Someone please tell me the title of the 1960s movie about a serial rapist and killer at large, in which a corpulent nurse turns out, at the end, to be the culprit in disguise. The most horrifying scene was when she took off her nurse's cap and wig to reveal his true identity.

The second most horrifying scene was an old woman in a wheelchair descending a steep staircase via a mechanism that allowed wheelchairs to go up and down. When the wheelchair reached the foot of the stairs, her head fell off.