Step 1: Read the story carefully.
A single mammal population $X$ was split into two groups by continental drift. They lived apart for about $1$ lakh years, and afterwards they could no longer produce fertile offspring together. We need to name the kind of isolation that caused this.
Step 2: Recall what speciation needs.
New species form when gene flow between groups is blocked long enough for them to drift apart genetically. The barrier that blocks gene flow is the key clue. Here the barrier is a physical one created by continental drift.
Step 3: Match the clue to the right term.
A physical, spatial barrier (oceans, mountains, drifting continents) that separates populations is called geographical isolation, and the resulting process is allopatric speciation. Continental drift is a textbook example of exactly this.
Step 4: Rule out temporal isolation.
Temporal isolation means the groups breed at different times, like different seasons or flowering periods. Nothing in the question mentions a timing difference, so this does not apply.
Step 5: Rule out mechanical isolation.
Mechanical isolation means reproductive structures are physically incompatible so mating cannot occur. The question gives no such structural mismatch; the cause stated is the land splitting apart. So this is not it either.
Step 6: Conclude.
Since both (A) and (B) are ruled out, option (D) ``Both (B) and (C)'' also fails. The single correct cause is the physical separation by continental drift, which is geographical isolation.
\[ \boxed{\text{Geographical isolation}} \]