Yes, bookkeeping is mandatory for all businesses except the sole proprietorship firm. Even the proprietorship firm has to maintain accounts after crossing a certain turnover. Additionally, the companies have to maintain accounts as per the accounting standards prescribed.
Audit of statements is mandatory for all the companies, but not in case of LLP. The financial statements of LLP must be audited if its turnover exceeds INR 40 Lakh or the partners’ contribution exceeds INR 25 Lakh.