The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 \mathrm{~cm}$ from its center is $1.5 \times 10^{-5} \mathrm{~T} \mathrm{~m}$. The magnetic moment of the dipole is _________ $A \mathrm{~m}^2$. (Given : $\frac{\mu_o}{4 \pi}=10^{-7} \mathrm{Tm} A^{-1}$ )

Let the sixth term in the binomial expansion of {\left( {\sqrt {{2^{{{\log }_2}\left( {10 - {3^x}} \right)}}} + \root 5 \of {{2^{(x - 2){{\log }_2}3}}} } \right)^m} in the increasing powers of $2^{(x-2) \log _{2} 3}$, be 21 . If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of $x$ is __________.

Match List - I with List - II :

Choose the most appropriate answer from the options given below :