List of top Questions asked in GATE ES- 2026

The area in the first quadrant bounded by the function \(y = (8-x)\) and the coordinate axes is ______ square units (answer in integer).
The characteristics of two types of solid waste are given in the table.

Type of solid wasteMoisture content (%)Nitrogen content (%)Carbon to Nitrogen (C/N) ratio
Leaves500.750
Sludge755.66.3

The quantity of sludge to be added to leaves to achieve a C/N ratio of 25 (on dry basis) for the mixed waste is ______ kg of sludge/kg of leaves (rounded off to three decimal places).
An agricultural land can support energy crops yield to produce 7000 L of bioethanol per hectare and energy content of bioethanol is 21 MJ/L. This bioethanol displaces fossil-based petrol.

The \(CO_2\) offset potential of land used for growing energy crops as a bioethanol feedstock is ______ \(\times 10^6\) g of \(CO_2\)/hectare (rounded off to one decimal place).

Consider \(CO_2\) footprints of 10 g and 80 g of \(CO_2\) per MJ for bioethanol and petrol, respectively.
The concentration of chemical A in ambient air is 50 \(\mu g/m^3\) and the toxicological index limit for a threshold health effect for this chemical is 5 mg.

If the average breathing rate is 4 L/min, the minimum time of exposure that can lead to any health effect is ______ days (rounded off to one decimal place).
A sewage treatment plant employing activated sludge process is operated under the following conditions:
Wastewater flow rate into the aeration tank = 0.150 m3/s
Soluble BOD5 in the influent = 84 mg/L
Soluble BOD5 in the effluent = 11 mg/L
Mean cell residence time = 5 days
Total yield co-efficient = 0.5 kg of MLVSS/kg BOD5 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).
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 m3/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 ______ × 10-4 m/s (rounded off to two decimal places).
Consider π = 3.14.
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)1/2 per hour, the required volume of the reactor is ______ m3 (answer in integer).
An anaerobic digestion system is operated for methane gas generation from organic fraction of municipal solid waste (OFMSW). The moisture content and volatile solids (VS) content of OFMSW are 20% and 90%, respectively. The biodegradable volatile solids (BVS) in the VS is 70%, and the BVS conversion efficiency to methane gas is 85%.
If the methane gas generation in the system is 12 m3 per kg of BVS converted, the total volume of gas produced from one kilogram of OFMSW is ______ m3 (rounded off to two decimal places).
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 SO2 concentrations through these sectors at this height are given in the table.
The mean SO2 concentration from the stack is ______ mg/m3 (rounded off to two decimal places).
Sector NumberVelocity (m/s)SO2 Concentration (mg/m3)
1151000
2171150
3191250
4211275

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

Time from start of rainfall (min)020406080100
Cumulative rainfall (cm)00.51.22.63.33.5

If the initial loss is 0.6 cm and φ-index is 0.6 cm/hour, the total surface runoff from the catchment is ______ cm (rounded off to one decimal place).

Reaction A → B follows first-order elementary kinetics and the reaction rate constant for A is 0.01 per min.

The time taken to reduce the concentration of A from 100 M to 10 M in a batch reactor is ______ min (rounded off to one decimal place).

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 \(1.3\times10^{-2}\ M\) (\(K_{S1}\)) and \(6.6\times10^{-8}\ M\) (\(K_{S2}\)), respectively.

If the pH of the system is 4.0 and the equilibrium concentration of \(SO_{2(aq)}\) is 1.0 M, the equilibrium concentration of \(SO_3^{2-}\) is ______ mM (rounded off to one decimal place).

\[SO_{2(aq)} \rightleftharpoons H^+ + HSO_3^- \quad (i)\]

\[HSO_3^- \rightleftharpoons H^+ + SO_3^{2-} \quad (ii)\]

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).

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.

The calibration graph between absorbance and the concentration of chromate (\(CrO_4^{2-}\)) in a water sample is shown in the figure.

The calibration line shown in the figure has the equation \(y = 0.8003x + 0.0055\), where \(y\) is the absorbance and \(x\) is the concentration of chromate (\(CrO_4^{2-}\), mg/L).

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.

The mixing ratio of CO2 at a pressure of 1 atm and at 300 K is reported as 340 ppmv.

Considering ideal gas conditions, the equivalent concentration of CO2 in air is ______ mg/m3 (rounded off to two decimal places).

The molecular weight of CO2 = 44 g/mol

Universal gas constant = 8.314 J/mol-K

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).

The BOD5 values (in mg/L) measured for five samples of wastewater are 20, 35, 40, 15, and 30. The standard deviation of these BOD5 values is ______ mg/L (rounded off to one decimal place).
Sound pressure levels were measured at a location over four consecutive 15-minute intervals as 65 dB, 70 dB, 68 dB, and 72 dB. The equivalent continuous sound level (Leq) over the total one-hour period is ______ dB (rounded off to two decimal places).
Which of the following statements is/are CORRECT regarding reverse osmosis (RO) as a water/wastewater treatment process?
In the context of biological wastewater treatment, which of the following pairs CORRECTLY match the electron donor/acceptor with the corresponding biological process?
Which ONE of the following statements is CORRECT regarding the eigenvalues of a real symmetric matrix?
Which of the following are valid assumptions of the Gaussian plume dispersion model used for estimating ground-level pollutant concentrations from a point source?
In the context of coagulation-flocculation used in water treatment, the compression of the electrical double layer around a colloidal particle, brought about by the addition of an electrolyte, primarily reduces the thickness of which ONE of the following layers?

The analysis of a water sample is shown in the table. The hardness of the water sample is ______ mg/L as CaCO3.

Atomic weight (g/mol): Ca = 40; Mg = 24; Na = 23; Cl = 35.5; S = 32; O = 16; N = 14

SpeciesConcentration (mg/L)
Na+30
Ca2+10
Mg2+15
Cl-30
SO42-60
NO3-5