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Vehicle make and model recognition (VMMR) is an important aspect of intelligent transportation systems (ITS). In VMMR systems, surveillance cameras capture vehicle images for real-time vehicle detection and recognition. These captured images pose challenges, including shadows, reflections, changes in weather and illumination, occlusions, and perspective distortion. Another significant challenge in VMMR is the multiclass classification. This scenario has two main categories: (a) multiplicity and (b) ambiguity. Multiplicity concerns the issue of different forms among car models manufactured by the same company, while the ambiguity problem arises when multiple models from the same manufacturer have visually similar appearances or when vehicle models of different makes have visually comparable rear/front views. This paper introduces a novel and robust VMMR model that can address the above-mentioned issues with accuracy comparable to state-of-the-art methods. Our proposed hybrid CNN model selects the best descriptive fine-grained features with the help of Fisher Discriminative Least Squares Regression (FDLSR). These features are extracted from a deep CNN model fine-tuned on the fine-grained vehicle datasets Stanford-196 and BoxCars21k. Using ResNet-152 features, our proposed model outperformed the SVM and FC layers in accuracy by 0.5% and 4% on Stanford-196 and 0.4 and 1% on BoxCars21k, respectively. Moreover, this model is well-suited for small-scale fine-grained vehicle datasets. [ABSTRACT FROM AUTHOR]