The assignment problem given requires four different jobs to be done on four different machines.

The minimum cost of assignment is ______.

The properties for a bivariate distribution of two random variables $X$ and $Y$ are given below.

$E(X) = 24, \quad E(Y) = 36,$

$\quad E(X^2) = 702, \quad E(Y^2) = 1524,$

$\quad E(XY) = 1004$

The correlation coefficient between $X$ and $Y$ is ______.

Biaxial stresses at a point inside a pillar are shown in the figure.

The magnitude of the maximum shear stress in MPa and its direction with the x-axis in degrees at the same point respectively are

A circular tunnel is constructed in a biaxial far field stress (vertical stress $p_0$ and horizontal stress $Kp_0$) as shown in the figure.

If the ratio of the tangential stress measured at the boundary points A and B is 3:1, the value of $K$ is ______.

Copper ore of average grade 0.65% is mined, milled, smelted and then refined. The following information is available:

Mill recovery rate : 85%

Average grade in mill concentrate : 20%

Loss in smelting process : 5 kg/tonne of concentrate

Loss in refining process : 2 kg/tonne of blister copper

The amount of refined copper obtained per tonne of ore in kg is

A cubical rock sample is enclosed between two fixed hard steel plates as shown in the figure below. The modulus of elasticity and Poisson's ratio of the rock are 2 GPa and 0.25, respectively. If the rock is subjected to the stresses as shown in the figure, the strain in x-direction, in mm/m, is ______.

The composited grade value, in %, between the RLs 10 m to 20 m for the following borehole configuration is ______.

In a binomial distribution, the probability of success $p \to 0$ and number of trials $n \to \infty$ such that $\lambda= np$ approaches to a finite value. The variance of the distribution is

In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only $\frac{8}{9}^{th}$ of the eligible men and $\frac{2}{3}^{rd}$ of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

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