List of top Questions asked in GATE ES

Given are two ordinary differential equations
P: $\dfrac{dy}{dx} + x = x \sin y$
Q: $\dfrac{dy}{dx} + x y = e^{x} y$
The correct choice is:

P and Q are square matrices. Consider the following:
X: $(P^{-1})^{-1} = P$
Y: Symmetric if $Q = -Q^T$
The correct choice is:

Given are two infinite series
P: $\displaystyle \sum \frac{n^2 + 1}{n^2}$
Q: $\displaystyle \sum \left(1 + \frac{1}{n}\right)^{-n}$
The correct choice is:

For testing alkalinity for a water sample, first phenolphthalein indicator is added. The water remains colorless. However, when a few drops of methyl orange are added to the sample, the color turns yellow. As per these observations, the correct choice is:

Permit : __________ :: Enforce : Relax (By word meaning)

Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?

A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

How many triangles are present in the given figure?

Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that surprisingly none of the students from the Department of Human Sciences had completed the registration process.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.
(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.
(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

Which one of the following options represents the given graph?

Given, $y = f(x)$; $\dfrac{d^2 y}{dx^2} + 4y = 0$; $y(0) = 0$; $\dfrac{dy}{dx}(0) = 1$. The problem is a/an

Average values of the re-aeration rate constant for river X and Y are 0.92 day$^{-1}$ and 1.12 day$^{-1}$ respectively. Average de-oxygenation rate constants are 0.23 day$^{-1}$ and 0.35 day$^{-1}$ for the same rivers. Which of the following statement(s) is/are correct?

The area of the region (rounded off to one decimal place) enclosed between the curves $y = x$ and $y = 3\sqrt{x}$ and between the lines $x = 0$ and $x = 1$ is ____________ units

A sewage treatment plant (capacity 10 MLD) treats wastewater using an aerobic biological process. Inlet BOD = 100 mg/L, outlet BOD = 30 mg/L. Microbial yield = 0.5 g VSS/g BOD removed. At 80% plant capacity, the sludge production rate (in kg/day, rounded off to one decimal place) is __________.

A ground level source emits 1000 g/day of SO$_2$. Wind speed = 2 m/s. Dispersion coefficients at 1000 m downwind are given. Estimate the ground-level SO$_2$ concentration (in $\mu$g/m$^3$, rounded off to two decimals) at 1000 m at the plume centerline.

The figure shows heat inflow and outflow for a waste-to-energy plant furnace. Assume:
(i) total heat loss = 3% of heat released from waste,
(ii) sensible heat of waste is negligible,
(iii) complete burning of waste.
Given waste feed rate = 70 kg/h, air heat input = 300 kcal/h,
flue gas = 90000 kcal/h, ash = 10000 kcal/h.
Find the heat content of waste (kcal/kg), rounded to one decimal place.

A solution has 0.001 mole/L zinc ions with pH = 6. The solubility product of zinc hydroxide is \[ K_{sp} = 8 \times 10^{-18}\ (\text{mol/L})^{3}. \] Ignoring activity corrections, find the ratio (rounded to two decimals) of the reaction quotient to the solubility product.

An isolated 3-hour storm occurred over a catchment.
Given the $\phi$–index and rainfall data, compute the total rainfall excess (rounded off to one decimal place).

Two reservoirs differ by 20 m in water levels and are connected through a confined aquifer (thickness = 5 m, length = 2 km, hydraulic conductivity $K = 3\times10^{-3}$ m/s, porosity $\eta = 0.3$). If Reservoir 1 is contaminated, the time (in days, rounded off to one decimal place) taken by the pollutant to reach Reservoir 2 by advection is __________.

A venturimeter with a differential manometer is installed to measure flow in a water pipeline. Taking water specific weight = 9810 N/m$^3$, compute the pressure difference (in Pa, rounded off to one decimal place) between points Q and P.