In this question, we are asked to identify which pair of cells are haploid. Haploid cells contain a single set of chromosomes.
- The egg cell is a haploid cell, as it contains half the number of chromosomes required for fertilization.
- Antipodal cells, which are formed in the female gametophyte, are also haploid.
On the other hand:
- The nucleus and polar nuclei are diploid (contain two sets of chromosomes).
- The nucleus of the ovule is also diploid.
Therefore, the correct answer is option (C), where both the egg cell and antipodal cells are haploid.