Mensuration & Basic Geometry Fading

The top of a table is rectangular and its dimensions are 6' \times 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5' \times 8' and each of them has exactl

A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total n

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 cu

What is the least possible number of cuts required to cut a cube into 64 identical pieces?

Consider the following : 1. 1000 litres = 1 m³ 2. 1 metric ton = 1000 kg 3. 1 hectare = 10000 m² Which of the above are correct?

125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side ?

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

A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into v

How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds?

There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?

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 triangul

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) ?

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 c

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 state

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

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

A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?

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?

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?

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

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?