$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is

There is an error of $\pm 0.04 \text{ cm}$ in the measurement of the diameter of a sphere. When the radius is $10 \text{ cm}$,the percentage error in the volume of the sphere is

The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is

Convergent evolution is illustrated by

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

The area bounded by the curve $y = x^2 + 2$,the $x$-axis,and the lines $x = 1$ and $x = 2$ is: