The SMOTE for the imbalance should be applied for the training data only, right? Can we still do it (perform SMOTE on training data) while we select the k-fold CV and does not go for splitting the data in separate train and test set? I have read somewhere that we must separate the train data ( apply the SMOTE) and then run the classifier on a separate test data.
You apply SMOTE only on your training set, build your model on it, and then test it on the unSMOTE-ed test set.
In CV you would perform this by applying SMOTE on your k-1 folds, build your model on them and test it on the remaining unSMOTE-ed fold.