GATE ES exam:gate PYQs & Answers — Page 6

Questions 51–60 of 390. Imported answers require independent review unless marked reviewed.

Topic practice 390 questionsPage 6 of 39

The following two reactions describe the chemistry of S(IV) in an aquatic system. Under ideal conditions, the equilibrium constants for reactions (i) and (ii) are 1.3 × 10⁻² M (Kₛ₁) and 6.6 × 10⁻⁸ M (Kₛ₂), respectively. If the pH of the system is 4.0 and the equilibrium concentration of SO₂(aq) is 1.0 M, the equilibrium concentration of SO₃²⁻ is ______ mM (rounded off to one decimal place).

SO₂(aq) ⇌ H⁺ + HSO₃⁻ (i)

HSO₃⁻ ⇌ H⁺ + SO₃²⁻ (ii)

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The calibration graph between absorbance and the concentration of chromate (CrO₄²⁻) in a water sample is shown in the figure. For an absorbance of 0.35 in a water sample, the estimated Cr(VI) concentration is ______ mg/L (rounded off to two decimal places). Use the atomic weight (g/mol) of Cr and O as 52 and 16, respectively.

Diagram for Environmental Science and Engineering question 52

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In a batch culture experiment, 2 cells of a microorganism were added to a growth medium. During the experiment, a lag phase of 1 hour was first experienced by the added cells, in which no cell multiplication occurred. Afterwards, cells started multiplying exponentially with a doubling time of 1 hour. After total 8 hours of experiment, the number of cells present in the growth medium was ______ (answer in integer).

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A thermal process, at a specific temperature, results in 2-log₁₀ removal of non-thermotolerant pathogenic microorganisms from a water sample in 20 min. The time needed to achieve 99.999% removal of these microorganisms under similar condition is ______ min (answer in integer).

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A cylindrical roller gate of diameter 6.0 m and length 10.0 m is placed on a dam to store water behind it, as shown in figure. The magnitude of the resultant force due to water acting on that gate when the water is about to spill is ______ × 10⁶ N (rounded off to two decimal places). Consider acceleration due to gravity (g) = 9.81 m/s²; density of water (ρ) = 1000 kg/m³; and π = 3.14.

Diagram for Environmental Science and Engineering question 55

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The mass curve of a rainfall event of 100 min duration over a catchment is given in the table.

If the initial loss is 0.6 cm and

-index is 0.6 cm/hour, the total surface runoff from the catchment is _____ cm (rounded off to one decimal place).

Time from start of rainfall (min)	0	20	40	60	80	100
Cumulative rainfall (cm)	0	0.5	1.2	2.6	3.3	3.5

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A well penetrates an unconfined aquifer. The water level (i.e., head) in the well prior to pumping is 25 m. After a long period of pumping at a constant rate of 0.05 m

/s, the drawdowns at distances of 50 m and 150 m from the well are observed to be 3 m and 1.2 m, respectively.

The hydraulic conductivity of the unconfined aquifer is _____

m/s (rounded off to two decimal places).

Consider

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A sewage treatment plant employing activated sludge process is operated under the following conditions:

Wastewater flow rate into the aeration tank = 0.150 m

Soluble BOD

in the influent = 84 mg/L

Soluble BOD

in the effluent = 11 mg/L

Mean cell residence time = 5 days

Total yield co-efficient = 0.5 kg of MLVS/kg BOD

removed

Decay rate of microorganism = 0.050/day

The net waste activated sludge produced in the plant is _____ kg of VSS/day (rounded off to two decimal places).

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A continuous flow stirred tank reactor (CSTR) operates under a steady-state condition with a flow rate of 300 L per hour. The influent concentration of a substrate entering the reactor is 150 mg/L.

To give a treatment efficiency of 76% for the substrate that decays according to half-order kinetics with a rate constant of 0.05 (mg/L)

per hour, the required volume of the reactor is _____ m

(answer in integer).

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In a stack emission measurement at an industry, the stack cross-sectional area at 30 m height was divided into four equal sectors. The measured velocities and SO

concentrations through these sectors at this height are given in the table.

The mean SO

concentration from the stack is _____ mg/m

(rounded off to two decimal places).

Sector Number	Velocity (m/s)	SO Concentration (mg/m )
1	15	1000
2	17	1150
3	19	1250
4	21	1275

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GATE ES exam:gate PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60