Neural Architectural Search (NAS) is a novel method capable of achieving state-of-the-art performance with limited computational resources and time. These coupled factors have resulted in its increasing popularity in many domains. NAS helps to discover an effective architecture for a given task. In parallel, learning through tests, a technique used in human learning aims at improving learning results: a chain of new assessments are conducted with increasing difficulty; the learner uses them to discover susceptible points, and those susceptible points are further addressed to pass the evaluation effectively. When applied in the case of learning in machines, this technique enhances their learning ability and is called Learning by passing tests(LPT). We propose to use the LPT technique in combination with NAS, particularly for Differentiable Architecture Search(DARTS), Progressive Differentiable Architecture Search(PDARTS) and, Partially Connected Differentiable Architecture Search(PCDARTS) to solve the medical challenge of Skin Cancer Classification. A bilevel optimization algorithm is formulated using LPT and is applied on the HAM10000 dataset and the Kaggle Skin Cancer: Malignant Vs. Benign dataset. Our LPT algorithm coupled with NAS can attain better performance than the traditional NAS methods and different state-of-the-art models for the given classification task.