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Aptitude miscellaneous
  1. The perimeter (in metres) of a semicircle is numerically equal to its area (in square metres). The length of its diameter is (take π = 22/7)








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,
    Let the radius of the semi – circle ber metre.
    According to the question, πr + 2r = πr²

    = π + 2 = ×
    πr²
    		⇒ 2π + 4 = πr
    2

    r =
    2π + 4
    		 = 2 +
    4
    		 = 2 +
    28
    		 = 2 +
    14
    		 =
    36
    ππ221111
    ∴ Diameter =
    2 × 36
    		 =
    72
    		 = 6
    6
    		metres
    111111

    Correct Option: C

    Using Rule 14,
    Let the radius of the semi – circle ber metre.
    According to the question, πr + 2r = πr²

    = π + 2 = ×
    πr²
    		⇒ 2π + 4 = πr
    2

    r =
    2π + 4
    		 = 2 +
    4
    		 = 2 +
    28
    		 = 2 +
    14
    		 =
    36
    ππ221111
    ∴ Diameter =
    2 × 36
    		 =
    72
    		 = 6
    6
    		metres
    111111

  1. The ratio of the numbers giving the measure of the circumference and the area of a circle of radius 3 cm is








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,
    Circumference of circle= 2πr
    = 2π × 3 = 6π cm
    Area of circle = πr² = π × 3 × 3 = 9π cm²
    ∴ Required ratio = 6π : 9π= 2 : 3

    Correct Option: B

    Using Rule 14,
    Circumference of circle= 2πr
    = 2π × 3 = 6π cm
    Area of circle = πr² = π × 3 × 3 = 9π cm²
    ∴ Required ratio = 6π : 9π= 2 : 3

  1. The ratio of the radii of two wheels is 3 : 4. The ratio of their circumference is








  1. View Hint View Answer Discuss in Forum

    Tricky Approach
    Ratio of the circumference = Ratio of radii = 3 : 4

    Correct Option: B

    Tricky Approach
    Ratio of the circumference = Ratio of radii = 3 : 4

  1. The length (in cm) of a chord of a circle of radius 13 cm at a distance of 12 cm from its centre is








  1. View Hint View Answer Discuss in Forum


    AC = √13² - 12² = √169 - 144
    = √25 =5 cm
    ∴ AB = 10 cm

    Correct Option: C


    AC = √13² - 12² = √169 - 144
    = √25 =5 cm
    ∴ AB = 10 cm

  1. The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is








  1. View Hint View Answer Discuss in Forum

    Using Rule 7,
    Distance covered by wheel in one revolution = circumference of the wheel

    = π × diameter =
    22
    		× 98 = 308 cm
    7

    ∴ Number of revolutions =
    1540 × 100
    		 = 500
    308

    Correct Option: A

    Using Rule 7,
    Distance covered by wheel in one revolution = circumference of the wheel

    = π × diameter =
    22
    		× 98 = 308 cm
    7

    ∴ Number of revolutions =
    1540 × 100
    		 = 500
    308