Mensuration and geometry

2011 · Q36

Consider the figure given below and answer the item that follows:

In the figure shown above, OP₁ and OP₂ are two plane mirrors kept perpendicular to each other. S is the direction of a beam of light falling on the mirror OP₁. The direction of the reflected beam of light from the mirror OP₂ will be

1. (a)Perpendicular to the direction S.
2. (b)At 45° to the direction S.
3. (c)Opposite and parallel to the direction S.UPSC key
4. (d)At 60° to the direction S.

2011 · Q38

Consider the following figure and answer the item that follows:

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?

1. (a)10
2. (b)11UPSC key
3. (c)15
4. (d)Cannot be determined as the given data are insufficient

2011 · Q43

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

1. (a)2 days
2. (b)3 daysUPSC key
3. (c)4 days
4. (d)5 days

2015 · Q76

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. (a)Z, U and W are parallel.
2. (b)X, V and Y are parallel.
3. (c)Z, V and U are all perpendicular to W.
4. (d)Y, V and W are parallel.UPSC key

2016 · Q39

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. (a)2 cm
2. (b)3 cm
3. (c)4 cmUPSC key
4. (d)6 cm

2016 · Q50

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. (a)400 sq mUPSC key
2. (b)300 sq m
3. (c)200 sq m
4. (d)80 sq m

2016 · Q57

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. (a)20 m
2. (b)25 mUPSC key
3. (c)30 m
4. (d)35 m

2016 · Q73

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

1. (a)$\dfrac{1}{3}$UPSC key
2. (b)$\dfrac{1}{2}$
3. (c)$\dfrac{1}{4}$
4. (d)$\dfrac{1}{6}$

2017 · Q75

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. (a)4UPSC key
2. (b)6
3. (c)12
4. (d)15

2018 · Q60

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. (a)$\dfrac{5}{7}$ sq cm
2. (b)$\dfrac{7}{5}$ sq cm
3. (c)1 sq cmUPSC key
4. (d)$\dfrac{25}{12}$ sq cm

2020 · Q38

Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?

1. (a)u = 4vUPSC key
2. (b)u = 2v
3. (c)v = u
4. (d)v = 4u

2020 · Q73

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?

1. (a)1 only
2. (b)2 onlyUPSC key
3. (c)Both 1 and 2
4. (d)Neither 1 nor 2

2020 · Q78

If 1 litre of water weighs 1 kg, then how many cubic millimetres of water will weigh 0·1 gm?

1. (a)1
2. (b)10
3. (c)100UPSC key
4. (d)1000

2021 · Q63

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?

1. (a)1
2. (b)2UPSC key
3. (c)3
4. (d)4

2021 · Q68

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)?

1. (a)1000
2. (b)10000
3. (c)100000
4. (d)1000000UPSC key

2022 · Q59

Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

1.It is possible to cut the sheet exactly into 4 square sheets.

2.It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is/are correct?

1. (a)1 only
2. (b)2 only
3. (c)Both 1 and 2UPSC key
4. (d)Neither 1 nor 2

2023 · Q67

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 such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

1. (a)6
2. (b)7
3. (c)8
4. (d)9UPSC key

2024 · Q30

Consider the following:

1.1000 litres = 1 $m^{3}$

2.1 metric ton = 1000 kg

3.1 hectare = 10000 $m^{2}$

Which of the above are correct?

1. (a)1 and 2 only
2. (b)2 and 3 only
3. (c)1 and 3 only
4. (d)1, 2 and 3UPSC key