What is the function of the germ pore in pollen grains?

The correct answer is Option (3) → Initiation of pollen tube

The outer wall of a pollen grain, the exine, is made of sporopollenin, a very hard and resistant material. At a few places the exine has openings called germ pores, where sporopollenin is absent. When a pollen grain lands on a suitable stigma, it germinates and the pollen tube comes out through one of these germ pores. The pollen tube then grows through the style to reach the ovule.

Option (1) Emergence of radicle — Incorrect. The radicle is part of the embryo inside a seed. It comes out when the seed germinates, long after pollination. A pollen grain has no radicle.

Option (2) Absorption of water for seed germination — Incorrect. A seed takes in water through the micropyle, the small pore left in the seed coat. The germ pore is an opening in the pollen wall, not in the seed.

NCERT Extract:
Stamen, Microsporangium and Pollen Grain – “… The hard outer layer called the exine is made up of sporopollenin which is one of the most resistant organic material known. It can withstand high temperatures and strong acids and alkali. No enzyme that degrades sporopollenin is so far known. Pollen grain exine has prominent apertures called germ pores where sporopollenin is absent.”
Pollination – “… As mentioned earlier, following compatible pollination, the pollen grain germinates on the stigma to produce a pollen tube through one of the germ pores (Figure 1.12a). The contents of the pollen grain move into the pollen tube.”