Social media plays a significant role in cross-cultural communication. A vast amount of this occurs in code-mixed and multilingual form, posing a significant challenge to Natural Language Processing (NLP) tools for processing such information, like language identification, topic modeling, and named-entity recognition. To address this, we introduce a large-scale multilingual, and multi-topic dataset (MMT) collected from Twitter (1.7 million Tweets), encompassing 13 coarse-grained and 63 fine-grained topics in the Indian context. We further annotate a subset of 5,346 tweets from the MMT dataset with various Indian languages and their code-mixed counterparts. Also, we demonstrate that the currently existing tools fail to capture the linguistic diversity in MMT on two downstream tasks, i.e., topic modeling and language identification. To facilitate future research, we will make the anonymized and annotated dataset available in the public domain.