A letter lock has 3 rings and each ring has 5 letters. Determine the maximum number of trails that may be required to open the lock.

A letter lock has 3 rings each containing 6 different letters. What is the maximum number of false trials that can be made before the lock is opened?

Find the number of ways in which 5 letters can be posted in 3 post boxes if any number of letters can be posted in a post box.

Determine the number of different words that can be formed with each of three letters of the word ENGLISH, if each letter is to be used not more than once.

A metallic ring of mass m and radius i (ring being horizontal) is falling under gravity in a region having a magnetic field . If z is the vertical direction, the z- component of magnetic field is B_z = B_0(1 + lambda z) If R is the resistance of the ring and if the ring falls with a velocity v, find the power lost in the resistance . If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B , lambda and acceleration due to gravity g.