Explore the options below.

Which of the following ROC curves produce AUC values greater than 0.5?
An ROC curve with a vertical line running from (0,0) to (0,1), and a horizontal from (0,1) to (1,1). The TP rate is 1.0 for all FP rates.

This is the best possible ROC curve, as it ranks all positives above all negatives. It has an AUC of 1.0.

In practice, if you have a "perfect" classifier with an AUC of 1.0, you should be suspicious, as it likely indicates a bug in your model. For example, you may have overfit to your training data, or the label data may be replicated in one of your features.

An ROC curve with a horizontal line running from (0,0) to (1,0), and a vertical line from (1,0) to (1,1). The FP rate is 1.0 for all TP rates
This is the worst possible ROC curve; it ranks all negatives above all positives, and has an AUC of 0.0. If you were to reverse every prediction (flip negatives to positives and postives to negatives), you'd actually have a perfect classifier!
An ROC curve with one diagonal line running from (0,0) to (1,1). TP and FP
         rates increase linearly at the same rate.
This ROC curve has an AUC of 0.5, meaning it ranks a random positive example higher than a random negative example 50% of the time. As such, the corresponding classification model is basically worthless, as its predictive ability is no better than random guessing.
An ROC curve that arcs up and right from (0,0) to (1,1). TP rate increases at
         a faster rate than FP rate.
This ROC curve has an AUC between 0.5 and 1.0, meaning it ranks a random positive example higher than a random negative example more than 50% of the time. Real-world binary classification AUC values generally fall into this range.
An ROC curve that arcs right and up from (0,0) to (1,1). FP rate increases at
         a faster rate than TP rate.
This ROC curve has an AUC between 0 and 0.5, meaning it ranks a random positive example higher than a random negative example less than 50% of the time. The corresponding model actually performs worse than random guessing! If you see an ROC curve like this, it likely indicates there's a bug in your data.