The growth of a pollen tube towards the ovule is caused by

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Hint It is the growth of organisms navigated by chemical stimuli from outside of the organism. It is found in the case of plants, fungi, and bacteria. A chemical gradient can influence the expansion of the organism in a positive or negative way.

Complete answer
During the chemotropism process, the movement of plant or plant parts in response to chemical stimuli.
When pollen grain comes in touch with the stigma, the ovary produces a positive chemical response for the pollen grain, which successively gives out the plant part that grows towards the ovary and carries the male gamete to the ovum for fertilization.

Additional information
In flowering plants, the main example of chemotropism is seen in plant fertilization and plant part elongation of angiosperms. Unlike animals, plants cannot move, and thus need a delivery mechanism for amphimixis. Pollen, which contains the male gametophyte, is transferred to a different plant via insects or wind. If the pollen is compatible it'll germinate and start to grow. The ovary releases chemicals that stimulate a positive chemotropic response from the developing plant part. In response, the tube develops an outlined tip growth area that promotes directional growth and elongation of the plant part thanks to a calcium gradient.
The roots grow towards useful minerals displaying positive chemotropism and grow faraway from harmful acids displaying negative chemotropism, it is an example of positive and negative chemotropism which is shown by a plant's roots.

So the correct answer is ‘Chemotropism’.

Note: In more complex organisms an example of chemotropic movement includes the growth of individual neuronal cell axons in response to extracellular signals. Secreted protein can either attract or repel particular neurons. Neurotrophins, semaphorins, netrins, and fibroblast growth factors are some signal proteins that have been helpful in neuronal growth.