GATE Environmental Science Mock Test - 1 - GATE Environmental Science MCQ

For the six-digit number 3x8z9y to be divisible by both 7 and 11, what is the average value of x, y, and z?

What is the mirror reflection of the text shown above when flipped about the x-axis?

Consider a square sheet with a side length of 4 units. The sheet is initially folded along the primary diagonal. This is followed by another fold along its axis of symmetry. Subsequently, the resulting folded shape is folded twice (one after another) along its axis of symmetry.
The area of each face of the final folded shape, in square units, equals _________

It is often not understood how gradually and with difficulty we arrive at the articulation of truth. We tend to be quite variable, eager to maintain politeness, and are frequently influenced by either caution or anger. Our thoughts swing back and forth like a pendulum: it requires time for them to settle. After that, appropriate adjustments and corrections need to be made for our personal fluctuations that hinder precision. Just as a compass needle does not point to true north, but rather to magnetic north, our minds can at best only suggest magnetic truth, affected by various factors that distort it similarly to how iron filings affect a compass. The pressure of maintaining one’s employment: what an iron filing that is on the compass of an individual's mind!

Which of the following statements supports the conclusion regarding "truth"? 

A student has documented the following concentrations of arsenic in water samples: 

Which of the following statements accurately describes the distribution of arsenic concentrations?

Let P be an m × n matrix, Q an n × l matrix, and R and S be n × n matrices, with the superscript T indicating transpose.
Consider the following relationships:
Relationship 1: (PQ)^T = Q^TP^T 
Relationship 2: (RS)^-1 = S^-1R^-1 
Which of the following statements is true? 

The measurement of specific conductance in water analysis is utilized to indirectly determine the concentration of dissolved solids. The approach used in this method considers

Identify the reaction order and calculate the corresponding rate constant.

Which type of plastic should be avoided for use in food containers due to the presence of BPA?

Which of the following cycles is the least rapid?

A sample of ten litres was passed through a membrane filter, and the filter was then placed onto solid agar media that promotes the growth of coliform organisms. Following an incubation period of 48 hours at 37^oC, the agar plates exhibited an average of 64 colonies per plate. What is the average concentration of coliform organisms (measured in Colony Forming Units per unit volume) in the original water sample?

The Reverse Transcriptase Polymerase Chain Reaction is a technique utilized for the identification of pathogenic microorganisms. Which of the following statements is NOT accurate in this regard? 

Which of the following is NOT a goal of the UN's Millennium Development Goals (MDGs)?

The obligation to perform an Environmental Impact Assessment (EIA) for developmental projects was established in India.

A solution to the ordinary differential equation d²y/dt² 5dy/dt 6y = 0 satisfies the conditions y(0) = 2 and y(1) = -(1-3e)/e³. What is the value of dy/dt(0)?

Given, The scenario is a/an

Which of the following generates contaminants in the soil that lead to soil pollution?

Note: This is a MSQ. One or more than one option can be correct.

Which of the following statements about lakes and their various zones is/are accurate?

Note: This is a Multiple Select Question (MSQ). One or more options may be correct.

The area of the region (rounded to one decimal place) that is enclosed by the curves y = x and y = 3√x, as well as between the lines x = 0 and x = 1, is ________ units.

A solitary storm lasting 3 hours took place over a catchment area as depicted below 

The total rainfall excess (in cm, rounded to one decimal place) across the catchment for this storm is ____________.

A sewage treatment facility with a daily capacity of 10 million litres (MLD) is processing sewage using an aerobic biological method. The BOD levels at the inlet and outlet are recorded as 100 mg/l and 30 mg/l, respectively. Given that the observed biomass yield of the mixed microbial culture is 0.5 g Volatile Suspended Solids (VSS) per g BOD, what will be the rate of sludge production (in kg per day, rounded to one decimal place) when the plant operates at 80% of its capacity?

The Henry’s law constant of CO₂ is 3.4×10^-2 M per atm in neutral water at 25⁰C. The dissolved CO₂ (i.e., CO₂.H₂O) at equilibrium undergoes the following reactions.
CO₂ . H₂O ⇌ H⁺ + HCO^-₃ (Equilibrium constant = 4.3 × 10^-7 M) 
HCO^-₃ ⇌ H⁺ + CO^2-₃ (Equilibrium constant = 4.7 × 10^-11 M) 
If ambient CO₂ concentration is 300 ppm, the total dissolved CO₂ (in µM, rounded off to one decimal place) is ________.

A coarse screen utilized in the treatment of raw water has a screen constant of k = 1.43. Determine the velocity through the screen (in m/s, rounded to two decimal places) given that the velocity of approach is 3 m/s and the head loss across the screen is 1.5 m.

In assessing rainfall in a specific region using the isohyetal technique, the following data has been collected. Determine the average rainfall recorded (in mm, rounded to two decimal places) in the area.

What is the area enclosed between the parabola defined by x² = 12y and the line given by y = 2? (Round your answer to two decimal places)

The lengths of a significant collection of titanium rods are distributed normally, with a mean (μ) of 350 mm and a standard deviation (σ) of 1 mm. What is the percentage of rods (rounded to the nearest integer) that have lengths between 349 mm and 352 mm?

A fair coin has two sides marked as 0 and 1. The coin is tossed twice independently. Let P and Q represent the labels for the results of these tosses. For the random variable X defined as X = max(P, Q), the expected value E(X) (rounded to two decimal places) is