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

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

For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is