Cubes CAT PYQs , 13 Questions with Solutions

A dice is thrown three times and its three different positions are given below. The number on the face opposite the face showing 3 is:

(Three dice shown side by side. Dice 1: top=2, front-left=1, front-right=3. Dice 2: top=3, front-left=1, front-right=5. Dice 3: top=4, front-left=2, front-right=3.)

How many triangles does the following figure have?

(An axis-aligned square with a second square rotated roughly 45 degrees, overlapping it at one corner in an isometric/wireframe style, with diagonal lines crossing through both squares.)

A cube of white material is painted red on all its surfaces. If it is cut into 125 smaller cubes of the same size, then how many cubes will have two sides painted red?

A cylinder is painted in 6 colours: Green, Blue, Yellow, Violet, Red and Pink. Three positions are shown below.

What is the colour in the empty space?

(Figure: three cylinder positions are shown, each with its curved side surface split into a top half and a bottom half, each half a different colour, plus one end-circle face, indicated by an arrow pointing to it, shown in a third colour. Position 1: side top-half = Green, side bottom-half = Blue, end-circle = Yellow. Position 2, the target, whose side top-half is blank/unlabeled and marked "?": side top-half = ? (to find), side bottom-half = Red, end-circle = Pink. Position 3: side top-half = Green, side bottom-half = Violet, end-circle = Pink.)

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

(Four dice images, each an isometric cube view showing a top face and two front side faces (front-left and front-right): Dice 1 shows top=6, front-left=2, front-right=4. Dice 2 shows top=2, front-left=3, front-right=4. Dice 3 shows top=3, front-left=5, front-right=4. Dice 4 shows top=1, front-left=3, front-right=2.)

The sheet of paper shown in the figure below is folded to form a box.

The net is a cross shape: a square labelled "2" on top; below it, a horizontal row of three squares labelled "4", "3", "6" from left to right; below the "3" square is a square labelled "1"; and below the "1" square is a square labelled "5".

Choose the correct alternative which will represent the position of numbers in the folded box: (a) A cube view showing top face = 2, front-left face = 3, front-right face = 5. (b) A cube view showing top face = 3, front-left face = 2, front-right face = 5. (c) A cube view showing top face = 4, front-left face = 6, front-right face = 3. (d) A cube view showing top face = 4, front-left face = 1, front-right face = 3.

How many squares does the figure have?

The water image of the above figure is?

An unfolded dice (net) is given below. Find the correct answer which can be formed by folding the unfolded dice.

Which of the answer figures given will complete the pattern of the question figure?

Three identical cones with base radius 'r' are placed on their bases so that each one is touching the other two. The radius of circle whose boundary touches the centre of these cones is

A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.

A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened?