Geometry and Mensuration — UPSC CSAT Previous Year Questions

The top of a table is rectangular and its dimensions are 6' × 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5' × 8' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?

There are three types of rectangular tiles: 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x − y is

A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6.

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?

A rectangular floor measures 4 m in length and 2.2 m in breadth. Tiles of size 140 cm by 60 cm have to be laid without overlap; either orientation is allowed with parallel edges. What is the maximum number of tiles?

There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to?

On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path?

A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel)?

Consider the following statements: 1. The minimum number of points of intersection of a square and a circle is 2. 2. The maximum number of points of intersection of a square and a circle is 8. Which of the above statements is/are correct?

If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?

A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:

An agricultural field is in the form of a rectangle having length X₁ meters and breadth X₂ meters (X₁ and X₂ are variable). If X₁ + X₂ = 40 meters, then the area of the agricultural field will not exceed which one of the following values?

AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:

A cylindrical overhead tank of radius 2 m and height 7 m is to be filled from an underground tank of size 5.5m × 4m × 6m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

A square is divided into four rectangles as shown above. The lengths of the sides of rectangles are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square?

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