I'm not aware of a "K" exam as a general term for an exam used across the industry, it may be specific to a certain fleet.
Rolling stock level 1 to 4 (the running maintenance done on depot, not the overhauls done at works) maintenance regimes generally, because they're are always exceptions, break down into one of two types.
Escalating or Balanced.
Escalating is where, as the name implies, the content of each examination (exams) escalates. So you start with an "A" exam, which is pretty much counting the wheels, checking the brake pads etc. The "B" is more arduous than the "A", because it contains everything in an "A" plus more tasks that need to be done less often. Some regimes, like the one above, only have "A" and a range of slightly different "B" exams. Then a "C" exam, which is more arduous than a "B" because it contains all of the "A" tasks and all of the "B" tasks plus more tasks that need to be even less often, and so on...
Tunes can then be played with the sequence of the escalating exams; some regimes go A,B,A,C,A,B,A,D and then start over, others got A,A,B,A,A,B,A,A,C and so on, or options thereof. It all depends on the exam frequency(time and/or mileage) and the frequency at which the tasks need to be done.
Balanced exams are where the maintenance tasks are balanced across the maintenance cycle. So each individual task, like changing compressor oil for example, is done at the correct frequency but other tasks with the same frequency are not necessarily done on the same exam. Balanced exams are generally given an "X" designator followed by a number. So, on class 465's axle ultrasonic testing used to be done on an X24 and X48 exams which means they got done every 240,000 miles because the exam frequency was every 10,000 miles. But there wasn't any other 240,000 mile tasks on those exams, they were on other exams to balance the tasks.
There's advantages and disadvantages to each.
Escalating exams require that units be delivered to depot by painted number and require very careful exam planning to ensure that the correct exam is planned for the service requirements, manpower available, shed space available etc.
Balanced exams are much more flexible, because the workload is balanced across the exams they generally all take the same length of time/resource to complete, so painted number doesn't matter. As a planner you can be pretty certain that no matter what unit is delivered for what exam it will always take the same length of time to complete. Some balanced exam regimes are designed that a train can come on depot as the last end of morning peak arrival, have an exam, and be out of the shed ready for the first evening peak departure.
But balanced exams are generally not good for fixing larger defects and managing deferred work; the planning of the balanced exam allows for a limited amount of "work arising" to be found on the exam and be fixed. It may allow for 4 brake pads needing to be changed, based on the average found on every exam, but you'll get a train on exam where lots of pads need changing (not through any fault just the different wear rates and previous pad changes all coming together) and you've got problems. And if you find something big on an exam, like a defective toilet, that can't be fixed, due to the time needed, on the exam BUT the unit can run with the defect then it gets deferred. But when do you fix it once it's been deferred? When SE still had the Networkers on a balanced regime the fleet, of 190 trains, was running with up to 3,000 deferred defects with no real way of bringing this down.
But for Escalating exams when you get to the higher exams, "C" & "D", you know the train is going to be stopped for several shifts so you've got time to attack the outstanding deferred work. Again, at SE the Networkers were changed from Balanced to Escalating in 2013/14 for this very reason. The "C" and "D" exams were planned to alternate with each other every year and trains were not allowed leave depot after a "C" or "D" with any deferred defects. An extra shift, purely for deferred work, was built into each "C" & "D" exam so at worst your deferred defect would only exist for 12 months.
HTH?