1. ABCD is a quadrilateral in which BD = 40 cm. The lengths of the perpendiculars drawn from the opposite vertices on BD are 16 cm and 12 cm. The area of the quadrilateral (in cm2 ) is

  • Option : A
  • Explanation :


    Given, BD = 40 cm, AM =16 cm , NC=12cm
    ∴ Here, BD divides quadrilateral in two triangles.
    Now,
    Area of ΔABD = 1/2 x BD xAM
    1/2 x 40 x 16 =320 cm∧2.
    ∴ Area of  ΔBCD = 1/2 x BD x NC
    =1/2 x40 x12=240 cm∧2
    Area of quadrilateral
    ABCD = 320 + 240 = 560 cm∧2

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2. A cuboid is of dimensions 5 cm × 2 cm × 5 cm. How many such cuboids may be joined to form a cube?

  • Option : D
  • Explanation : (D) Given that, sides of a cuboid are 5cm, 2cm and 5cm.
    Volume of cuboid = 5 × 2 × 5 = 50cm3
    Let the side of the cube formed with minimum number of cuboids = x
    Hence, volume of the cube = x3
    Let, number of cuboids required = n
    Hence, n × 50 = x3
    n × 50 must be perfect cube i.e.
    minimum value of n = 2 × 2 × 5 = 20
    Volume of the cube formed = 20 × 50 = 1000 cm3
    So, required cuboids = 20

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3. The sum of the length, breadth and depth of a cuboid is 20 cm and its diagonal is 4√5 cm. The surface area of cuboid will be

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4. The area of three adjacent faces of a cuboid are x, y and z, respectively. The volume of cuboid will be

  • Option : C
  • Explanation : Given, lb = x.
    bh=y,lb=z.
    lb x bh x lh = xyz.
    l2 b2 b2 =xyz
    Volume = lbh = √xyz

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5. A cylinder, a hemisphere and a cone stand on equal bases and have same heights. The ratio of their volumes will be

  • Option : A
  • Explanation : Here h =r
    ∴ Required ratio
    =πr2h: (2/3)πr3  : (1/3) πr2h
    =1:2/3:1/3 =3:2:1

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