Which of the following pairs of hormones are not antagonistic (having opposite effects) to each other?

Relaxin and Inhibin do not have an opposing effect. 

Relaxin is a hormone produced by the ovary and the placenta with important effects in the female reproductive system and during pregnancy. In preparation for childbirth, it relaxes the ligaments in the pelvis and softens and widens the cervix. 

Inhibin is a protein secreted by the Sertoli cells in men and by the granulosa cells in women. It inhibits the synthesis and release of FSH.

Aldosterone and ANF are antagonistic hormones. Aldosterone increases the blood pressure while ANF (Atrial Natriuretic Factor) decreases it.

Parathormone and calcitonin are antagonistic hormones. Parathormone is a hypercalcemic hormone while calcitonin is a hypocalcemic hormone.

Glucagon and insulin are antagonistic hormones. Glucagon is a hyperglycemic hormone while insulin is a hypoglycemic hormone.