If $$T(x, y, z)$$ $$ = {x^2} + {y^2} + 2{z^2}$$ defines the temperature at any location $$(x, y, z)$$ then the magnitude of the temperature gradient at point $$P(1,1,1)$$ is _________.

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