It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of events follow a poisson distribution.

The solution of the differential equation $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$ with $${C_1}$$ and $${C_2}$$ as constants is

Water is flowing through a horizontal pipe of constant diameter and the flow is laminar. If the diameter of the pipe is increased by $$50\% $$ keeping the volume flow rate constant, then the pressure drop in the pipe due to friction will decrease by

Cold water flowing at $$0.1$$ $$kg/s$$ is heated from $${20^ \circ }C$$ to $${70^ \circ }C$$ in a counter-flow type heat exchanger by a hot water stream flowing at $$0.1$$ $$kg/s$$ and entering at $${90^ \circ }C$$. The specific heat of water is $$4200$$ $$J$$($$kg$$ $$K$$) and density is $$1000$$ $$kg/{m^3}.$$ If the overall heat transfer coefficient $$U$$ for the heat exchanger is $$2000$$ $$W/\,\,\left( {{m^2}\,\,K} \right),$$ the required heat exchange area (in $${{m^2}}$$) is