Given $$y = {x^2} + 2x + 10\,\,\,$$ the value of $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 1}}\,\,$$ is equal to

The expression $${e^{ - ln\,x}}$$ for $$x > 0$$ is equal to

Consider the function $$\,\,y = {x^2} - 6x + 9.\,\,\,$$ The maximum value of $$y$$ obtained when $$x$$ varies over the interval $$2$$ to $$5$$ is

Consider a Gaussian distributed random variable with zero mean and standard deviation $$\sigma .\,\,\,$$ The value of its cumulative distribution function at the origin will be