The solution of $$x{{dy} \over {dx}} + y = {x^4}$$ with condition $$y\left( 1 \right) = {6 \over 5}$$

A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is applied at a distance of $$2L/3$$ from the hinge so thatthe rod swings to the right. The reaction at the hinge is

A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is $$\mu = 0.2.$$ A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 $$N$$. What will be the tension, $$T$$ (inN) in the cable if the man is just able to move the block to the right?

Water at $${25^0}C$$ is flowing through a $$1.0km$$ long $$G.I.$$ pipe of $$200mm$$ diameter at the rate of $$0.07$$ $${m^3}/s.$$ If value of Darcy friction factor for this pipe is $$0.02$$ and density of water is $$1000\,\,kg/{m^3}$$, the pumping power (in $$kW$$) required to maintain the flow is