Identify the set of cells which have haploid number of chromosomes ?

The correct answer is Option (1) → Egg cell and Synergid cell

All cells of the embryo sac come from the haploid functional megaspore by mitosis, so they are haploid. The nucellus is part of the diploid ovule, and the zygote is diploid.

Option (1) Egg cell and Synergid cell — Correct. All the cells of the embryo sac are formed by mitosis from a haploid megaspore, so they are haploid. The egg cell and the synergids make up the egg apparatus at the micropylar end, and both are haploid.

Option (2) Egg cell and Nucellar cell — Incorrect. The egg cell is haploid, but the nucellus lies outside the embryo sac, as part of the ovule. Its cells are diploid, so this pair is not all haploid.

Option (3) Zygote and Egg cell — Incorrect. The zygote is diploid, formed by fusion of two haploid gametes.

Option (4) Zygote and Antipodal cell — Incorrect. The antipodal cell is haploid, but the zygote is diploid.