List of practice Questions

Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $

Evaluate the derivative of $ y = \cos x \times \sin y, \quad \frac{dy}{dx} \text{ at } \left( \frac{\pi}{6}, \frac{\pi}{5} \right) $

Match the type of deposit with the corresponding process of formation:

The relevant information on metal extraction from a copper mine are given below: Selling price of copper (Rs./kg) = 900
Mining cost (Rs./tonne of ore) = 500
Processing cost (Rs./tonne of ore) = 2000
Overall recovery of copper metal (%) = 70
Ignoring all other costs, the breakeven cutoff grade of copper, in %, is:

In a GP 9, 3, $ \frac{1}{3} $, $ \frac{1}{9} $, … find the 25th term.

If the in-situ density of coal is 1320 kg/m$^3$ and the density of blasted coal is 952 kg/m$^3$, the swell factor is:

In a bord and pillar panel, the following data are obtained:
Number of blasting rounds per shift: 8
Face dimension (m × m): 4.2 × 2.5
Average pull (m): 1.2
Specific gravity of coal: 1.4
Manpower per shift: 100
The OMS (output per manshift) of the panel, in tonne, is __________ (rounded off to 2 decimal places)}

The unadjusted RMR of a tunnel roof is 64. A single joint set exists in the roof as shown in the figure.

Using the abridged RMR table for adjustment orientation, the RMR is _______ (in integer)

The box plot of a data set is shown below.

The interquartile range of the data set is _______ (in integer).

An HMX explosive having Velocity of Detonation (VOD) of 10500 m/s is tested by D'Auriche method with a detonating fuse of VOD 7000 m/s, as shown in the figure. The impression mark on the lead plate will be obtained at a distance $L$, in m, from the midpoint of the fuse, is:

In a shovel dumper combination, the loading time of a dumper is 3 minutes. The shovel serves 8 dumpers. If the cycle time of a dumper, including its loading time, is 22 minutes, the waiting time of a dumper, in minutes, is:

As per CMR 2017, haulage ropes shall be recapped once at least in every:

Pressure head characteristic of a mine fan and a mine characteristic curves are shown in the figure below:

Match the points with their corresponding nomenclatures

The figure below shows four profiles of the environmental lapse rate. Given that the dry adiabatic lapse rate is $ -10^\circ {C/km} $, the atmosphere is highly unstable for the profile:

Match the source of error with the corresponding correction in surveying with steel tape.

Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $ m_1 $ and $ m_2 $, in kg, respectively are:

In a Brazilian test, the front view of a homogeneous rock sample is shown in the figure. The failure initiates at the point, where the rock sample is subjected to stress. The failure initiates at the point marked as:

The major ($ \sigma_1 $) and minor ($ \sigma_3 $) principal stresses and the maximum shear stress ($ \tau_{{max}} $) are related as $ |\tau_{{max}}| = \sigma_1 = - \sigma_3 $. The magnitude of normal stress on the plane where $ \tau_{{max}} $ acts is:

The metal that belongs to Rare Earth Element category is

The rank of $3 \times 3$ matrix $A$ is 2. The determinant of the matrix is

If $ y = x^x $, then $ \frac{dy}{dx} $ is:

A steeply dipping metalliferous ore body is non-susceptible to spontaneous heating. The blasted ore is used as the platform to work in a stope. Appropriate mining method for this orebody is

A non-transit theodolite does NOT have

A wastewater sample has an ultimate BOD of 300 mg/L. BOD reaction rate constant is 0.22 per day at 20 ℃. If the temperature coefficient is 1.05, the 5-day BOD at 25 ℃, in mg/L, is:

A pit slope has the following information: Number of benches = 5, Height of each bench = 8 m, Bench slope angle = 70° If the width of one bench is 24 m and that of other four benches is 10 m each, the overall pit slope angle, in degree, is ________ (rounded off to 2 decimal places).