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

Direction: Read the information given below and answer the question.
(I) In a family of six persons A, B, C, D, E and F, there are two married couples.
(II) D is the grandmother of A and mother of B.
(III) C is the wife of B and mother of F.
(IV) F is the granddaughter of E.

Who among the following is one of the couples?

The volume of a solid hemisphere is numerically equal to its total surface area. Its radius is:

There are five positive observations. The average of the first three observations is $8$ and that of the last three observations is $6$. If the average of all five observations is $6$, what is the third observation?

Five bells ring at intervals of 3, 5, 6, 8 and 9 seconds. If all the bells ring once together, after how long a period would the bells ring together again?

Find the minimum value of $5\sin \theta +12\cos \theta$.