List of top Questions asked in GATE ES

Consider a function \[ y = f(x) \text{ which satisfies the following equation:} \] \[ \frac{d^2y}{dx^2} - \frac{dy}{dx} = 0. \] As \( x \to -\infty, y = 1 \), and at \( x = 0, y = 2 \). The value of \[ \frac{dy}{dx} \text{ at } x = 0 \text{ is } _______ \text{ (answer in integer).}
The concentration of NO\(_2\) in the air at NTP is reported as 0.30 ppm (ppm by volume). The concentration of NO\(_2\) in \(\mu g/m^3\) is _______ (rounded off to the nearest integer).
In open channel flow, the specific energy is the total energy per unit weight of a liquid, where the component potential energy is measured from the bed of the channel as the datum.
In the context of water quality, which of the following is/are correct for the most probable number (MPN) of a water sample?
For any particular location, which of the following would influence the solar radiation incident on a rooftop solar water heater?
If \[ f(x) + 3f(g(x)) = x - 2, \] where \[ g(x) = \frac{3x + 1}{x - 3}, \] then the value of the ratio \[ \frac{f(5)}{f(8)} \text{ is } _______ \text{ (answer in integer).}
In air pollution, which of the following is/are classified as primary pollutants?
Which of the following is/are correct for the process of glycolysis?
Which of the following is true for the nitrifying bacteria belonging to genus Nitrobacter?
Which of the following is/are the dominant mechanism(s) for the removal of spherical particles with diameter less than 10 µm from a gas stream using a fabric filter?
The characteristics of a water sample are as follows: Na\(^+\) = 92 mg/L, K\(^+\) = 19.5 mg/L, Ca\(^{2+}\) = 40 mg/L, and Mg\(^{2+}\) = 24 mg/L. What is the sodium adsorption ratio (SAR) of the water sample which may be considered for irrigation purposes?
A 200 mL sample of water has an initial pH = 9. In order to determine alkalinity, the sample was titrated using 0.02 N \( \text{H}_2\text{SO}_4 \) acid to an end point of pH = 4.5. In the titration, 25 mL of 0.02 N \( \text{H}_2\text{SO}_4 \) acid was required. What is the total alkalinity of the sample in ‘mg/L as NaHCO\(_3\)’? [Atomic weight (g/mol): Ca = 40, Na = 23, H = 1, C = 12, S = 32, and O = 16]
A sewage treatment plant (STP) receives sewage at a flow rate of 20000 m\(^3\) per day. The sewage has 200 mg/L of suspended solids. Assume 60% suspended solids are removed in the primary clarifier. The underflow (i.e. sludge) removed from the clarifier contains 5% solids (by weight).
The daily volume of the sludge generated will be ________ m\(^3\) per day.
Assume sludge density = 1000 kg/m\(^3\).
An ideal PFR or an ideal CFSTR may be used to degrade a pollutant with first order reaction kinetics. Both the reactors are fed with the same inlet concentration and the same volumetric flow rate, and are designed to achieve the same outlet concentration. Which of the following statements is true when comparing PFR with CFSTR?
A biased die has six faces numbered as \( k = 1, 2, 3, 4, 5, 6 \). On rolling the die, the probability of the number \( k \) appearing is proportional to \( k^2 \). What is the probability that an even number will appear on rolling the die?
A flocculation tank used for water treatment has a velocity gradient (G) of 800 s\(^{-1}\). The volume of the tank is 40 m\(^3\). The dynamic viscosity of water is \(9 \times 10^{-4}\) N.s/m\(^2\). The theoretical power required to maintain the given velocity gradient is _______ kW (rounded off to the nearest integer).
In a sample, the growth of microbial cells started with an initial concentration of \(5 \times 10^4\) cells per millilitre (mL) of the sample. After a certain time period, the cell concentration was found to be \(1280 \times 10^4\) cells per mL of the sample. Assuming binary fission of cells and no cell death, the number of generations of cell growth occurred in this time period is _______ (answer in integer).
A water jet discharging from a 4 cm diameter orifice has a diameter of 3.5 cm at its vena contracta. The coefficient of velocity is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity of the jet. If the coefficient of velocity is 0.98, the coefficient of discharge for the orifice will be _______ (rounded off to two decimal places).
The ordinary differential equation \[ \frac{dy}{dx} = x^2 y \] has \( y \) as the dependent variable and \( x \) as the independent variable. Which of the following classification(s) is/are applicable to the equation?
Consider the following equation: \[ x^3 - 10x^2 + 31x - 30 = 0 \] Which of the following is/are the root(s) of the above equation?
A wind rose is a representation of meteorological conditions. Which of the following is/are included in this representation?
The oxidation states of ‘N’ in \( \text{NH}_4^+ \), \( \text{NO}_2^- \), and \( \text{NO} \) are _______ , respectively.
What is the pH of a water sample having \( H^+ \) concentration of 10 mg/L? The atomic weight of H is 1 g/mol.
Which of the following pairing of nucleotide bases is present in double helix DNA?
Which of the following is/are both greenhouse gas(es) and ozone depleting substance(s)?