$A$ ray of light travels from an optically denser to a rarer medium. The critical angle for the two media is $C$. The maximum possible deviation of the ray will be

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,then $\operatorname{det}(\operatorname{adj} A)$ is equal to

Archaeopteryx,a transitional fossil between birds and reptiles,was discovered from rocks of which of the following periods?

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is:

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta$,where $\theta$ is the angle by which it has rotated,is given as $K \theta^2$. If its moment of inertia is $I$,then the angular acceleration of the disc is:

$A$ right circular cylinder has a mass $m$,radius $r$,and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$,as shown in the diagram. What is the magnitude of the net force on the cylinder?