Identify the order in which the spin-only magnetic moment (in $BM$) increases for the following four ions:
$I. Fe^{2+}$
$II. Ti^{2+}$
$III. Cu^{2+}$
$IV. V^{2+}$

$A$ fireman of mass $60 \, kg$ slides down a pole. He is pressing the pole with a force of $600 \, N$. The coefficient of friction between the hands and the pole is $0.5$. With what acceleration will the fireman slide down (in $, m/s^2$)? (Take $g = 10 \, m/s^2$)

If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :

$(\sqrt{3}+i)^7+(\sqrt{3}-i)^7$ is equal to (in $\sqrt{3}$)

The percentage of gold in $14$ carat gold is: (in $\%$)

The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be: