Tarun Bharat Sangh is an organization based in a village near Alwar, Rajasthan. This organization has garnered fame due to its work in `Rain-water harvesting`, which is the correct answer denoted by option 4. Let`s assess each option to understand why this is so.
Option 1, `Cultivation of genetically modified cotton`, is not connected with the work of Tarun Bharat Sangh. This typically refers to the scientific development and cultivation of cotton strains, which is not the focus of this organization.
Option 2, `Rehabilitation of women victims of AIDS` refers to providing support to women affected by AIDS. Again, this is not a key activity of Tarun Bharat Sangh, so this option is not correct.
Missing this focus again, option 3, `Livelihood projects for destitute rural women` suggests providing employment opportunities for impoverished rural women, which though crucial, does not align with Tarun Bharat Sangh`s primary focus.
Option 4 `Rain-water harvesting` is the correct answer, as this is precisely what Tarun Bharat Sangh is known for. The organization has done significant work in conserving water and promoting sustainable water use through rain-water harvesting.