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GS Prelims Paper II Geometry & Mensuration up to 2019

Civil Services Examination 2019


1. A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?

  1. 4
  2. 6
  3. 8
  4. 10


2. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

  1. 18
  2. 24
  3. 32
  4. 36


3. P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R?

  1. 140 km
  2. 130 km
  3. 10 km
  4. 100 km


4. 'A' started from his house and walked 20 m towards East, where his friend B joined him. They together walked 10 m in the same direction. Then 'A' turned left while 'B' turned right and travelled 2 m and 8 m respectively. Again 'B' turned left to travel 4 m followed by 5 m to his right to reach his office. 'A' turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices?

  1. 15 m
  2. 17 m
  3. 19 m
  4. 20 m


Civil Services Examination 2018


1. Consider the following three- dimensional figure

How many triangles does the above figure have?

  1. 18
  2. 20
  3. 22
  4. 24


2. How many diagonals can be drawn by joining the vertices of an octagon?

  1. 20
  2. 24
  3. 28
  4. 64


3. There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?

  1. 4
  2. 6
  3. 8
  4. 12


4. Twelve equal squares are placed to fit in a rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?

  1. 5/7 sq cm
  2. 7/5 sq cm
  3. 1 sq cm
  4. 25/12 sq cm


Civil Services Examination 2017


1. The outer surface of a 4 cm x 4 cm x 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty four 1 cm x 1 cm x 1 cm small cubes. How many small cubes do not have painted faces?

  1. 8
  2. 16
  3. 24
  4. 36


2. Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?

  1. 4
  2. 6
  3. 12
  4. 15


Civil Services Examination 2016


1. 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:

  1. 2 cm
  2. 3 cm
  3. 4 cm
  4. 7 cm


2. A person climbs a hill in a straight path from point 'O' on the ground in the direction of north-east and reaches a point 'A' after travelling a distance of 5 km. Then, from the point 'A' he moves to point 'B' in the direction of north-west. Let the distance AB be 12 km. Now, how far is the person away from the starting point 'O'?

  1. 7 km
  2. 13 km
  3. 17 km
  4. 11 km


3. 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?

  1. 400 sq m
  2. 300 sq m
  3. 200 sq m
  4. 80 sq m


4. 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:

  1. 20 m
  2. 25 m
  3. 30 m
  4. 35 m


5. A person walks 12 km due north, then 15 km due east, after that 19 km due west and then 15 km due south. How far is he from the starting point?

  1. 5 km
  2. 9 km
  3. 37 km
  4. 61 km


6. A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:

  1. 32
  2. 24
  3. 16
  4. 8


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

  1. 1/3
  2. 1/2
  3. 1/4
  4. 1/6


8. A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target?

  1. 0.40
  2. 0.20
  3. 0.16
  4. 0.04


9. Shahid and Rohit start from the same point in opposite directions. After each 1 km, Shahid always turns left and Rohit always turns right. Which of the following statements is correct?

  1. After both have travelled 2 km, the distance between them is 4 km.
  2. They meet after each has travelled 3km.
  3. They meet for the first time after each has travelled 4 km.
  4. They go on without ever meeting again.


Civil Services Examination 2015


1. In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V.

Which one of the following statements is correct?

  1. Z, U and W are parallel.
  2. X, V and Y are parallel.
  3. Z, V and U are all perpendicular to W.
  4. Y, V and W are parallel.


Civil Services Examination 2014


1. Consider the following statements:

There are six villages A, B, C, D, E and F. F is 1 km to the west of D.
B is 1 km to the east of E. A is 2 km to the north of E. C is 1 km to the east of A. D is 1 km to the south of A.

Which three villages are in a line?

  1. A, C, B
  2. A, D, E
  3. C, B, F
  4. E, B, D


2. Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is

  1. 60
  2. 13
  3. 17
  4. 7


3. A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden

  1. has increased by 20%
  2. has increased by 12%
  3. has increased by 8%
  4. is exactly the same as the old area.


Civil Services Examination 2011


1. Consider the following figure and answer the items that follows:

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

  1. 10
  2. 11
  3. 15
  4. Cannot be determined as the given data are Insufficient


2. A village having a population of 4000 requires 150 liters 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. 2 days
  2. 3 days
  3. 4 days
  4. 5 days


3. The houses of A and B face each other on a road going north-south, A's being on the western side. A comes out of his house, turns left, travels 5 km, turns right, travels 5 km to the front of D'shouse. B does exactly the same and reaches the front of C's house. In this context, which one of the following statements is correct?

  1. C and D live on the same street.
  2. C's house faces south.
  3. The houses of C and D are less than 20 km apart.
  4. None of the above