Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any time $$\mathrm{t}$$. If depth is $$4 \mathrm{~m}$$ when $$\mathrm{t}=2$$ hours, then after 3.5 hours the depth (in meters) is

The area (in sq. units) of the smaller part of the circle $$x^2+y^2=\mathrm{a}^2$$ cut off by the line $$x=\frac{\mathrm{a}}{\sqrt{2}}$$ is

$$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=$$ _________, if $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{k}}$$, then its variance is