Concept:The correct modal verb must convey a firm promise or sense of duty not to betray a secret.
Explanation:The sentence is about making a commitment to keep something secret.
"Shan't" is the contraction of "shall not" and expresses a strong personal intention or promise.
"I shan't tell anyone" means "I will definitely not tell anyone," which matches the expectation of secrecy.
"Couldn't" suggests inability, not a deliberate choice.
"Needn't" means "it is not necessary," which does not fit the obligation of secrecy.
"Mightn't" shows possibility, leaving doubt about whether the secret will be kept.
Therefore, only "shan't" reflects the required sense of obligation and determination.
Answer:B. shan't