At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production $$\mathrm{P}$$ w.r.t. additional number of worker $$x$$ is given by $$\frac{\mathrm{dp}}{\mathrm{d} x}=100-12 \sqrt{x}$$. If the firm employees 9 more workers, then the new level of production of items is

The maximum value of $$z=3 x+5 y$$ subject to the constraints $$3 x+2 y \leq 18, x \leq 4, y \leq 6, x, y \geq 0$$, is

If $$\mathrm{I}=\int \sin (\log (x)) \mathrm{d} x$$, then $$\mathrm{I}$$ is given by

If both mean and variance of 50 observations $$x_1, x_2, \ldots \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mean of $$\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots\left(x_{50}-5\right)^2$$ is