The operation of a nuclear reactor is said to be critical when the value of the neutron multiplication factor $K$ is:

The maximum value of $Z=x+y$,subjected to $x+y \leq 10$,$5x+3y \geq 15$,$x \leq 6$,$x, y \geq 0$.

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \, dx$ is equal to

The temperature of the system decreases in the process of

The weight in grams of a non-volatile solute (mol. wt. $60$) to be dissolved in $90 \ g$ of water to produce a relative lowering of vapour pressure of $0.02$ is

Two plane mirrors $A$ and $B$ are placed parallel to each other as shown in the figure. $A$ light ray is incident at an angle of $30^{\circ}$ at a point on mirror $A$. The plane of incidence coincides with the plane of the figure. What is the maximum number of reflections (including the first one) the ray will undergo before it emerges?