Which of these glands is large at the time of birth but in adults, it reduces to a very small size?

The correct option is C Thymus
Thymus is a lymphoid gland behind the breast bone. At birth, thymus commonly weighs between $10$ and $15\text{gm}$. It continues to grow up to the age of puberty when its weight ranges between $30$ and $40\text{gm}$. Thereafter, this gland undergoes atrophy at puberty. It generally progressively diminishes in size undergoing gradual atrophy and replacement by fat so that after mid adult life it may weigh only about $10\text{gm}$.

The rest three glands that are, thyroid, spleen and adrenal gland do not degenerate with the age.
So, the correct answer is 'Thymus'$\text{C}$.