List of practice Questions

The vectors $\vec{a}$ and $\vec{b}$ act in a plane as shown below. The magnitude of the vector} \[ \vec{c} = (\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) \] is

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 Ns^2\text{m}^8 and 0.5 Ns^2\text{m}^8, respectively. If the panels are supplied with minimum permissible quantity as per CMR 2018, the requisite regulator resistance to meet the conditions in Ns^2\text{m}^8 is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).
In an analysis of fragmented blast muck, the mean fragment size is found to be 60 cm with uniformity index of 1.25. Considering Rosin-Ramler equation, the cumulative mass fraction, in percent, to pass the grizzly screen size of 100 cm is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)
A single-acting reciprocating ram pump, while running at 120 rpm, delivers water at a rate of 10 litres per second. Considering the ram diameter is 150 mm and stroke length is 300 mm, the volumetric efficiency of the pump, in percent, is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
In a sand stowing arrangement, the slurry has a sand concentration of 35% by volume. The specific gravity of sand grain is 2.6. The concentration of sand by weight, in percent, in the slurry is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
Rate of fuel consumption \( f_c \) (litres per hour) of a truck varies with truck speed \( x \), (kmph) as given below \[ f_c = 20 + \frac{x^2}{50} \] The fuel price is Rs. 70 per litre. Other costs amount to Rs. 500 per hour. If the truck travels 100 km from a coal mine to a thermal plant, the speed of the truck, in kmph, that minimizes the total cost is \(\underline{\hspace{2cm}}\) (round off to one decimal place).
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 \( H_0: \mu_{\text{Fe}} = 62% \) and alternative hypothesis \( H_a: \mu_{\text{Fe}} < 62% \). 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
For a dumpy level, the bubble tube has sensitivity of 40" for one division. While taking a staff reading at a distance of 60 m, the bubble is out of centre by 2 divisions. The error in staff reading in mm is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
On an old plan of scale 1:1000, leasehold area of a mine is now measured as 802 cm^2 using a planimeter. The plan is found to have shrunk, such that the original line of 10 cm is now measured as 9.8 cm on the plan. True lease hold mine area, in m^2 is \(\underline{\hspace{2cm}}\) (round off to the nearest integer).
CO is released from a point source on a level ground at a rate of 25 g/s. The average wind speed is 5 m/s. The dispersion coefficients are 150 m and 200 m in horizontal and vertical directions, respectively, at a receiver station located on the ground along the downwind direction. Assuming the plume follows Gaussian dispersion model, the concentration of CO, in \, \mu g/m^3 at the station is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).
Assume that COVID-19 growth rate of number of infections per day (c) in a certain population is represented by the following differential equation. \[ 100 \frac{dc}{dt} - 7c = 0 \] Where, t stands for time in days. Time taken for the number of infections per day to double, in days, is \(\underline{\hspace{2cm}}\) (round off to the nearest integer).
Ore is hoisted from 620 m depth using a single skip of 7 tonne pay load. The skip winding system has constant acceleration/deceleration of 1 m/s\(^2\) and a constant speed of 10 m/s. The skip loading time and unloading time are 120 s and 60 s, respectively. Considering the overall utilization of the skip as 70%, the maximum daily capacity of the winding system, in tonne, is \(\underline{\hspace{1cm}}\). (round off to the nearest integer)
A dump truck moves up an incline of 5° with constant tractive force of 800 kN. The gross mass of the truck is 250 tonne and its rolling resistance is 545 kN. The acceleration due to gravity is 10 m²/s. The time required, in s, to reach a speed of 3.3 m/s from 1.0 m/s is
In a longwall panel, face is supported with shields of yield capacity 460 tonne per shield. The distance from the canopy tip to coal face is 0.15 m when the support is fully advanced. The depth of web is 0.60 m. The shields are set skin to skin at the face. Length of the canopy of the shield is 3.25 m and width 1.5 m. Setting capacity is 80% of the yield capacity. The setting resistance at the maximum and minimum span of the coal face, in tonne/m\(^2\), respectively are
A 10 ml sample of wastewater is diluted with water having no BOD, to fill a 300 ml BOD bottle. The initial DO of the diluted waste water is 9.0 mg/l. If the BOD\(_5\) of the waste water sample is 60 mg/l, the final DO of the diluted waste water in mg/l, is
A coal sample having moisture content of 8.0% has unit weight 15.6 kN/m\(^3\). The dry unit weight of the sample, in kN/m\(^3\) is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)
In sound frequency analysis, the lower and upper frequencies of a 1/1 octave band are 710 Hz and 1420 Hz respectively. The centre frequency of the band in Hz is \(\underline{\hspace{1cm}}\). (round off to the nearest integer)
In Battle Environmental Evaluation System (BEES) of Environmental Impact Assessment (EIA), "air pollution'' has a Parameter Importance Unit (PIU) of 52. The Environmental Quality (EQ) score of a project with respect to air pollution was 0.8 before implementation and 0.6 after implementation. The difference in Environmental Impact Unit (EIU) is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)
A system consists of four components in parallel. Their reliabilities are 0.40, 0.60, 0.50, and 0.40. The system reliability is \(\underline{\hspace{1cm}}\). (round off to 3 decimal places)
A vehicle moving at 12 m/s stops in 15 m with constant deceleration. Assuming \( g = 10\ \text{m/s}^2 \), compute the coefficient of kinetic friction between tyres and road. (round off to 2 decimal places)
In a bord and pillar panel six shuttle cars, each of 10 tonne capacity, are deployed to transport coal produced by two continuous miners to a belt conveyor. Each shuttle car on an average carries 80% of its rated capacity and makes 7 round trips in an hour. The belt conveyor has a capacity such that the effective material cross section area is of 0.09 m$^{2$ and runs at a speed 1.1 m/s. The broken coal has a bulk density of 1.2 tonne/m$^{3}$. The ratio between the production and the capacity of the belt conveyor, in percent is}
Variance of the sum of two statistically independent random variables \(X\) and \(Y\), \( \sigma^2_{X+Y} \), is
The difference between depreciation and amortization allowances in tax calculation is that
Owning cost of a machine does NOT include
Folds are the structural features resulting from