The rapid expansion of social media has led toan increase in code-mixed content, presentingsignificant challenges in the effective detectionof hate speech and fake narratives. To advanceresearch in this area, a shared task titled De-coding Fake Narratives in Spreading HatefulStories (Faux-Hate) was organized as part ofICON 2024. This paper introduces a multi-task learning model designed to classify Hindi-English code-mixed tweets into two distinct cat-egories: hate speech and false content. The pro-posed framework utilizes fastText embeddingsto create a shared feature space that adeptly cap-tures the semantic and syntactic intricacies ofcode-mixed text, including transliterated termsand out-of-vocabulary words. These sharedembeddings are then processed through twoindependent Support Vector Machine (SVM)classifiers, each specifically tailored for oneof the classification tasks. Our team, secured10th place among the participating teams, asevaluated by the organizers based on Macro F1scores.