The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point function evaluation exceeds the exact value by

The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at $$x=1$$ is

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The probability that the annual precipitation will be more than $$1200$$ mm is