List of top Questions asked in GATE MN

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
Given impeller diameter $D$, speed of rotation $n$ and air density $\rho$, for geometrically similar fans, the fan pressure is proportional to
NONEL is used as down-the-hole initiator to
As per MMDR Act 1957, for the allocation of lease of minor minerals
In photogrammetry, the 'Tilt of a photograph' refers to the angle between the
The hydraulic sand stowing pipeline layout should be such that
For a "positive definite" square matrix, the TRUE statement is
The standard normal distribution is a
Resuing method of mining is practiced for
The equipment used for both drop cut and terrace cut in surface mining is
Surface miner does NOT have a