In many real-life classification problems, we may not get exact class labels for training samples. One such example is bandit feedback in multiclass classification. In this setting, we only get to know whether our predicted label is correct or not. Due to which, we are left in uncertainty about the actual class label when we predict the wrong class. This paper proposes exact passive-aggressive online algorithms for multiclass classification under bandit feedback (EPABF). The proposed approach uses an exploration-exploitation strategy to guess the class label in every trial. To update the weights, we solve a quadratic optimization problem under multiple class separability constraints and find the exact solution. We do this by finding active constraints using the KKT conditions of the optimization problem. These constraints form a support set that determines the classes for which the weight vector needs to be updated. We propose three different variants of the weight update rule, which vary based on the aggressiveness to correct the mistake. These are called EPABF, EPABF-I, and EPABF-II. We also provide mistake bounds for the proposed EPABF, EPABF-I, and EPABF-II. Experiments demonstrated that our proposed algorithms perform better than other bandit feedback-based approaches and comparably to the full information approaches.