List of top Questions asked in GATE ES

A city generates on average 1000 metric tonnes/day (t/d) of municipal solid waste and follows an integrated waste management system. 15% of the total waste is recycled, 40% used to produce compost, 25% converted to refuse derived fuel (RDF) with 80% efficiency, and the remaining disposed in a sanitary landfill. The calorific value of the RDF is 15 MJ/kg. The electrical energy that could be generated from the RDF with a thermal-to-electrical conversion efficiency of 20% is ____________________ (in MWh/d, rounded off to two decimal places).

Ms. Anita uses a BS-IV two-wheeler petrol scooter (mileage $=50$ km/L) to travel $30$ km every day. She exchanges this with an electric scooter that consumes electricity at $0.1$ kWh per $10$ km (i.e., $0.01$ kWh/km). Petrol and electricity prices are Rs. $90$/L and Rs. $3.5$/kWh, respectively. Maintenance costs of both are negligible. The \emph{operational cost saved in a year} is __________________ (in Rs., in integer).

An aeration tank is to be installed for removal of a VOC from water. Flow through the tank $Q=180{,}000$ m$^3$/d. Permissible limit in water $C_{\text{out}}=12\ \mu$g/L. Saturation concentration in water $C^* = 5\ \mu$g/L. Gas-transfer rate constant $k=0.40$ s$^{-1}$ at $25^\circ$C. Initial concentration $C_{\text{in}}=33\ \mu$g/L. Find the required tank volume at $25^\circ$C (in m$^3$, rounded to two decimals).

The following figure (not to scale) shows a catchment (Q, S, U, T, Q) and adjoining raingauge stations P, Q, R, S, U, V. Due to a storm, rainfall depths were recorded as follows: - P = 20 mm, Q = 25 mm, R = 30 mm, S = 15 mm, U = 22 mm, V = 18 mm.

The corresponding mean rainfall over the catchment using Thiessen polygon method is ............... (in mm, rounded off to two decimal places).

A trapezoidal canal lined with cement concrete (\(n = 0.01\)) is designed to carry a discharge of 20 m\(^3\)/s at a bed slope 1 in 400. The bed width is twice the depth of flow and side slope of the canal section is 2 (1 vertical : 2 horizontal). The corresponding depth of flow will be ............. (in m, rounded off to two decimal places).

A plunger weighing 314 kN is balanced in a cylindrical vessel of diameter 1.5 m and filled with an oil (specific gravity 0.9) as shown in the following figure (not to the scale).

If a pressure gauge is connected with the vessel using 1.5 cm diameter tube, the reading of the gauge will be .......... (in kPa, rounded off to two decimal places).

A fully penetrating well is installed in a homogenous and isotropic confined aquifer. The aquifer has uniform thickness of 16 m and hydraulic conductivity of 25 m/d. Water is being pumped out from the well at a constant rate of 0.1 m$^3$/s till steady state condition is reached. If a drawdown of 3.5 m is observed at a distance of 75 m from the well then the drawdown at a distance of 150 m from the well will be ....................... (in m, rounded off to two decimal places).

A biological reactor is getting wastewater containing 1 mole/L acetate ions as carbon source. The following reaction takes place in the bio-reactor: \[ 0.125CH_3COO^- + 0.0295NH_4^+ + 0.103O_2 \;\;\Rightarrow\;\; 0.0295C_5H_7O_2N + 0.0955H_2O + 0.095HCO_3^- + 0.007CO_2 \] Assume that all acetate ions are consumed and ammonia serves as a nutrient source. Given that 1 g acetate exerts 1.07 g COD; 1 mole bacteria = 113 g VSS; 1 mole acetate ion = 59 g. Value of observed yield is ________________________ (in g VSS/g COD, rounded off to two decimal places).

A flask (100 mL volume) has wastewater with 0.12 mg/L geosmin. Activated carbon adsorbs geosmin as per Freundlich isotherm: \[ Q = 2.6 \, C^{0.73} \] where \( Q \) is mg adsorbate/mg adsorbent, and \( C \) is equilibrium concentration (mg/L). Activated carbon is added to reduce final geosmin concentration to 0.05 mg/L. Activated carbon dose required is ________________ (in mg/L, rounded off to three decimal places).

A pipeline delivers 20 L/s of oil (kinematic viscosity = \( 6 \times 10^{-6} \, m^2/s \), specific gravity = 0.9) under laminar flow. Minimum diameter of pipe is ________________ (in m, rounded off to two decimal places).

A BOD\(_5\) test is conducted. 25 mL wastewater with ultimate BOD of 75 mg/L is diluted to 300 mL. Initial DO = 6.5 mg/L. DO at 7th day = 1.25 mg/L. Find BOD\(_5\) of wastewater sample (mg/L, rounded off to two decimals).

In a 30 m$^3$ room, a stove in operation consumes wood at the rate of 0.25 kg/h. The inflow and outflow rate of air in the room is the same, i.e., 500 m$^3$/h. This stove emits a VOC species at a rate of 0.2 g/kg-wood. The VOC species gets converted to CO$_2$ at a rate of 0.4 per hour. Given: (i) the air in the room is completely mixed, (ii) initial concentration of the VOC species in the room is negligible, and (iii) concentration of the VOC species in the air entering the room is negligible. The concentration of the VOC species due to two hours of stove operation in the room is __________________________________ (in $\mu$g/m$^3$, rounded off to one decimal place).

Which of the following statements is/are NOT true?

Read the following statements about aerobic composting of organic fraction of municipal solid waste:
I. The majority of the odour problem in an aerobic composting process is due to the development of anaerobic conditions within the compost pile.
II. All organic carbon present in the waste will completely biodegrade in 14 days.
III. At high C/N ratio, ammonia would be released and biological activity may also be impeded.
IV. Optimum moisture content for aerobic composting process would be 50–60%. Lower moisture would slow down the biological process. Excessive moisture will make it difficult to maintain aerobic conditions.
The correct choice(s) is/are:

Products P and Q have life cycle phases of material extraction, production, use, and end of life disposal. CH$_4$, CO$_2$ emissions and mass used per functional unit (f.u.) from the different phases of the products are given in the following tables. Product P \[ \begin{array}{|c|c|c|c|} \hline \text{Phase} & \text{CO$_2$ emissions (kg/tonne)} & \text{CH$_4$ emissions (kg/tonne)} & \text{Mass (tonne/f.u.)} \\ \hline \text{Material Extraction} & 1.0 & 0.75 & 4.0 \\ \text{Production} & 1.5 & 1.0 & 2.0 \\ \text{Use} & 0.5 & 0.0 & 1.0 \\ \text{End of life disposal} & 1.0 & 0.25 & 1.0 \\ \hline \end{array} \] Product Q \[ \begin{array}{|c|c|c|c|} \hline \text{Phase} & \text{CO$_2$ emissions (kg/tonne)} & \text{CH$_4$ emissions (kg/tonne)} & \text{Mass (tonne/f.u.)} \\ \hline \text{Material Extraction} & 0.75 & 0.75 & 3.0 \\ \text{Production} & 0.25 & 1.0 & 2.5 \\ \text{Use} & 0.0 & 0.5 & 0.75 \\ \text{End of life disposal} & 2.0 & 0.0 & 0.75 \\ \hline \end{array} \] Given: Global warming potential (GWP) of CH$_4$ = 23 kg CO$_2$ equivalent per kg of CH$_4$.

Second order ordinary differential equation \[ \frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0 \] has values \(y=2\) and \(\frac{dy}{dx} = 1\) at \(x=0\). The value of \(y\) at \(x=1\) is ............ (rounded off to three decimal places).

Consider two matrices \[ P = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}, Q = \begin{bmatrix} 5 & 4 \\ 0 & 2 \end{bmatrix}. \] If \(R = (PQ)^T\), then \(\det R\) is ............ (in integer).

For the function \[ f(x) = x \sqrt{4 - x^2}, \] the maximum value in the range \(-2 \leq x \leq 2\) is ...................... (rounded off to two decimal places).

Which one of the following statements is NOT correct?

Read the following statements:
I. Bacteriophage is an anaerobic bacterium.
II. Male-specific bacteriophage infect via the pili of other microorganisms including viruses.
III. Bacteriophage is found in human as well as in animal excreta.
IV. Bacteriophage cannot indicate the presence of bacteria.
The correct choice is:

Read the following statements:
i. In endogenous metabolism by aerobic bacteria, electron acceptor is present inside the cells.
ii. In endogenous metabolism by aerobic bacteria, electron acceptor is dissolved oxygen.
iii. The endogenous metabolism is linked to fermentative metabolism.
iv. In exogenous metabolism by aerobic bacteria, enzyme mediated electron transfer happens within the cells.
The correct choice is:

A boiler in an industry, located where high plume rise is expected, releases flue gas with fine particulate matter. Which one of the following options is most suited and efficient if this particulate matter is intended for reuse?

Match the following: \[ \begin{aligned} \text{J) Dalton’s law} & & i) \, \text{Diffusion} \\ \text{K) Fick’s law} & & ii) \, \text{Pressure exerted by a mixture of gases} \\ \text{L) Henry’s law} & & iii) \, \text{Gravitational settling} \\ \text{M) Stoke’s law} & & iv) \, \text{Gas-liquid phase transfer} \\ \end{aligned} \]

Read the following statements:
I. According to the Liebig’s law of minimum, the growth is regulated by the limited factors i.e., resources in scarcity and not by the resources in abundance.
II. Shelford’s law of tolerance states that, only the factors present in excess/abundance can affect the growth, development of an organism or rate of biological process.
III. Shelford’s law of tolerance states that, an organism's success is based on a complex set of conditions and that each organism has a certain minimum, maximum, and optimum levels of environmental factor or combination of factors that determine success.
The correct choice is: