1. Group 13 elements are: $\mathrm{B,\, Al,\, Ga,\, In,\, Tl}$

2. We need the elements with highest and lowest first ionisation enthalpy.

3. General trend down a group: ionisation enthalpy usually decreases because:

   • atomic size increases,
   • shielding increases,
   • valence electron is easier to remove.

   So one may expect: $\mathrm{B} \text{ highest, and } \mathrm{Tl} \text{ lowest}$

4. But Group 13 shows irregularity due to poor shielding by d and f electrons.

   Approximate first ionisation enthalpies are:

   • $\mathrm{B} \approx 801\ \text{kJ mol}^{-1}$
   • $\mathrm{Al} \approx 578\ \text{kJ mol}^{-1}$
   • $\mathrm{Ga} \approx 579\ \text{kJ mol}^{-1}$
   • $\mathrm{In} \approx 558\ \text{kJ mol}^{-1}$
   • $\mathrm{Tl} \approx 589\ \text{kJ mol}^{-1}$

5. From these values:

   • Highest first ionisation enthalpy = $\mathrm{B}$
   • Lowest first ionisation enthalpy = $\mathrm{In}$

6. Therefore, the correct pair is: $\boxed{\mathrm{B\ \&\ In}}$

7. Option checking:

   • A: $\mathrm{B \& Tl}$ → incorrect, since $\mathrm{Tl}$ is not the lowest.
   • B: $\mathrm{Tl \& B}$ → incorrect order and values.
   • C: $\mathrm{B \& In}$ → correct.
   • D: $\mathrm{B \& Ga}$ → incorrect, $\mathrm{Ga}$ is not the lowest.

Hence, the correct answer is Option C.