The correct answer is option A) Taittiya Aryanka, Aiteriya Upanishads.

Explanation:
The Taittiya Aryanka and Aiteriya Upanishads directed the ladies to leave the hall of learning where some principles of gynaecology were explained, as these principles were considered indelicate for the female ear. Let's understand this in more detail.

1. Taittiya Aryanka:
The Taittiya Aryanka is a part of the Taittiriya Shakha of the Krishna Yajur Veda. It consists of explanations and rituals related to the Yajurveda. The Taittiya Aryanka contains sections called Brahmanas, which provide explanations of the rituals mentioned in the Yajur Veda.

2. Aiteriya Upanishads:
The Aiteriya Upanishads is a collection of ancient Sanskrit texts that are part of the Aitareya Shakha of the Rig Veda. It is one of the oldest Upanishads and contains philosophical and spiritual teachings. The Aiteriya Upanishads discuss various topics such as the nature of the soul, the nature of reality, and the path to enlightenment.

Indelicate Principles of Gynaecology:
In ancient times, certain principles of gynaecology were considered indelicate or inappropriate for the female ear. This may have been due to cultural norms and beliefs surrounding women's roles and societal expectations. These principles might have been related to reproductive health, childbirth, or other aspects of women's bodies and health.

The Direction to Leave the Hall of Learning:
The Taittiya Aryanka and Aiteriya Upanishads directed the ladies to leave the hall of learning when these indelicate principles of gynaecology were being explained. It is important to note that this directive does not imply that women were considered inferior or unworthy of knowledge. Rather, it reflects the cultural norms and customs of that time period.

Conclusion:
In conclusion, the Taittiya Aryanka and Aiteriya Upanishads directed the ladies to leave the hall of learning where indelicate principles of gynaecology were being explained. This directive was likely based on the cultural norms and beliefs surrounding women's roles and societal expectations during that time period.