Psychological assessment tools have long helped humans understand behavioural patterns. While Large Language Models (LLMs) can generate content comparable to that of humans, we explore whether they exhibit personality traits. To this end, this work applies psychological tools to LLMs in diverse scenarios to generate personality profiles. Using established trait-based questionnaires such as the Big Five Inventory and by addressing the possibility of training data contamination, we examine the dimensional variability and dominance of LLMs across five core personality dimensions: Openness, Conscientiousness, Extraversion, Agreeableness, and Neuroticism. Our findings reveal that LLMs exhibit unique dominant traits, varying characteristics, and distinct personality profiles even within the same family of models.