List of top Questions asked in GATE ES- 2025

Water from a hand pump located near a landfill has 1 mg/L arsenic (oral carcinogenic potency factor = 1.75 (kg-day)/mg). A person who lives nearby drinks 2 L/day of water from this hand pump for 10 years. Assume a body weight of 70 kg and an average life duration of 70 years. The chances of this person getting an excess risk of cancer is ________ $\times 10^{-3$ (rounded off to three decimal places).}
An industry releases three greenhouse gases (GHGs), CO2 (5 kg/day), CH4 (0.5 kg/day), and N2O (0.1 kg/day). The industry flares the CH4 before it is released to the atmosphere. The Global Warming Potential (GWP) are as follows: CO2 = 1, CH4 = 21, N2O = 310. The annual GWP of GHGs released from the industry is ________ kg CO2 equivalent (rounded off to the nearest integer).
A solid waste of composition \( C_{60}H_{135}O_{50}N_5 \) is to be composted aerobically in a closed vessel mechanical composting facility. Given: all ammonia generated escapes the facility; air contains 23% of Oxygen by weight; 100% excess air requirement for the closed vessel composting facility. The atomic weights: C – 12, H – 1, O – 16, N – 14. The actual air required for composting is:

A particle dispersoid has 1510 spherical particles of uniform density. An air purifier is proposed to be used to remove these particles. The diameter-specific number of particles in the dispersoid, along with the number removal efficiency of the proposed purifier is shown in the following table:

The overall mass removal efficiency of the proposed purifier is ________% (rounded off to one decimal place).

A boiler burns coal at a rate of 1 kg/s. If the coal has 3% sulfur content, assuming that there is no sulfur in ash, SO2 emitted is ________ kg/day. (rounded off to nearest integer)
A common effluent treatment plant with a capacity of 2 million litres per day (MLD) employs reverse osmosis (RO) for water reuse. The RO unit removes 95% of the total dissolved solids (TDS) and the water recovery rate is 70%. If the TDS concentration in the RO feed is 8000 parts per million (ppm), the TDS in the RO reject is ________ g/L. (rounded off to one decimal place)
A circular sewer pipe, having Manning’s coefficient (n) of 0.01, is laid at a bed slope of 1:100. If it is flowing 80% full for a discharge of 2 m\(^3\)/s, then its diameter is ________ m. (rounded off to three decimal places)
Diameter ($d$) and length ($l$) of each pipe are as presented in figure and all pipes are of same material having friction factor ($f$) of 0.02. Assume acceleration due to gravity ($g$) as 10.0 m/s$^2$. If the head difference between $P$ and $Q$ is 10 m, then the head loss between $Q$ and $R$ is ________ m. (rounded off to two decimal places)

The following table and figure (not to scale) show characteristics of a catchment

The hyetograph resulting from a storm that occurred uniformly over the catchment, is as follows

Assuming a constant base flow of 40 m$^3$/s, the peak of the runoff hydrograph produced by storm for the catchment at the outlet $O$ is ________ m$^3$/s. (rounded off to two decimal places)

The value of \( \int_0^\infty \frac{\sin(4x)}{\pi x} \, dx \) is ________
The following is a system of linear equations

Equation (1):
\( x - 2y + z = 34 \)

Equation (2):
\( 2x + y + z = 102 \)

Equation (3):
\( x + y - 3z = 17 \)

The value of \( x + y + z \) is ________. (rounded off to two decimal places)

A residential family is considering two cities for relocation. The data related to pollutant exposure and associated health cost per year are given in the following figure.

The pollutant exposure is characterized in high, mild and low exposure categories with respective probability values. The difference in expected value of health cost of City1 with respect to that of City 2 is ________ lakhs/year. (rounded off to two decimal places).

An unconfined aquifer of areal extent 20 km × 20 km has hydraulic conductivity of 4 m/day, porosity of 0.32, and storage coefficient (specific yield) of 0.18. If the initial saturated thickness of the aquifer is 30 m, and 4×10^8 m\(^3\) of water is extracted from the aquifer, then the decline in the saturated thickness is ____________ m.
Evaluate the following limit: \[ \lim_{x \to 0} \frac{\ln(1+x)}{2 \sin(x)} \quad {(rounded off to two decimal places).} \]
An incandescent light bulb operated for two hours per day uses 12.2 kWh of energy per month. Burning of one kg of coal generates 2 kWh of electrical energy and releases 7 g of PM10. The reduction in PM10 emitted per month, if this incandescent bulb is replaced with a light emitting diode (LED) bulb which consumes 1/6th of energy, is ________ g (rounded off to one decimal place).
Length of the streets, in km, are shown on the network. The minimum distance travelled by the sweeping machine for completing the job of sweeping all the streets is ________ km. (rounded off to nearest integer)
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If the storm produced a direct runoff of 12.5 mm, then the $\phi$-index of the storm for the catchment is ________ mm/hour. (rounded off to two decimal places)
A homogeneous isotropic confined aquifer of uniform thickness 30 m has hydraulic conductivity of 5 m/day and porosity of 0.3. There are two observation wells X and Y along a radial line from a fully penetrating pumping well at 100 m and 200 m distance, respectively. The well is pumped at a uniform rate to produce steady drawdown of 5 m at X and 3 m at Y. If a non-reactive pollutant enters at the observation well Y, then the time taken by the pollutant (under advection) to reach the observation well X is ________ days. (rounded off to two decimal places)
You conducted a batch experiment in the lab for 10 minutes to degrade a toxic compound, which follows first-order kinetics. The compound degrades from \( 2 \times 10^{-3} \, {M} \) to \( 2 \times 10^{-4} \, {M} \). The information from the lab experiment will be used to design a plug flow reactor in field conditions.
Given field conditions:
• Flow rate of contaminated water to be treated: 1 m\(^3\)/hour
• Concentration of toxic compound in contaminated water: \( 5 \times 10^{-1} \, {M} \)
• Target concentration of toxic compound in treated water: \( 1 \times 10^{-4} \, {M} \)
• Temperature is the same in lab and field conditions.
The required volume of the plug flow reactor is ________ m\(^3\). (rounded off to two decimal places)
A tank has inflow, outflow, and a stirring mechanism. Initially, the tank holds 500 L of a brine solution of concentration 200 g/L. At \( t = 0 \), an inflow of another brine solution of concentration 100 g/L starts entering the tank at the rate of 15 L/minute. At the same time, the outflow of thoroughly stirred mixture also takes place at the same rate so that the volume of brine in the tank remains constant. The brine concentration \( C \) (g/L) in the tank at any time \( t \) (minute) can be expressed by the following differential equation: \[ \frac{dC}{dt} + 0.03 C = 3 \] The brine concentration in the tank at \( t = 1.5 \) hour is ________ g/L. (rounded off to two decimal places)
Aerobic biomass has a yield coefficient value of 0.4 for glucose (molecular weight = 180 g/mole) substrate. The bacteria is represented as \( {C}_5{H}_7{O}_2{N} \) (molecular weight = 113 g/mole). Assume that no endogenous metabolism occurs. The percentage of carbon going into CO2 from 1 mole/L glucose is ________ % (rounded off to two decimal places).

Courage : Bravery :: Yearning : 
Select the most appropriate option to complete the analogy.

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:


 

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is  ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?