WBCS Mains 2020 Official Paper-VI

A hemispherical bowl is made of a steel sheet $0.8\text{cm}$ thick. The inside radius of the bowl is $5\text{cm}$. The volume of steel used in making it is approximately:

If

then which of the following relations is correct?

A person walks from his house at a speed of $4\text{km/h}$ and reaches his school $5$ minutes late. If his speed had been $5\text{km/h}$, he would have reached $10$ minutes earlier. The distance of the school from his house is:

The greatest and the least value of $a+b\sin \theta$ ($0^{\circ }\le \theta \le 90^{\circ }$) are $7$ and $3$ respectively. Find the values of $a$ and $b$.

If $P(1,2)$, $Q(4,6)$, $R(5,7)$, and $S(a,b)$ are the vertices of a parallelogram $PQRS$, then the values of $a$ and $b$ are: