A project consists of $$14$$ activities, $$A$$ to $$N$$. The duration of these activities (in days) are shown in brackets on the network diagram. The latest finish time (in days) for node $$10$$ is _____________

In a single-channel queuing model, the customer arrival rate is $$12$$ per hour and the serving rate is $$24$$ per hour. The expected time that a customer is in queue is _______ minutes.

A mass of $$2000$$ kg is currently being lowered at a velocity of $$2$$ $$m/s$$ from the drum as shown in the figure. The mass moment of inertia of the drum is $$150$$ kg-m². On applying the brake, the mass is brought to rest in a distance of $$0.5$$ $$m.$$ The energy absorbed by the brake (in $$kJ$$) is __________________.

A machine element $$XY,$$ fixed at end $$X,$$ is subjected to an axial load $$P,$$ transverse load $$F,$$ and a twisting moment $$T$$ at its free end $$Y.$$ The most critical point from the strength point of view is