A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is ______ weeks (in integer).

Activity	Time estimates (in weeks)			Immediate predecessor(s)
	Optimistic time	Most likely time	Pessimistic time
A	4	5	6	None
B	1	3	5	A
C	1	2	3	A
D	2	4	6	C
E	3	4	5	B, D

A manufacturing unit produces two products Pl and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹ ______

	M1	M2	M3	Profit per piece ( ₹)
P1	2	2	0	150
P2	3	1	2	100
Maximum quantity available per day	70	50	40

Which one of the following CANNOT impart linear motion in a CNC machine?

A shaft AC rotating at a constant speed carries a thin pulley of radius r = 0.4 m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque M, about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = L = 0.5 m. The taut and slack side tensions of the belt are T₁ = 300 N and T₂ = 100 N, respectively. The allowable shear stress for the shaft material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of π available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is mm (round off to 2 decimal places).