In India, which one of the following compiles information on industrial disputes, closures, retrenchments and lay-offs in factories employing workers ?

The correct option is Labour Bureau.

Let us understand why this is the correct answer by looking at the roles and functions of the various organizations mentioned in the options:
1. Labour Bureau: This is an attached office of the Ministry of Labour and Employment, Government of India. It is specifically tasked with the collection, compilation, analysis, and dissemination of statistics related to different aspects of labour. This includes compiling comprehensive data on industrial disputes, closures, retrenchments, and lay-offs in factories and industries employing workers across India.
2. Central Statistics Office (CSO): Now part of the National Statistical Office (NSO), the CSO is responsible for coordination of statistical activities in the country, and for evolving and maintaining statistical standards. Its activities include compiling National Accounts Statistics (GDP), conducting the Annual Survey of Industries (ASI), and Consumer Price Index (CPI) for urban/rural sectors, but it does not directly compile administrative labour statistics like closures and disputes.
3. Department for Promotion of Industry and Internal Trade (DPIIT): Operating under the Ministry of Commerce and Industry, DPIIT is responsible for formulation and implementation of promotional and developmental measures for the growth of the industrial sector, keeping track of FDI inflows, and promoting ease of doing business. It does not handle labour relations and disputes statistics.
4. National Technical Manpower Information System (NTMIS): This system was set up to provide estimations of the requirement and availability of technical manpower in the country to help in planning technical education, and is not involved in compiling factory-level labour dispute or closure statistics.

Therefore, the compilation of statistics on industrial disputes, closures, retrenchments, and lay-offs in factories falls directly and exclusively under the mandate of the Labour Bureau.