Brake Caliper Problem?

From : bob m

Q: my 01 ram 1500 is still pulling to the right. ive gotten 3 new sets of tires on it and had the alignment checked by 3 shops. all say the alignment is within specs and if anything should be pulling to the left. the last shop inspected my ball joints and said they are ok. i have 39000 miles on the truck. lately i have been hearing a clicking noise that appears to be coming from the front end. this noise occurs when im pulling into my garage and lightly apply the brakes. the same noise occurs when i let off the pedal after coming to a stop. the noise isnt a clunk but a one time click as i apply the brakes or let off the brakes. is it possible that the front right brake caliper is causing a drag on the wheel making the truck pull to the right when i apply the brakes the amount of pull does not change. other than 2 dead mopar batteries and a bad fuel gauge sensor this truck has been perfect. i really love it but this pulling problem is really annoying and id like to get it fixed. thanks to anyone who can help. bob .