Two vertical shafts of a mine have the following parameters:

The gradient of the drift connecting the shaft bottoms, in degrees, is_____

Match the following for the prismatic compass shown below

$X^4 + C$ is the general integral of

For a station 'A' on the Earth's surface, as shown in the figure, match the following

A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

If $X = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$, then $XX^T$ is

The values of $x$ satisfying the following condition are

An azimuth of $330^\circ$ corresponds to a quadrant bearing of

Tri-cone drill bit is a type of

Out of the support categories given for an underground coal mine, identify the ‘active support’.