A force of 50 N is applied to a wrench as shown in the figure. The magnitude of the moment in N-mm of this force about the point P is ______.

The covariance of copper grade for a certain lag distance in an ore body is $6.0\%^2$. If the sill is $10\%^2$, the semivariogram for the same lag distance in $\%^2$ is

The matrix $A= \begin{bmatrix} -4/6 & 2/6 & 4/6 \\ 4/6 & 4/6 & 2/6 \\ 2/6 & -4/6 & 4/6 \end{bmatrix}$ is

What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in each case?

A mine fan running at 300 rpm delivers 150 m$^3$/s of air at a pressure of 900 Pa. Fan and motor efficiencies are 75% and 90% respectively. If the fan speed is reduced to 250 rpm, the saving in electric power input to the motor in kW is ______.

Subsidence profile function, s(x), along the lateral cross-section over a flat longwall panel is given as

$s(x) = 0.8 \left[ 0.996 - \tanh \left( \frac{8.3x}{D} \right) \right], \, \text{m}$

where $x$ = distance (m) from the inflection point and $D$ = depth (m) of the seam. Considering that the inflection point lies vertically above the edge of the panel, the angle of draw in degrees for a depth of 250 m is ______.

A goat void of 250 m$^3$ is filled in 3 hours by hydraulic sand stowing method. Density of the sand is 2.6 tonne/m$^3$. If the filling factor of goat void is 0.9 and sand to water ratio in the stowing mixture is 1.0 tonne to 1.1 m$^3$, the stowing rate in m$^3$/h is ______.

A single-acting reciprocating pump delivers 0.018 m$^3$/s of water when running at 45 cycles per minute. The piston diameter is 300 mm and stroke length is 400 mm. The volumetric efficiency of the pump in % is ______.

Match the method of mining with strength of orebody, type of support and orebody geometry.

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