Mensuration

1

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for

  1. 3 days
  2. 2 days
  3. 4 days
  4. 5 days
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2

A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?

  1. 34
  2. 24
  3. 32
  4. 14
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3

A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs.25/- per square metre?

  1. Rs.800
  2. Rs.480
  3. Rs.400
  4. Rs.240
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4

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

  1. 12 cm
  2. 24 cm
  3. 30 cm
  4. 36 cm
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5

10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs.5 per square metre?

  1. Rs.400
  2. Rs.440
  3. Rs.480
  4. Rs.500
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6

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

  1. 4.5 cm
  2. 2.25 cm
  3. 2 cm
  4. 1.5 cm
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7

If the height of a right circular cone is increased by 200%, and the radius of the base is reduced by 50%, then the volume of the cone

  1. remains unaltered
  2. decreases by 25%
  3. increases by 50%
  4. increases by 25%
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8

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

  1. 3 : 2
  2. 1 : 2
  3. 2 : 1
  4. 2 : 3
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9

The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is

  1. 327 π
  2. 307 π
  3. 293 π
  4. 273 π
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10

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equal to?

  1. 0.001 cm
  2. 0.01 cm
  3. 0.1 cm
  4. 1.0 cm
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11

What is the number of wax balls, each of radius 1 cm, that can be molded out of a sphere of radius 8 cm?

  1. 1024
  2. 768
  3. 512
  4. 256
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12

In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to?

  1. 10 : 5 : 7
  2. 8 : 4 : 7
  3. 2 : 1 : 2
  4. 8 : 4 : 5
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13

In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?

  1. D(√2 - 1)
  2. D(√2 + 1)
  3. D(√2 + 2)
  4. D(2 - √2)
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14

A field is divided into four regions as shown in the given figure. What is the area of the field in square metres?

  1. 6 + 3√5/4
  2. 5 + 3√3/2
  3. 9 + 3√15/4
  4. 7 + 2√2
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15

ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB = 32 cm and AD = 24 cm, then what is OD equal to?

  1. 22 cm
  2. 20 cm
  3. 18 cm
  4. 16 cm
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16

The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by

  1. 31.25%
  2. 32.25%
  3. 33.25%
  4. 34.25%
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17

Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is

  1. 950
  2. 1000
  3. 1050
  4. 1100
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18

In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?

  1. Ratio of OB to OD
  2. Ratio of BC to CD
  3. Ratio of AD to AB
  4. Ratio of AC to BD
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19

If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to

  1. One-fourth
  2. One-third
  3. One-fifth
  4. One-ninth
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20

A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, it encloses an area equal to

  1. 121 cm2
  2. 144 cm2
  3. 154 cm2
  4. 168 cm2
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21

If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone?

  1. p2
  2. 2p2
  3. p2/100
  4. p(2 + p/100)
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22

The area of a regular hexagon of side 'a' is equal to

  1. √2/3 a2 square units
  2. 3√3/2 a2 square units
  3. 1/3 a2 square units
  4. √3/2 a2 square units
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23

Three circles each of radius 3.5 cm touch one another. The area subtended between them is

  1. 6(√3π - 2) square units
  2. 6(2π - √3) square units
  3. 49/8 (2√3 - π) square units
  4. 49/8 (√3 - π) square units 8
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24

A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

  1. 2200 square cm
  2. 4400 square cm
  3. 8800 square cm
  4. 17600 square cm
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25

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is

  1. 6 cm
  2. 5 cm
  3. 4.5 cm
  4. 4 cm
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26

The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by

  1. 34.75%
  2. 32.25%
  3. 31%
  4. 30%
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27

If each of the dimensions of a rectangle is increased by 200%, the area is increased by

  1. 300%
  2. 400%
  3. 600%
  4. 800%
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28

The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

  1. 4 m
  2. 8 m
  3. 9 m
  4. 10 m
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