From which of the following minerals is $Ra$ (Radium) obtained?

An ideal gas heat engine operates in a Carnot cycle between $227\,^{\circ}C$ and $127\,^{\circ}C$. It absorbs $6\, kcal$ at the higher temperature. The amount of heat (in $kcal$) converted into work is equal to

The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).

The Biuret test is not given by:

In an experiment with a beam balance,an unknown mass $m$ is balanced by two known masses of $16 \, kg$ and $4 \, kg$ as shown in the figure. The value of the unknown mass $m$ is ....... $kg$.

The incentre of the triangle with vertices $A(1, \sqrt{3})$,$B(0,0)$,and $C(2,0)$ is