The initial investment for a small scale mining project is Rs. 5.0 crore. Annual cash inflow for a life period of 4 years is given below.

The net present value of the project at an annual discount rate of 10% in Rs. crore is ______.

Acceleration of a particle moving in a straight line is expressed by

$\frac{d^2 s}{dt^2} = 2t$

where, $s$ denotes distance (m) and $t$, time (s). At time $t = 0$, the distance and velocity of the particle are 0 m and 3 m/s respectively. The distance travelled by the particle in m after 3 s is

If area S, in the x-y plane, is bounded by a triangle with vertices (0, 0), (10, 1) and (1, 1), the value of $\iint_S \sqrt{y-y^2} \, dx \, dy$ is ______.

The ratio of horizontal to vertical in-situ stresses, $K$, at a mine field varies with depth, $D$ (in m) as

$K = 1.25 + \frac{267}{D}$

If the unit weight of overburden rock is 25 kN/m$^3$, the horizontal stress in MPa at a depth of 400 m is ______.

A coal seam of 2 m thickness is extracted by a longwall retreating panel with face length of 120 m. Web depth of the shearer is 0.6 m. Average manpower in the longwall face in a shift is 20. The specific gravity of in-situ coal is 1.4. If the shearer makes 4 full-face cuts in 3 shifts, the face OMS in tonne is ______.

A loaded dumper of total mass 75 tonne, having wheel diameter 1250 mm, runs on a haul road which offers an average specific rolling resistance of 260 N/tonne. The engine develops an axle torque of 15 kN-m. The starting acceleration of the dumper in m/s$^2$ is ______.

Given the following linear programming problem,

Maximise $z = 3x_1 + 4x_2$

Subject to

$2x_1 + x_2 \leq 6$

$2x_1 + 3x_2 \leq 9$

$x_1 \geq 0, x_2 \geq 0$

the corner point feasible solution in terms of $(x_1, x_2)$ is

The 3-period torque-time diagram of a statically balanced hoist is shown in the figure.

The rms torque for the motor in kN-m is ______.

Airborne PM$_{10}$ concentration in a residential area is monitored for 24 hours by a respirable dust sampler. Initial and final weights of the filter paper are 2.3125 g and 2.6996 g respectively. The average airflow rate during sampling is 1.2 m$^3$/min. The PM$_{10}$ concentration of the area in $\mu g \, \text{m}^{-3}$ is ______.

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