WBCS Mains 2020 Official Paper-VI

A right circular cone, a right circular cylinder and a hemisphere all have the same radius, and the heights of the cone and cylinder equal their diameters. Then their volumes are proportional respectively to:

A merchant purchases $11$ toys for Rs. $10$ and sells $10$ toys for Rs. $11$. His profit percentage is:

A sum of money lent at simple interest becomes double of itself in $8$ years. Then the sum will triple itself in:

An article is sold at Rs. $972$, yielding a profit of $8\%$. If it is sold at Rs. $872$, then there is a loss of:

If $\tan \theta +\sin \theta =m$ and $\tan \theta -\sin \theta =n$, then which one of the following relations is correct?