Logical Reasoning · General Aptitude · GATE Data Science and Artificial Intelligence

The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1,2 , and 3 , respectively. Which one among the given options is the most appropriate combination of P , Q , and R ?

Three different views of a dice are shown in the figure below.

The piece of paper that can be folded to make this dice is

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let $a_1$ and $a_2$ (in years) denote the ages of the brothers and $a_1 < a_2$.

Which one of the following statements is correct about their age on the day when they attain the same weight?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r \mathrm{~cm}$ as shown in the figure. The side of the dodecagon is d cm . All the triangles (numbered 1 to 12) in the figure are used to form squares of side $r \mathrm{~cm}$ and each numbered triangle is used only once to form a square.

The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Note: The figure shown is representative.