Five square pyramids are stacked as shown in the figure below with the bottom layer consisting of four pyramids in a 2 x 2 grid. If the bottom layer consists of pyramids in 6 x 7 grid, and they are stacked in a similar manner to its maximum height, how many pyramids will the formation contain? [Figure: see page 4 of source PDF]

In the square ABCD, line XY is drawn parallel to the base as shown in the figure below. P and Q are any two arbitrary points on XY, forming triangles ABQ and CDP. What fraction of the area of the square is the total green shaded area? [Figure: see page 3 of source PDF]

A bank needs to upgrade its ATM kiosks to be wheel-chair accessible. An ATM kiosk entrance has four steps rising up to reach the floor level of the kiosk. Each step is 1000 mm in length, 300 mm in breadth, and 150 mm in height. The bank proposes to create a wheel-chair accessible…

What are the least number of lines required to generate a 3D form such that it creates shadows similar to the figure shown below? [Figure: see page 3 of source PDF]

A system of frictionless and massless pulleys is being used to pull up a load of 2520 N. What is the minimum force (in Newtons) required at the end of the rope (shown in dashed lines)? [Figure: see page 5 of source PDF]

An irregular solid is cut into seven pieces as shown. The pieces are neither rotated nor scaled, but are kept in a random sequence. Find the correct sequence to get the smooth form. The sequence should be written from left to right. [Figure: see page 2 of source PDF]

Shown below are three views of the same solid. Count the number of edges. [Figure: see page 5 of source PDF]

Solid 1, Solid 2 and Solid 3 are joined together to form a cuboid as shown in Figure 1. The cuboid is then painted from all the sides. How many surfaces are there without the paint when you separate all the three solids? [Figure: see page 2 of source PDF]

Imagine a pentagon shaped building. The walls of the building are sides of the pentagon, and there is a watchtower at each vertex. Each watchtower can have guards who can watch two walls connected to the watchtower. What is the minimum number of guards required if each wall needs…