Q 1) Let X de:notes the minimum of the two numbers that appear when a pM of fau dice is thrown once. Dctcrmine

(i) probability distribution
(ii) Mean
(iii) Variance.

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)