Difference between existence of partial derivatives, continuity, and differentiability — IITM BS previous year questions

Difference between existence of partial derivatives, continuity, and differentiability is part of Differentiability and Maths 2 Review, Week 11 in Mathematics 2. Prasnya files every IIT Madras BS previous year question from this subtopic here, each one with a worked explanation. Take the whole set as a timed mock and you get accuracy, pacing and per-question analysis back.