Which one of the following pairs of food components in humans reaches the stomach totally undigested?

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is:

The number of five-digit numbers divisible by $5$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition is:

If $\tan x + \tan \left(x + \frac{\pi}{3}\right) + \tan \left(x + \frac{2\pi}{3}\right) = 3$,then $\tan 3x$ is equal to

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \ldots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

In the figure,suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also,let the center disk be rotated on the common axis with an angular speed $\omega$. If unpolarized light is incident on the left disk with an intensity $I_{max}$,the intensity of the beam emerging from the right disk is given by: