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. What will this distance be when the angle ABR is changed to 60 degrees? [Figure: see page 6 of source PDF]

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]

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 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]

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]

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…

The figure shows two concentric equilateral triangles with a circle within, such that the circle touches all the edges of the triangle. If the radius of the circle is √3 (square root of three), what is the total length of the star shaped outer border formed by the two intersectin…

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…

Except for one number, all the four-digit numbers given below are written using a single font. Identify the number that does not use the same font as the other numbers. [Figure: see page 7 of source PDF]