Unlearning the data observed during the training of a machine learning (ML) model is an important task that can play a pivotal role in fortifying the privacy and security of ML-based applications. This paper raises the following questions: (i) can we unlearn a single or multiple class(es) of data from a ML model without looking at the full training data even once? (ii) can we make the process of unlearning fast and scalable to large datasets, and generalize it to different deep networks? We introduce a novel machine unlearning framework with error-maximizing noise generation and impair-repair based weight manipulation that offers an efficient solution to the above questions. An error-maximizing noise matrix is learned for the class to be unlearned using the original model. The noise matrix is used to manipulate the model weights to unlearn the targeted class of data. We introduce impair and repair steps for a controlled manipulation of the network weights. In the impair step, the noise matrix along with a very high learning rate is used to induce sharp unlearning in the model. Thereafter, the repair step is used to regain the overall performance. With very few update steps, we show excellent unlearning while substantially retaining the overall model accuracy. Unlearning multiple classes requires a similar number of update steps as for a single class, making our approach scalable to large problems. Our method is quite efficient in comparison to the existing methods, works for multi-class unlearning, does not put any constraints on the original optimization mechanism or network design, and works well in both small and large-scale vision tasks. This work is an important step towards fast and easy implementation of unlearning in deep networks. Source code: https://github.com/vikram2000b/Fast-Machine-Unlearning