WBCS Mains 2021 (Held On May 2022) Official Paper-VI

The sum of the first five multiples of $3$ is:

If $\cot \theta =\frac{x}{y}$, then what is the value of $\frac{x\cos \theta -y\sin \theta }{x\cos \theta +y\sin \theta }$?

Find the correct answer figure in which the given question figure (consisting of a smaller letter 'Z' shape) is completely embedded.

Two problem figures have a specific common characteristic feature: both figures consist of a regular polygon where the number of internal dots is exactly equal to the number of sides of the polygon (e.g., a triangle with $3$ dots, a square with $4$ dots). Find the answer figure which shares this same characteristic feature.

Which of the following is the value of $\frac{256\times 256-144\times 144}{112}$?