Why jain People who don t eat garlic,onion, carrot are more prone to risk of cancer ?

I may be unable to answer your question because I really don't know what you mean by "jain People", but I do know that certain foods have cancer fighting chemicals in them. IF you do not eat a lot of these foods, I suppose that someone may be prone to get Cancer easier then those who include these certain foods in their diet. Almost everything appears to give you Cancer these days so your overall environment should be taken into consideration as well. Asbestos, gas fumes, inhaling chemicals on a daily basis, exposure to harmful sun rays, all play a part in some kind of Cancer. Precaution is the key, as well as a good diet of nutritional and cancer fighting foods.