A coal mine operating in three shifts produces 400 tonnes of coal per day with a face OMS of 1.0 from panel A, and 200 tonnes of coal with face OMS of 1.0 from panel B. The panel A and panel B are in parallel with resistance 0.6 Ns²/m⁸ and 0.5 Ns²/m⁸, respectively. If the panels are supplied with minimum permissible quantity as per CMR 2018, the requisite regulator resistance to meet the conditions in Ns²/m⁸ is _____.

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is ______

With reference to the figure related to rock cutting by point attack tool, match the angle with corresponding name.

In order to check whether iron ore is supplied to the specification of 62% Fe, a steel company has conducted a hypothesis test with the null hypothesis as $H_0: \mu_{Fe} = 62\%$ and alternative hypothesis $H_a: \mu_{Fe} < 62\%$. A random sample of 5 observations reveal the following grade values of the lot, 58%, 56%, 60%, 64%, 62%. The t-test statistic for the hypothesis is

A triangular distributed load is applied on top of a beam as shown in the figure. The value of maximum bending moment in kN-m is _____.

In a surface mine, third bench from the pit bottom is blasted, as shown in the figure. The width, height and slope angle of each bench are 8 m, 6 m, and 80°, respectively. A fly rock is projected at an angle of 45° with the horizontal with initial velocity, v. If the acceleration due to gravity is 10 m/s² then the minimum velocity (v) in m/s required for the fly rock to reach just beyond toe of the pit slope is _____.

Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below.

The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is _______ [round off to 2 decimal places]

A cement company has three factories which transport cement to four distribution centres. The daily production of each factory, the demand at each distribution centre, and the associated transportation cost per tonne from factory to distribution centre are given in the Table.

The initial basic feasible solution using the least-cost rule is _______ [in integer]

A set of three steel bars of equal cross-sectional area of 0.01 m² are loaded, as shown in the figure. The elastic modulus of steel is 200 GPa. The overall change of length of the complete set of bars, in mm, is _____.

Let $\oplus$ and $\odot$ be two operators on numbers $p$ and $q$ such that

$p \odot q = p - q$, and $p \oplus q = p \times q$

Then, $(9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5)) =$ ?