Is it permissible for a married couple to visit a doctor and undergo the necessary examinations to ascertain their ability to conceive, even if it requires exposing their awrah when necessary, given that they have not conceived after two years of marriage?

"It is obligatory to be careful in preserving one's private parts (awrah). A male doctor should not examine a woman unless there is an urgent necessity and no female doctor is available. When there is such a necessity, it is stipulated that there should be no khalwah (private seclusion) and that no more than what is necessary should be exposed. It is permissible for a man to treat a woman and vice-versa when necessary, as mentioned in the hadith of Al-Rubayyi' bint Mu'awwidh. One should seek a female doctor to examine the wife if the examination is not an urgent necessity."