WBCS Mains 2020 Official Paper-VI

A conical container of base diameter $2R$ and height $H$ is full of water which is poured into a cylindrical container of diameter $2pR$. Then it will occupy a height equal to:

If the time taken to go from one station to another is required to be decreased by $20\%$, then by what percent must the speed of the train be increased?

Satyajit is younger than Diganta by $8$ years. If their ages are in the ratio of $5:7$, then how old is Satyajit?

The mean of five observations $x$, $x+2$, $x+6$, $x+4$, $x+8$ is $11$. The mean of the last three observations is:

In a right-angled triangle $\Delta ABC$, $\angle B=90^{\circ }$, $AB=6\text{cm}$, and $BC=8\text{cm}$. The radius $r$ of the inscribed circle is: