A cube is created by stacking 27 smaller cubes as shown in the figure. A plane, going through vertices A, B and C, cuts the cube as shown in the figure. How many smaller cubes will get cut? [Figure: see page 5 of source PDF]

The image is a ceramic tile of dimension 20 cm x 20 cm. How many distinct patterns can you create by using two such ceramic tiles in a rectangular patch of 40 cm x 20 cm on the wall? [Figure: see page 5 of source PDF]

At most how many triangles can appear by adding two straight lines to the figure? [Figure: see page 6 of source PDF]

Area of black surface in the following image is ________ cm². Note: 1. All curves have same radii. 2. Use the value of pi as 22/7 [Figure: see page 4 of source PDF]

How many distinct motifs appear in the figure on the right? Flips and rotations are to be counted separately, for example the motifs P and Q are distinct. [Figure: see page 6 of source PDF]

Twenty points are arranged on a plane as shown in the figure below. What is the highest number of squares that can be drawn using any four points as corners? [Figure: see page 4 of source PDF]

A family of four—grandfather, father, son and daughter—are caught in a heavy rain and are stranded at a bus stop close to their home. However they have only one umbrella with them. The umbrella can take a maximum of two people without either of them getting wet. The four members…

Figure to the left shows an unfolded pattern of a die. If four such identical dice are stacked one on top of another, as shown on the right, what is the sum of the numbers appearing on the faces which are parallel to the ground? [Figure: see page 3 of source PDF]

Six cards are laid out on a table as shown in the figure below. Each of the cards has a number on one side and a letter on the other side. What is the minimum number of cards you need to flip and see to make sure the rule, “cards that have a vowel on one side always have an even…