Recently, there is an increasing interest in multilingual automatic speech recognition (ASR) where a speech recognition system caters to multiple low resource languages by taking advantage of low amounts of labelled corpora in multiple languages. With multilingualism becoming common in today’s world, there has been increasing interest in code-switching ASR as well. In code-switching, multiple languages are freely interchanged within a single sentence or between sentences. The success of low-resource multilingual and code-switching (MUCS) ASR often depends on the variety of languages in terms of their acoustics, linguistic characteristics as well as the amount of data available and how these are carefully considered in building the ASR system. In this MUCS 2021 challenge, we would like to focus on building MUCS ASR systems through two different subtasks related to a total of seven Indian languages, namely Hindi, Marathi, Odia, Tamil, Telugu, Gujarati and Bengali. For this purpose, we provide a total of ~600 hours of transcribed speech data, comprising train and test sets, in these languages, including two code-switched language pairs, Hindi-English and Bengali-English. We also provide baseline recipes for both the subtasks with 30.73% and 32.45% word error rate on the MUCS test sets, respectively.