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 intersecting triangles? [Figure: see page 7 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]

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]

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…

Two perspective views of the same solid object are shown below. Count the total number of surfaces in the object. Assume hidden surfaces to be flat. [Figure: see page 8 of source PDF]

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…

The image given below is made out of separate pieces. What is the least number of pieces that need to be moved and/or rotated and/or flipped for achieving symmetry about the central vertical axis? [Figure: see page 8 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]

A logo was designed by creating a pattern of orange petals using four semicircles. These petals were then inscribed in a green circular shape with an inner diameter of 14√2 (fourteen times square root of two) units, what is the area of the orange part in the logo? (Assume π = 22/…