Question

which part of the plant cell permits it to with stand very dilute external medium without bursting

Answer 1

It is the cell wall which protects the cell from bursting due to osmosis in dilute external medium.

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Answer 2

Though plant cell consists cell wall, its main function is to give the cell structural support and protection from physical damage. But it is often permeable. The next layer, the cell membrane is semipermeable or sometimes  selectively permeable which stops the external solute molecules to enter inside the cell and thus prevents the bursting of the plant cell in dilute external medium.