List of practice Questions

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:
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:
A constant feed of 400 mL/s is maintained by a Xanthate column of height H as shown in the figure. The outlet cross section area is \(1.0 \times 10^{-4} \, {m}^2\). The acceleration due to gravity is \(10 \, {m/s}^2\). Neglecting friction and other losses, the value of H, in cm, is (rounded off to 2 decimal places):
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A continuous miner serves two shuttle cars of 12 tonne capacity each. Shuttle cars I and II operate with a total cycle time of 12 minutes and 15 minutes respectively, which includes loading time of 8 minutes for each car. The production rate of the continuous miner, in tonne/hour, is:
In a sublevel stope, a ringhole blast round is designed for winning 2500 tonne of ore with 8.0% metal content. The blast results into breakage of 90.0% of the design blast round. Overbreak of 250 tonne wallrock with 0.5% metal content dilutes the blasted ore. The total metal content, in tonne, considering 95% recovery of the blasted muck from the stope, is:
Hydraulic fracturing method is used to determine the major principal stress (\( \sigma_1 \)) in an underground rock strata having tensile strength of 6 MPa. The minor principal stress (\( \sigma_3 \)) in the strata is 8 MPa. If fluid pressure of 10 MPa is required to fracture the vertical borehole in that strata, the magnitude of \( \sigma_1 \), in MPa, is:
For crease resist finishing of cotton, 70 gpl aqueous solution of DMDHEU (molecular weight - 178) is applied by padding. If the DMDHEU is available as 50% (w/v) aqueous solution, then the required amount of DMDHEU solution (ml) for preparation of 1000 ml padding liquor 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:
A polymer melt being extruded through a spinneret hole of circular cross-section exhibits a die-swell ratio of 2.2. The extrusion velocity and volumetric flow rate during this extrusion process are 20 m/min and \(2.6 \times 10^{-8}\) m\(^3\)/s, respectively. The maximum diameter (mm) of the extruded melt after exit from the spinneret hole (rounded off to 2 decimal places) is:
A chute feed system feeds a fibre batt of linear density 300 g/m to a card. The waste extracted by the card is 5% and the total mechanical draft is 100. The linear density (ktex) of card sliver (correct up to 2 decimal places) is:
A spun yarn made of circular polyester fibres of 10 µm diameter is cut normal to the yarn axis. If the helix angle of a fibre is \( 40^\circ \), then the area (µm\(^2\)) of that fibre projected on the cut-section of the yarn (rounded off to 1 decimal place) is:
A needlepunching machine has two needle boards which operate sequentially at the same frequency to produce nonwoven with 200 punches/cm\(^2\). Each needle board has 40000 needles per meter width. If the delivery speed of the machine is 80 m/min, then the frequency (strokes/min) of each needle board is:
In a projectile weaving machine, the projectile travels through the shed at an average speed of 24 m/s taking \( \frac{2}{3} \) of the loom cycle. If the efficiency of the weaving machine is 90%, the weft insertion rate (m/min) is:
The breaking strain of a yarn is 1.5. If the stress (\( \sigma \)) and the strain (\( \epsilon \)) of the yarn are related as, \( \sigma = 1.5 \epsilon^2 \), then the work factor of the yarn (rounded off to 2 decimal places) is:
In a tensile test, a 50 tex yarn specimen of 500 cm length extends by 10% at 600 cN. The length of the yarn after the removal of the load is 525 cm. The elastic recovery (%) of the yarn is:
In a water vapour transmission test of a fabric by evaporative dish method, the initial mass of the dish is 198 g. After 20 h of test, the mass of the dish becomes 188 g. The inner and outer diameters of the dish are 6.5 cm and 6.9 cm, respectively. The water vapour transmission rate (g/m\(^2\)/h) of the fabric is:
A blowroom line has three beaters, each having a trash removal efficiency (cleaning index) of 30%. The trash removal efficiency (%) of the blowroom line (rounded off to 1 decimal place) is _________
The molarity (moles per litre) of 34% (w/v) H\(_2\)O\(_2\) aqueous solution (answer in integer) is _________.
Let \( X \) be a Poisson distributed random variable with parameter \( \lambda (> 0) \) such that it satisfies the equation \[ P(X = 1) = 3P(X = 3) - P(X = 2) {. Then, the value of } \lambda { is:} \]
If \( u(x, y, z) = x^2y + y^2z + z^2x \), the value of \[ \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} { at the point } (1,1,1) { is:} \]
A circular hollow polyester fibre with a tenacity of 0.02 N/tex breaks at 0.2 N. If the density of polyester is 1.38 g/cm\(^3\) and the inner diameter of the fibre is 40 µm, the outer diameter (µm) of the fibre (rounded off to 1 decimal place) is:
A ship moving at a steady forward speed of \(10 \, {m/s}\) experiences a total resistance of \(140 \, {kN}\). The Quasi Propulsive Coefficient (QPC) is \(0.70\); the propeller shaft losses are \(5%\) and the mechanical efficiency of the main engine is \(80%\).
The indicated power of the main engine is ________ kW (rounded off to two decimal places).
A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are \(1 \, {rad/sec}\) and \(0.01\) respectively.
The reduction in peak amplitude over three cycles is ________ % (rounded off to one decimal place).
When the probability of Type I error (\(\alpha\)) is 0.05 and the maximum acceptable probability of Type II error (\(\beta\)) is 0.20, the researcher is willing to accept that Type I error is ........ (answer in integer) times more serious than a Type II error.
In the first heating cycle of a differential scanning calorimetry (DSC) experiment, an as-spun Nylon 6 fibre showed an enthalpy change of 40 J/g during cold crystallization and an enthalpy change of 150 J/g during melting. If the heat of fusion of 100% crystalline Nylon 6 is 240 J/g, the percentage degree of crystallinity of as-spun Nylon 6 fibre (rounded off to 1 decimal place) is _________