If the expression $5^{2 n}-48 n+\mathrm{k}$ is divisible by 24 for all $n \in \mathbb{N}$, then the least positive integral value of $k$ is

• A

  $47$
• B

  $48$
• C

  $24$
• Correct answer
  D

  $23$

Hence, the correct answer is option: 'D'.