Ferrous ion changes to $X$ ion upon reacting with acidified hydrogen peroxide. The number of $d$-electrons present in $X$ and its magnetic moment (in $BM$) are,respectively:

The product of the given reaction is:

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1 / e$ after a time:

An ideal heat engine operates on a Carnot cycle between $227\,^{\circ}C$ and $127\,^{\circ}C$. It absorbs $6 \times 10^4\, \text{cal}$ at the higher temperature. The amount of heat converted into work is equal to:

If $A+B+C=270^{\circ}$,then $\cos 2A+\cos 2B+\cos 2C$ is equal to: