Which one of the following statements is not true?

The correct answer is Option (3) → The nucleus of the functional megaspore divides meiotically to form the embryo sac.

The embryo sac develops from a single functional megaspore. The megaspore itself is formed by meiosis of the megaspore mother cell, but after that the nucleus of the functional megaspore divides only by mitosis, three times in a row, to give the 2-, 4- and 8-nucleate stages.

Option (1) Pollen grains shed at the 2-celled stage contain a vegetative cell and a generative cell. — A correct statement. A mature pollen grain shed at the 2-celled stage has a large vegetative cell and a small generative cell.

Option (2) Each cell of the sporogenous tissue is a potential pollen or microspore mother cell. — A correct statement. Each cell of the sporogenous tissue can give rise to a microspore tetrad, so each one is a potential pollen or microspore mother cell.

Option (3) The nucleus of the functional megaspore divides meiotically to form the embryo sac. — An incorrect statement. The nucleus of the functional megaspore divides mitotically, not meiotically. These divisions are free nuclear, and cell walls are laid down only after the 8-nucleate stage.

Option (4) The primary endosperm cell divides repeatedly to form a triploid endosperm tissue. — A correct statement. After triple fusion, the primary endosperm cell divides repeatedly to form a triploid endosperm tissue that feeds the embryo.

NCERT Extract:
The Pistil, Megasporangium (Ovule) and Embryo Sac – “… Let us study about the formation of the embryo sac in detail. … The nucleus of the functional megaspore divides mitotically to form two nuclei which move to the opposite poles, forming the 2nucleate embryo sac. Two more sequential mitotic nuclear divisions result in the formation of the 4-nucleate and later the 8-nucleate stages of the embryo sac.”
Stamen, Microsporangium and Pollen Grain – “As each cell of the sporogenous tissue is capable of giving rise to a microspore tetrad. Each one is a potential pollen or microspore mother cell.”
Endosperm – “… The primary endosperm cell divides repeatedly and forms a triploid endosperm tissue.”