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 number of pieces produced by applying n cuts is denoted by xn. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x4?

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 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?

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 triangular sheets of equal area.

Which of the above statements is/are correct?

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

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?

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 the mass of Q is two times that of P. Let u=m/x and v=n/y. Which one of the following is correct?

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?

There are three pillars X,Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6cm but slips down 1cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is height of shortest pillar?

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

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

A piece of tin is in the form of rectangle having length 12 cm and width 08 cm. This is used to construct a closed cube. The side of the cube is:

A cylindrical overhead tank of radius 2m and height 7m 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?

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 of following statement is correct?

A village having 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

Consider the following figure and answer the item that follows:

A square is divided into four rectangles as shown above.

The lengths of the side of rectangle are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square?

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 the ratio PQ : PR, then what is n?

P, Q and Rare 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?

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