope of length 7m. The area (in m2) ungrazed by the cows is

  • 336

  • 259

  • 154

  • 77

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96.

If the radius of a circle is increased by 50%, its area is increased by

  • 125%

  • 100%

  • 75%

  • 50%

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97.

A rectangular garden is 100 m x 80 m. There is a path along the garden and just outside it. Width of the path is 10 m. The area of the path is

  • 1900 sq m

  • 2400 sq m

  • 3660 sq m

  • 4000 sq m

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98.

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 m?

  • 91.64 m

  • 90.46 m

  • 89.64 m

  • 93.64 m

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99.

When a pendulum of length 50 cm oscillates, it produces an arc of 16 cm. The angle so formed in degree measure is (approx.)

  • 18°25'

  • 18°35'

  • 18°20'

  • 18°08'

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100.

Side AB of rectangle ABCD is divided into four equal parts by points x, y, z. The ratio of the

is

  • 1/6

  • 1/9

  • 1/8

  • 1/7

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