A solid object made of cubes is shown below. This object is symmetric about all three axes, and does not contain cavities (no hollow spaces). How many cubes does the solid contain? [Figure: see page 5 of source PDF]

A UNION of two solids, a pentagonal prism and a hexagonal prism is shown below. The side view (on the right) depicts how the solids intersect. Visualise the new solid formed by their INTERSECTION (the part common to both of them). How many surfaces will the new solid have? [Figur…

A solid is drilled using a cylindrical drill in a direction, as shown below. How many surfaces will the solid have after the drilling is complete? [Figure: see page 5 of source PDF]

A diagram of three blocks A, B and C and their direction of movement is shown below. The blocks move continuously in units and change directions after hitting the side walls. From the given position, if block A moves at a speed of 2 units per second, and block B and block C move…

The figure below shows a hinged structure made up of 12 sticks. The structure can be elongated and compressed by changing the angle ABR. As shown in the figure, the distance between B and Q is 150√6 (one hundred and fifty times root six) units when the angle ABR is 90 degrees. Wh…

Three transparent glass pieces with different engravings are shown below. They are to be overlapped, one on top of the other, with the red corner exactly matching each other. What is the total number of triangles in the resultant figure? [Figure: see page 4 of source PDF]

In a new form of decimal system, the numbers 0 to 9 are represented by a new set of symbols. For example, the equation 1 + 4 = 5 is represented as equation (i). If in the solution to equation (iv) one digit appears twice, what number will replace the question mark? [Figure: see p…

A cube has its six faces numbered 1 to 6. A school boy tosses up the cube twice and notes down the two numbers appearing on top in these two tosses. He multiplies these two numbers and notes down the multiplication result. How many unique multiplication results can he possibly ge…

What is the area (in cm²) of the black portion, if the square is of length 16 cm? [Figure: see page 6 of source PDF]