The correct answer is option 'C': Estrogen secretion increases.

Explanation:
When an ovum fails to get fertilized, the hormonal changes that occur in the female reproductive system are aimed at preparing for the shedding of the uterine lining during menstruation. Let's analyze each option to understand why option 'C' is unlikely.

a) Corpus luteum will disintegrate:
After ovulation, the ruptured follicle in the ovary transforms into a structure called the corpus luteum. The corpus luteum secretes hormones, primarily progesterone, which is necessary for the maintenance of the uterine lining in case fertilization occurs. However, if fertilization does not occur, the corpus luteum will eventually disintegrate, leading to a decrease in progesterone secretion.

b) Progesterone secretion rapidly declines:
As mentioned above, progesterone is primarily secreted by the corpus luteum. If fertilization does not occur, the corpus luteum will disintegrate, resulting in a rapid decline in progesterone secretion. This decline in progesterone levels triggers the shedding of the uterine lining during menstruation.

c) Estrogen secretion increases:
Estrogen is primarily secreted by the developing follicles in the ovary before ovulation occurs. After ovulation, the estrogen secretion decreases. If fertilization does not occur, the corpus luteum disintegrates, leading to a decrease in progesterone secretion. This decrease in progesterone levels results in a relative increase in estrogen levels, as there is no longer progesterone to balance its effects. This increase in estrogen levels stimulates the growth of new follicles in the ovary, initiating a new menstrual cycle.

d) Primary follicle starts developing:
A primary follicle is an immature ovarian follicle that contains an immature ovum. It takes several weeks for a primary follicle to develop and mature into a secondary follicle before ovulation. If an ovum fails to get fertilized, the existing primary follicles will not start developing immediately. Instead, the hormonal changes will initiate the growth of new primary follicles in the ovary for the next menstrual cycle.

In summary, when an ovum fails to get fertilized, the corpus luteum disintegrates, progesterone secretion rapidly declines, and new primary follicles start developing. However, estrogen secretion does not increase; it decreases due to the disintegration of the corpus luteum. Therefore, option 'C' is unlikely.