**GATE-2021**

**ES: Environmental Science and Engineering**

**GA- General Aptitude**

**Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).**

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A) 9,92,500

(B) 9,95,006

(C) 10,00,000

(D) 12,51,506

2. p and q are positive integers and

(A) 3

(B) 7

(C) 9

(D) 11

3.

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A) 4

(B) 3

(C) 6

(D) 7

4. *Nostalgia* is to *anticipation* as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Present, past

(B) Future, past

(C) Past, future

(D) Future, present

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iii)

(C) (ii) and (iii)

(D) (i) and (iv)

**Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).**

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct.

(B) Only conclusion II is correct.

(C) Either conclusion I or II is correct.

(D) Both conclusion I and II are correct.

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A) (ii) and (iii)

(B) (ii) and (iv)

(C) (i), (iii) and (iv)

(D) (i) and (iii)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A) π/3

(B) 2π/3

(C) 3π/2

(D) 3π

9.

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A) 4

(B) 5

(C) 6

(D) 7

10.

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A) 2 : 3

(B) 3 : 4

(C) 4 : 5

(D) 5 : 6

**Environmental Science and Engineering**

**Q.1 – Q.18 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).**

1. A tangent is drawn on the curve of the function y = x^{2} at the point (x, y) = (3, 9). The slope of the tangent is __________.

(A) 3

(B) 6

(C) 9

(D) 12

2.

(A) 0

(B) 1

(C) 2

(D) −1

3. The table below shows the carbon content of four samples of powdered coal. If these four samples are mixed completely, what would be the resultant carbon percentage of the mixture by weight?

(A) 58%

(B) 86%

(C) 87%

(D) 90%

4. A sample of air is collected in the morning at an ambient temperature of 25°C. The concentration of carbon monoxide (CO) in this sample is 30 ppmv (ppm by volume). The same sample is analysed later in the afternoon when the sample temperature is 35 °C. The analysis results will show the CO concentration as ___________.

(A) < 29 ppmv

(B) > 30 ppmv

(C) = 30 ppmv

(D) = 29 ppmv

5. In fluid statics, the line of action of the buoyant force always acts through the __________.

(A) centre of gravity of any submerged body

(B) centroid of the volume of any floating body

(C) centroid of the displaced volume of fluid by the body

(D) centroid of the volume of fluid vertically above the body

6. What is the order of preference of the various elements in integrated waste management hierarchy (highest preference to lowest preference)?

(A) Reduce > Reuse & recycle > Energy recovery > Landfilling

(B) Reuse & recycle > Reduce > Energy recovery > Landfilling

(C) Reduce > Energy recovery > Reuse & recycle > Landfilling

(D) Reduce > Reuse & recycle > Landfilling > Energy recovery

7. If d is the depth of an aquifer through which water is flowing, then the relationship between permeability K and transmissibility (also known as transmissivity) T is given by ____________.

(A) T = Kd

(B) T = K/d

(C) T = √Kd

(D) K = √Td

8. Which of the following is the terminal electron acceptor in the electron transport chain of aerobic respiration?

(A) Water

(B) NADH

(C) O_{2}

(D) Cytochrome-c

9. Which of the following causes ‘Type-I’ settling in a sedimentation tank?

(A) Agglomeration

(B) Compression

(C) Force of gravity

(D) Charge neutralization

10. In the context of noise pollution, SPL is the sound pressure level in decibels (dB). The relationship between SPL, the root mean square (rms) sound pressure p, and the reference (hearing threshold) pressure p_{0} is expressed as

11. The following block diagram highlights the typical phases of the life cycle of a product. In the figure, ‘P’, ‘Q’, and ‘R’ represent various possible scopes of analyses in life cycle assessment. Which of the following statements is true?

(A) ‘R’ represents cradle-to-grave analysis.

(B) ‘P’ represents cradle-to-gate analysis.

(C) ‘Q’ represents gate-to-grave analysis.

(D) ‘R’ represents gate-to-gate analysis.

12. The United Nations Conference on Environment and Development was held in 1992 in Rio de Janeiro, Brazil. During this conference, several environmental management principles were adopted by many countries.

Which one of the following principles allows the governments to take mitigation measures on the environmental issues having serious threats or irreversible damage, even if there is scientific uncertainty about such issues?

(A) Polluters pay principle

(B) Precautionary principle

(C) Extended producer responsibility

(D) Common but differentiated responsibilities

13. Choose the correct order of biodegradability (highest to lowest) of the following municipal solid waste components.

(A) Food waste > Newspaper > Polyvinyl Chloride (PVC)

(B) Newspaper > Food waste > Polyvinyl Chloride (PVC)

(C) Food waste > Polyvinyl Chloride (PVC) > Newspaper

(D) Polyvinyl Chloride (PVC) > Food waste > Newspaper

14. In proximate analysis, when a 10 kg moisture-free solid sample is heated in a furnace at 950 °C in the absence of air, its mass is reduced by 6 kg. If the same 10 kg moisture-free solid sample is heated in the furnace at the same temperature in the presence of air, its mass is reduced by 7 kg. The percentage of fixed carbon in the sample is ____________.

(A) 20%

(B) 60%

(C) 10%

(D) 30%

15. Chlorine is most effective as a water disinfectant at a pH of ____________.

(A) 6

(B) 8

(C) 10

(D) 12

16. The oxidation states of ‘N’ in NH_{4}^{+}, O_{2}^{−}, and NO are __________, respectively.

(A) +2, −3, and +3

(B) −3, +3, and +2

(C) −3, +3, and −4

(D) +4, −2, and +2

17. What is the pH of a water sample having H^{+} concentration of 10 mg/L? The atomic weight of H is 1 g/mol.

(A) 2

(B) 4

(C) 6

(D) 8

18. Which of the following pairing of nucleotide bases is present in double helix DNA?

(A) Thymine – Cytosine

(B) Adenine – Thymine

(C) Cytosine – Adenine

(D) Uracil – Thymine

**Q.19 – Q.22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).**

19. Which of the following is/are both greenhouse gas(es) and ozone depleting substance(s)?

(A) CFC-11

(B) CO_{2}

(C) HCFC-22

(D) N_{2}O

20. The ordinary differential equation has y as the dependent variable and x as the independent variable. Which of the following classification(s) is/are applicable to the equation?

(A) Linear

(B) Non-linear

(C) First order

(D) Second order

21. 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) 1

(B) 2

(C) 3

(D) 4

22. A wind rose is a representation of meteorological conditions. Which of the following is/are included in this representation?

(A) Mixing height

(B) Wind speed

(C) Wind direction

(D) Percentage of time

**Q.23 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).**

23. 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 9×10^{−}^{4} N·s/m^{2}. The theoretical power required to maintain the given velocity gradient is ____________ kW (rounded off to the nearest integer).

24. In a sample, the growth of microbial cells started with an initial concentration of 5×104 cells per millilitre (mL) of the sample. After a certain time period, the cell concentration was found to be 1280 × 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).

25. 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).

**Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).**

26. The 2×2 matrices P and Q satisfy the following relations:

The matrix Q is equal to ____________.

27. A biased die has six faces numbered as k = 1, 2, 3, 4, 5, and 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) 35/91

(B) 56/91

(C) 12/21

(D) 9/21

28. Match the entries in Column I with the correct entries in Column II.

(A) P-(iii), Q-(ii), R-(i)

(B) P-(ii), Q-(i), R-(iii)

(C) P-(i), Q-(iii), R-(ii)

(D) P-(ii), Q-(iii), R-(i)

29. Which of the following international multilateral agreements (conventions, protocols) from Column I match with the entries in Column II?

(A) P-(iv), Q-(iii), R-(ii), S-(i)

(B) P-(iv), Q-(ii), R-(iii), S-(i)

(C) P-(iii), Q-(i), R-(ii), S-(iv)

(D) P-(i), Q-(iii), R-(iv), S-(ii)

30. 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?

PFR is Plug Flow Reactor.

CFSTR is Continuous Flow Stirred Tank Reactor (also referred to as CSTR).

(A) PFR will always require less reactor volume than CFSTR.

(B) PFR will require the same reactor volume as CFSTR.

(C) CFSTR will always require less reactor volume than PFR.

(D) CFSTR can sometimes require less reactor volume than PFR.

31. A 200 mL sample of water has an initial pH = 9. In order to determine alkalinity, the sample was titrated using 0.02 N H_{2}SO_{4} acid to an end point of pH = 4.5. In the titration, 25 mL of 0.02 N H_{2}SO_{4} acid was required. What is the total alkalinity of the sample in ‘mg/L as NaHCO_{3}’?

(A) 20

(B) 125

(C) 210

(D) 305

32. A sewage treatment plant (STP) receives sewage at a flow rate of 20000 m3 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}

(A) 48

(B) 80

(C) 480

(D) 800

33. In context of municipal solid waste treatment, match the equipment in List I with their function in List II.

(A) P-(iii), Q-(iv), R-(i), S-(ii)

(B) P-(iii), Q-(ii), R-(iv), S-(i)

(C) P-(i), Q-(iv), R-(iii), S-(ii)

(D) P-(iv), Q-(ii), R-(i), S-(iii)

34. 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?

[Atomic weight (g/mol): Na = 23, K = 39, Ca = 40, and Mg = 24]

(A) 2.83

(B) 1.94

(C) 2.00

(D) 4.00

**Q.35 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).**

35. Which of the following is true for the nitrifying bacteria belonging to genus *Nitrobacter*?

(A) They are autotrophs.

(B) They are eukaryotes.

(C) They convert chemical energy to cellular energy using mitochondria.

(D) They convert NO_{3}^{−} to NO_{2}^{−}

36. 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?

(A) Impaction

(B) Gravitation

(C) Interception

(D) Diffusion

37. In air pollution, which of the following is/are classified as primary pollutants?

(A) Carbon monoxide (CO)

(B) Sulphur dioxide (SO_{2})

(C) Ozone (O_{3})

(D) Nitrogen dioxide (NO_{2})

38. Which of the following is/are correct for the process of glycolysis?

(A) There is net decrease in standard Gibbs free energy.

(B) The end product is glyceraldehyde 3-phosphate.

(C) First phase includes the phosphorylation of the glucose molecule.

(D) It results in the net gain of NADH.

39. In the context of water quality, which of the following is/are correct for the most probable number (MPN) of a water sample?

(A) The estimated organisms are gram negative.

(B) It is based on the assumption of Poisson distribution.

(C) It measures the exact number of microorganisms present in the sample.

(D) It includes the quantification of pathogenic virus.

40. For any particular location, which of the following would influence the solar radiation incident on a rooftop solar water heater?

(A) Heater surface temperature

(B) Day of the year

(C) Hot water temperature

(D) Sky clearness

**Q.41 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).**

41. If f(x) + 3f(g(x)) = x − 2,

then the value of the ratio is _______ (answer in integer).

42. Consider a function y = f(x) which satisfies the following equation:

As x → −∞, y = 1, and at x = 0, y = 2.

The value of at x = 0 is _______ (answer in integer).

43. The concentration of NO2 in the air at NTP is reported as 0.30 ppmv (ppm by volume). The concentration of NO_{2} in μg/m^{3} is __________ (rounded off to the nearest integer).

[At NTP, temperature = 298 K, pressure = 1 atm, and one mole of ideal gas occupies 24.45 L]

[Molecular weight of NO_{2} = 46 g/mol]

44. 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.

A rectangular channel of 10 m width carries 20 m^{3}/s of water. The depth of flowing water is 1 m. The specific energy for this flow condition is ____________ m (rounded off to one decimal place).

Consider acceleration due to gravity (g) = 10 m/s^{2}.

45. Two reservoirs are connected by a pipeline consisting of two pipes ‘A’ and ‘B’ in series. The two pipes are of same length and have the same Darcy friction factor. If the internal diameter of pipe ‘B’ is twice as large as the internal diameter of pipe ‘A’, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is ____________ (answer in integer). Neglect all minor losses.

46. In a field test of a geological formation of permeable soil (porosity = 20 %), the hydraulic gradient was found to be 2 %. The actual seepage velocity of the flow was found to be 0.0025 m/s. Assume that the flow is in the laminar regime. The permeability (K) of the aquifer is __________ m/s (rounded off to three decimal places).

47. An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.

Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.

In this case, the contaminant concentration expected at the well under steady state conditions is ____________ mg/L (rounded off to two decimal places).

48. The net profit expected from a manufacturing unit is Rs. 6000 per year. The operational life of the unit is 15 years. Assuming a fixed discount rate of 8% per annum, the net present worth of the profit earned over the operational life is Rs. ____________ (answer in integer).

49. A 900 mm internal diameter sewer is laid at a slope of 0.004 and has an actual flow of 0.15 m^{3}/s. Assuming Manning’s roughness coefficient to be 0.013, the ratio of the actual flow to the flow when the sewer is running full is _________ (rounded off to two decimal places).

Take π = 3.14.

50. A 10 million litres per day (MLD) sewage treatment plant (STP) is based on the Activated Sludge Process (ASP). First, the sewage undergoes primary treatment and the resulting treated sewage has BOD_{5} of 140 mg/L concentration. This is further passed through a 1500 m^{3} capacity aeration tank (in ASP), where the mixed liquor volatile suspended solids (MLVSS) concentration is maintained at 3000 mg/L. The concentration of BOD_{5} of the treated sewage is 5 mg/L.

The Food to Microorganisms ratio (F/M) of the ASP is ____________ day^{−}^{1}

(rounded off to two decimal places).

51. The municipal solid waste (MSW) generated in a community (population = 100000) is disposed on a 12 × 10^{4} m^{2} landfill site, which can be filled to a total depth of 25 m (including soil cover). Assume that MSW is generated at a rate of 2.5 kg per person per day and its compacted density is 800 kg/m^{3}. If the volumetric ratio of MSW and soil cover is 5:1, the useful life of the landfill site is

52. A mechanized stationary container system is proposed for waste collection from a commercial area. The container unloading time is 0.1 hours per container. There are two containers at each location and the drive time between the two locations is 0.2 hours. The maximum waste ‘pick-up time’ is 2.4 hours per trip.

The ‘pick-up time’ starts at the instant the truck arrives at the first pick-up location and ends when the last container on the route is emptied. The maximum number of locations which can be covered in a trip by the collection vehicle are ____________ (answer in integer).

53. The molar concentrations (M, i.e. mol/L) of some ionic species in a water sample were estimated as follows:

Na^{+} = 0.25 M; Ca^{2+} = 0.12 M; Cl^{−} = 0.32 M; HCO_{3}^{−} = 0.05 M.

The ionic strength of this water sample is __________ M (correct up to two decimal places).

54. Excess amount of solid calcium sulphate (CaSO_{4}) was added to a pure water sample (pH = 7) so that some solids remain undissolved at the equilibrium. The solubility product of CaSO_{4} is 2×10^{−5 }mol^{2}/L^{2}. The molar concentration of SO_{4}^{2−} in this water sample at equilibrium will be ____________ mol/L (rounded off to three decimal places).

55. A facultative pond system for sewage treatment consists of two ponds in series. The hydraulic retention time (HRT) of each pond is 6 days. The total BOD5 reduction through the entire pond system is 90 %. If the ponds are considered to be completely mixed, then the rate constant describing the BOD5 removal is _________ day^{−}^{1} (rounded off to two decimal points). Assume that the rate constant is same for both the ponds.

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