Nuts (almonds pistachios etc) are eaten widely, which are the main health benefits of eating nuts?are these useful for brain also?

Many benefits, yes: Regular consumption of nuts reduces risk of heart attack, stroke, cancer and diabetes and in moderation maintains healthy weight. Walnuts are esp. good for brain due to DHA content. See http://www.brainhq.com/brain-resources/everyday-brain-fitness/brain-healthy-foods-nutrition/nuts-brain-health and http://well.blogs.nytimes.com/2015/03/30/nuts-are-a-nutritional-powerhouse-for-rich-and-poor/?_r=0