## HCS CSAT I UPSC IAS CSAT I RAS Prelims Math I Previous year questions math I Geometry mensuration

HCS CSAT I UPSC IAS CSAT I RAS Prelims Math I Previous year questions math I Geometry mensuration

- A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be

(a) 6623%

(b) 78.5%

(c) 100%

(d) More than 100% (that is, some liquid will still be left in the bowl)

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- A man is standing on the 6m long pole whose length of shadow is 8 m. If the length of his shadow is 2.4 m, what is the height of the man?

(a) 1.4 m

(b) 1.6 m

(c) 1.8 m

(d) 2.0 m

- If the angles of a triangle are in the ratio 4 : 3 : 2, then the triangle

(a) is obtuse angled triangle

(b) has one angle greater than 80°

(c) is a right triangle

(d) is acute angled triangle

## Video Explanation

- At a given time, two players are standing on a playfield. The cartesian coordinates of their locations are (20, 60) and (-40, -20) units. What is the distance between the players?

(a) 60 units

(b) 80 units

(c) 100 units

(d) 140 units

- The area of an ellipse is twice that of a circle. The major diameter of the ellipse is twice that of the minor diameter. The radius of the circle is

(a) 50% of minor diameter of the ellipse

(b) 50% of major diameter of the ellipse

(c) minor diameter of the ellipse

(d) major diameter of the ellipse

- In the given figure,

∠OQP = 30° and ∠ORP = 20°, then ∠QOR is equal to

(a) 100°

(b) 120°

(c) 130°

(d) 140°

- Which one of the following has a greater perimeter than the rest?

(a) A square with an area of 36 sq. cm

(b) An equilateral triangle with a side of 9 cm

(c) A rectangle with 10 cm as length and 40 sq. cm as area

(d) A circle with a radius of 4 cm

- A goat is tied to two poles P and Q with ropes that are 15 metres long. P and Q are 20 metres apart as shown in the given diagram :

Which one of the following shaded portions indicates the total area over which the goat can graze?

(a)

(b)

(c)

(d)

- What is the maximum number of pieces of 5 cm x 5 cm x 10 cm of cake that can be cut from a big cake of 5 cm x 30 cm x 30 cm?

(a) 10

(b) 15

(c) 18

(d) 30

- A rectangular water tank measures 15 m x 6 m at the top and is 10 m deep. It is full of water. If water is drawn out lowering the level by 1 m, how much of water has been drawn out?

(a) 90000 litres

(b) 45000 litres

(c) 4500 litres

(d) 900 litres

- In the given figure, all line segments of the shaded portion are of same length and at right angles to each other. The same can be out of a board of side 10 cm. What is the area of the shaded portion?

(a) 36 cm2

(b) 48 cm2

(c) 52 cm2

(d) 64 cm2

- A rectangular piece of iron sheet measuring 50 cm x 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting the cylinder is ₹50 per square metre, then what will be the cost of painting the outer surface of the cylinder?

(a) ₹25.00

(b) ₹37.50

(c) ₹75.00

(d) ₹87.50

- A circle of radius 1 m is drawn inside a square as shown in the figure. What is the area of the shaded portion (in m2)?

(a) (4 – )

(b) (1 – 2)

(c) (14– 4)

(d) (1 – 4)

- In the given figure, ABCD is a cyclic quadrilateral, AB = BC and ∠BAC = 70°, then ∠ADC is

(a) 40°

(b) 80°

(c) 110°

(d) 140°

- The length of the longest pole that can be placed in a room 12 m long, 9 m wide and 8 m high, is

(a) 12 m

(b) 14 m

(c) 17 m

(d) 21 m

- Consider the volumes of the following :
- A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
- A cube of each side 4 cm
- A cylinder of radius 3 cm and length 3 cm
- A sphere of radius 3 cm

The volumes of these in the decreasing order is

(a) 1, 3, 2, 4

(b) 4, 2, 3, 1

(c) 1, 2, 3, 4

(d) 4, 3, 2, 1

- A big rectangular plot of area 4320 m2 is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot?

(a) 160 m x 27 m

(b) 240 m x 15 m

(c) 120 m x 36 m

(d) 135 m x 32 m

- The diameters of two circular coins are in the ratio 1 : 3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times is the smaller coin rolled around the bigger coin?

(a) 9

(b) 6

(c) 3

(d) 1.5

- A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. Find the diameter of the base of the cone.

(a) 158.76 cm

(b) 79.38 cm

(c) 12.6 cm

(d) 39.69 cm

- A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

(a) 1 : 2

(b) 2 : 1

(c) 3 : 1

(d) None of these

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