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General Aptitude

10 Questions
GATE→2024→General Aptitude→Verbal Ability
Q1
MCQ[1 Mark]
If '→\rightarrow' denotes increasing order of intensity, then the meaning of the words [sick →\rightarrow infirm →\rightarrow moribund] is analogous to [silly →\rightarrow _____ →\rightarrow daft]. Which one of the given options is appropriate to fill the blank?
GATE→2024→General Aptitude→Quantitative Aptitude
Q2
MCQ[1 Mark]
The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is
Figure for Question 2
GATE→2024→General Aptitude→Quantitative Aptitude
Q3
MCQ[1 Mark]
How many 4-digit positive integers divisible by 3 can be formed using only the digits {1,3,4,6,7}\{1, 3, 4, 6, 7\}, such that no digit appears more than once in a number?
GATE→2024→General Aptitude→Quantitative Aptitude
Q4
MCQ[1 Mark]
The sum of the following infinite series is 2+12+13+14+18+19+116+127+⋯2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{8} + \frac{1}{9} + \frac{1}{16} + \frac{1}{27} + \cdots
GATE→2024→General Aptitude→Data Interpretation
Q5
MCQ[1 Mark]
In an election, the share of valid votes received by the four candidates A, B, C, and D is represented by the pie chart shown. The total number of votes cast in the election were 1,15,0001,15,000, out of which 5,0005,000 were invalid. Based on the data provided, the total number of valid votes received by the candidates B and C is
Figure for Question 5
GATE→2024→General Aptitude→Verbal Ability
Q6
MCQ[2 Marks]
Thousands of years ago, some people began dairy farming. This coincided with a number of mutations in a particular gene that resulted in these people developing the ability to digest dairy milk. Based on the given passage, which of the following can be inferred?
GATE→2024→General Aptitude→Quantitative Aptitude
Q7
MCQ[2 Marks]
The probability of having only three children with two girls and one boy is
GATE→2024→General Aptitude→Quantitative Aptitude
Q8
MCQ[2 Marks]
Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table. - Person 1: A = ₹10,000, B = ₹20,000, C = ₹20,000 - Person 2: A = ₹20,000, B = ₹15,000, C = ₹15,000 At the end of one year, the total amount that Person 1 gets is ₹500 more than Person 2. The annual rate of return for the mutual funds B and C is 15% each. What is the annual rate of return for the mutual fund A?
GATE→2024→General Aptitude→Quantitative Aptitude
Q9
MCQ[2 Marks]
Three different views of a dice are shown in the figure below. The piece of paper that can be folded to make this dice is
Figure for Question 9
GATE→2024→General Aptitude→Quantitative Aptitude
Q10
MCQ[2 Marks]
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?

Mathematics Foundation

9 Questions
GATE→2024→Mathematics Foundation→Probability and Statistics
Q11
MCQ[1 Mark]
Ten cards in a pack are numbered as 1, 2, 3, ..., 10. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is
GATE→2024→Mathematics Foundation→Linear Algebra
Q12
MSQ[1 Mark]
The eigenvalues of the matrix A=[4334]A = \begin{bmatrix} 4 & 3 \\ 3 & 4 \end{bmatrix} are
GATE→2024→Mathematics Foundation→Linear Algebra
Q13
MSQ[1 Mark]
If XX is a vector, and AA and BB are linear operators; then the correct mathematical relationship(s) is/are
GATE→2024→Mathematics Foundation→Calculus
Q14
NAT[1 Mark]
f(x)=x3−4.5x2−12xf(x) = x^3 - 4.5x^2 - 12x has a local maximum at x=x = _____ (an integer value) in the range x=−2x = -2 to +2+2.
GATE→2024→Mathematics Foundation→Calculus
Q15
NAT[1 Mark]
Consider the equation dydx−x2+ex=0\frac{dy}{dx} - x^2 + e^x = 0; with y=1y = 1 at x=0x = 0. The value of yy at x=1x = 1 is _____ (rounded off to 2 decimal places). (Take e=2.7e = 2.7)
GATE→2024→Mathematics Foundation→Probability and Statistics
Q16
MCQ[2 Marks]
A population follows normal distribution. Ten samples (N=10N=10) are drawn at random with a mean value of x‾\overline{x} and standard deviation of SS. Following table provides confidence limits C(t)C(t) for Student's tt-distribution two-tailed test with degrees of freedom DD. Which one of the following expression is correct for testing the null hypothesis H0:μ=0H_0: \mu = 0 at 10%10\% significance level?
GATE→2024→Mathematics Foundation→Calculus
Q17
MCQ[2 Marks]
Which one is the solution y(x)y(x) for the following ordinary differential equation and the specified boundary conditions? d2ydx2−3dydx+2y=2e−x\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + 2y = 2e^{-x}; y(0)=2y(0) = 2; (dydx)x=0=1\left(\frac{dy}{dx}\right)_{x=0} = 1
GATE→2024→Mathematics Foundation→Calculus
Q18
MSQ[2 Marks]
Consider the function f(x)=ln⁡(sin⁡(x))f(x) = \ln(\sin(x)). Expand f(x+h)f(x+h) using Taylor's series. In this context, the correct statement(s) is/are
GATE→2024→Mathematics Foundation→Calculus
Q19
NAT[2 Marks]
Consider the equation for a curve, y=f(x)=x2+xy = f(x) = x^2 + x. The area enclosed by the curve, the xx-axis (y=0y=0 line); the vertical lines passing through x=1x = 1 and x=2x = 2 is _____ (rounded off to 2 decimal places).

Environmental Chemistry

5 Questions
GATE→2024→Environmental Chemistry→Principles of Water Chemistry
Q20
MCQ[1 Mark]
Hardness in water is NOT caused by
GATE→2024→Environmental Chemistry→Fundamentals of Environmental Chemistry
Q21
MCQ[1 Mark]
The maximum coordination number of Sn4+Sn^{4+} is
GATE→2024→Environmental Chemistry→Principles of Water Chemistry
Q22
MCQ[2 Marks]
A saturated stock solution is existing at 25∘C25^\circ\text{C}. In one experiment (i) 25 g Na2CO325\text{ g } Na_2CO_3 is added to the stock solution. In another experiment (ii) 25 g Na2SO425\text{ g } Na_2SO_4 is added to the stock solution. Select the correct statement from the following.
GATE→2024→Environmental Chemistry→Principles of Water Chemistry
Q23
NAT[2 Marks]
The pH of a solution containing 0.1 M0.1\text{ M} of acetic acid and 0.05 M0.05\text{ M} of sodium acetate is _____ (rounded off to 2 decimal places). The pKapK_a value of ionization of acetic acid is 4.764.76.
GATE→2024→Environmental Chemistry→Principles of Water Chemistry
Q24
NAT[2 Marks]
The ionic strength of a solution containing 0.01 M0.01\text{ M} of CaCl2CaCl_2 and 0.001 M0.001\text{ M} of Na2SO4Na_2SO_4 is _____ M (rounded off to 3 decimal places).

Environmental Microbiology

6 Questions
GATE→2024→Environmental Microbiology→Prokaryotic and Eukaryotic Microorganisms
Q25
MCQ[1 Mark]
Rod shaped bacterial cells are called
GATE→2024→Environmental Microbiology→Microbiology and Health
Q26
MCQ[1 Mark]
Tuberculosis is predominantly caused by
GATE→2024→Environmental Microbiology→Prokaryotic and Eukaryotic Microorganisms
Q27
MCQ[1 Mark]
Which one of the following is associated with biological nitrogen fixation?
GATE→2024→Environmental Microbiology→Microbial Metabolism
Q28
MSQ[2 Marks]
Enzymes with the class of enzymes are listed in the table. - (a) Lactate dehydrogenase - (b) Alanine racemase - (c) Lipase - (d) Hexokinase Classes: (i) Isomerases, (ii) Transferases, (iii) Oxidoreductases, (iv) Hydrolases Select the correct match(es)
GATE→2024→Environmental Microbiology→Growth and Control of Microorganisms
Q29
MSQ[2 Marks]
With reference to disinfection, which of the following statement(s) is/are CORRECT?
GATE→2024→Environmental Microbiology→Cell Chemistry and Cell Biology
Q30
MSQ[2 Marks]
Which of the following statement(s) is/are CORRECT?

Water Resources and Environmental Hydraulics

7 Questions
GATE→2024→Water Resources and Environmental Hydraulics→Environmental Hydraulics
Q31
MSQ[1 Mark]
In the context of fluid flow, which of the following statement(s) is/are correct?
GATE→2024→Water Resources and Environmental Hydraulics→Environmental Hydraulics
Q32
MSQ[1 Mark]
In a rectangular open channel, the flow is critical, and the flow depth is 2 m2\text{ m}. Select the correct statement(s)
GATE→2024→Water Resources and Environmental Hydraulics→Surface Water Resources
Q33
NAT[1 Mark]
A Class-A pan was setup adjacent to a lake for measuring evaporation losses in the lake. The depth of water in the pan at the beginning of a certain week was 250 mm250\text{ mm}. In that week, there was a rainfall event with 10 mm10\text{ mm} depth. Water depth in the pan at the end of the week was 240 mm240\text{ mm}. The pan coefficient is 0.80.8. The estimated lake evaporation during the week was _____ mm (an integer value).
GATE→2024→Water Resources and Environmental Hydraulics→Groundwater Resources
Q34
MCQ[2 Marks]
Consider two horizontal layers of an aquifer as shown in figure. Each layer is isotropic and homogeneous. Flow is parallel to the stratification. Thickness and horizontal hydraulic conductivity of layer-1 are h1h_1 and K1K_1, respectively. Thickness and horizontal hydraulic conductivity of layer-2 are h2h_2 and K2K_2, respectively. The equivalent horizontal conductivity KxK_x for the aquifer system is given by
Figure for Question 34
GATE→2024→Water Resources and Environmental Hydraulics→Environmental Hydraulics
Q35
MSQ[2 Marks]
Water is flowing FULL through a rectangular tunnel of size 3 m (width)×2 m (height)3\text{ m (width)} \times 2\text{ m (height)}. The average velocity of flow is 1 m/s1\text{ m/s}. The frictional head loss is observed to be 1 m per km1\text{ m per km}. Consider acceleration due to gravity (gg) as 10 m/s210\text{ m/s}^2. The correct statement(s) is/are
GATE→2024→Water Resources and Environmental Hydraulics→Surface Water Resources
Q36
NAT[2 Marks]
Consider a watershed and isohyets as shown in the figure. The average rainfall in the watershed is _____ mm (an integer value).
Figure for Question 36
GATE→2024→Water Resources and Environmental Hydraulics→Environmental Hydraulics
Q37
NAT[2 Marks]
With reference to the gate shown in the figure, the gate will start opening automatically when the water level 'hh' above the hinge is _____ m (rounded off to 2 decimal places).
Figure for Question 37

Water & Wastewater Treatment and Management

7 Questions
GATE→2024→Water & Wastewater Treatment and Management→Sewage Treatment, Sludge & Wastewater Management
Q38
MCQ[1 Mark]
Crown corrosion of reinforced cement concrete sewer is caused by
GATE→2024→Water & Wastewater Treatment and Management→Water Treatment Methods & Distribution
Q39
MCQ[1 Mark]
The processes of removal of particles in a rapid sand filter with their description is given in the table. - (i) Straining -> P: Removes only particles large enough to get caught in pores - (ii) Sedimentation -> Q: Larger/heavier particles settle on sand grain - (iii) Interception -> R: Particles following streamline but too large caught by brushing against sand - (iv) Diffusion -> S: Very small particles experiencing Brownian motion Select the correct match.
GATE→2024→Water & Wastewater Treatment and Management→Water Treatment Methods & Distribution
Q40
MSQ[1 Mark]
With respect to particle settling in wastewater treatment systems; the correct statement(s) is/are
GATE→2024→Water & Wastewater Treatment and Management→Kinetics and Reactor Design
Q41
MCQ[2 Marks]
Consider second order kinetics (rc=−kC2r_c = -kC^2) under steady state condition. The ratio of volume of a complete mixed reactor (CMR) to that of a plug flow reactor (PFR) to achieve 90%90\% reduction in the concentration is (Inlet concentrations in both the reactors are same).
GATE→2024→Water & Wastewater Treatment and Management→Water and Wastewater Quality Parameters & River Pollution
Q42
MSQ[2 Marks]
The Streeter-Phelp's oxygen sag equation for a river is based on a few assumptions. The correct assumption(s) is/are
GATE→2024→Water & Wastewater Treatment and Management→Sewage Treatment, Sludge & Wastewater Management
Q43
NAT[2 Marks]
One million liters per day (MLD) of wastewater with a soluble BOD of 200 mg/L200\text{ mg/L} is treated in an activated sludge process. The BOD of treated wastewater is 20 mg/L20\text{ mg/L}. The observed yield coefficient of the biological system is 0.350.35. The daily biomass generation in the system is _____ kg (an integer value).
GATE→2024→Water & Wastewater Treatment and Management→Water and Wastewater Quality Parameters & River Pollution
Q44
NAT[2 Marks]
An industry discharges 2 MLD2\text{ MLD} of wastewater with a temperature of 45∘C45^\circ\text{C} and a pH of 22, whereas the neighboring industry produces 3 MLD3\text{ MLD} of wastewater with a temperature of 30∘C30^\circ\text{C} and pH of 88. If both the wastewaters are mixed and carried, the resulting pH is _____ (rounded off to 2 decimal places). (Neglect buffering capacity and temperature effect on pH)

Air and Noise Pollution

8 Questions
GATE→2024→Air and Noise Pollution→Air Quality Management and Dispersion Modelling
Q45
MCQ[1 Mark]
The environmental temperature increases by 6∘C/km6^\circ\text{C/km} with height at a particular location. The stability condition of the atmosphere at the location is
GATE→2024→Air and Noise Pollution→Particulate Pollutants: Measurement and Control
Q46
MSQ[1 Mark]
The equipment that can be used to control particulate air pollution in an industrial unit is/are
GATE→2024→Air and Noise Pollution→Atmospheric Processes and Air Quality Parameters
Q47
MSQ[1 Mark]
Which is/are the secondary air pollutant(s)?
GATE→2024→Air and Noise Pollution→Particulate Pollutants: Measurement and Control
Q48
MCQ[2 Marks]
A gravity settling chamber of height 'HH' and length 'LL' is designed to control particulate air pollution. In the chamber, the horizontal velocity of air flow is 'VhV_h' and terminal settling velocity of the target particle is 'VtV_t'. Which one of the following expressions is the correct concept used to calculate the minimum size of the target particle that will be removed with 100%100\% efficiency?
GATE→2024→Air and Noise Pollution→Atmospheric Processes and Air Quality Parameters
Q49
NAT[2 Marks]
The concentration of Ozone (O3O_3) corresponding to a mixing ratio of 120 ppbv120\text{ ppbv} at pressure of 1 atm1\text{ atm} and temperature of 25∘C25^\circ\text{C} is _____ μg/m3\mu\text{g/m}^3 (rounded off to 1 decimal place). (Atomic weight of oxygen = 1616, R=8.314 J/K-molR = 8.314\text{ J/K-mol})
GATE→2024→Air and Noise Pollution→Particulate Pollutants: Measurement and Control
Q50
NAT[2 Marks]
In a cyclone separator of radius 25 cm25\text{ cm}, a particle is travelling with a gas stream at velocity of 18 m/s18\text{ m/s}. The ratio of centrifugal force to the gravitational force acting on the particle is _____ (rounded off to 2 decimal places). (Consider g=9.8 m/s2g = 9.8\text{ m/s}^2)
GATE→2024→Air and Noise Pollution→Noise Pollution
Q51
NAT[2 Marks]
Two sources of noise, adjacent to each other in a room, have sound pressure levels of 3030 and 40 decibel (dB)40\text{ decibel (dB)}. The combined sound pressure level in the room is _____ dB (rounded off to 2 decimal places).
GATE→2024→Air and Noise Pollution→Air Quality Management and Dispersion Modelling
Q52
NAT[2 Marks]
An industrial stack emits 100 g/s100\text{ g/s} of COCO at an effective height of HH, where the wind speed is 5 m/s5\text{ m/s}. At 3 km3\text{ km} distance downwind, the values of dispersion coefficient in yy-direction and zz-direction are 50 m50\text{ m} and 25 m25\text{ m}, respectively. The COCO concentration at the centerline of the plume at 3 km3\text{ km} distance downwind is _____ mg/m3\text{mg/m}^3 (rounded off to 2 decimal places). (Use Gaussian plume model and π=3.14\pi = 3.14, ground-level centerline formula)

Solid and Hazardous Waste Management

7 Questions
GATE→2024→Solid and Hazardous Waste Management→Biomedical, Plastic, C&D, E-Waste & Energy Sector Waste
Q53
MCQ[1 Mark]
As per the United Nations Environmental Program (UNEP) guidelines 2004, the maximum size of microplastics is
GATE→2024→Solid and Hazardous Waste Management→Integrated Solid Waste Management & Municipal Waste
Q54
MCQ[1 Mark]
The costliest functional element in an urban centralized Municipal Solid Waste management infrastructure for a typical Indian Tier I city is
GATE→2024→Solid and Hazardous Waste Management→Hazardous Waste Management and Soil Contamination
Q55
MSQ[1 Mark]
As per the Hazardous Waste (Management and Handling) Rules, which is/are the characteristic(s) that must be exhibited by a waste to be classified as a "characteristic" hazardous waste?
GATE→2024→Solid and Hazardous Waste Management→Integrated Solid Waste Management & Municipal Waste
Q56
NAT[1 Mark]
A municipal solid waste digester generates 1000 kg1000\text{ kg} of methane gas. The volume of the tank needed to store this gas at 30∘C30^\circ\text{C} and 3 atm3\text{ atm} pressure is _____ liters (an integer value). (R=0.082 L-atm/mol-KR = 0.082\text{ L-atm/mol-K}, C=12C=12, H=1H=1)
GATE→2024→Solid and Hazardous Waste Management→Integrated Solid Waste Management & Municipal Waste
Q57
NAT[2 Marks]
Two hypothetical organic waste streams A and B are mixed prior to composting process. Waste-A has 2.16%2.16\% of C and 1.20%1.20\% of N. Waste-B has 19.10%19.10\% of C and 0.14%0.14\% of N. The quantity of Waste-B that should be mixed with per kg of Waste-A to achieve the desired C:N ratio of 25 is _____ kg (rounded off to 2 decimal places).
GATE→2024→Solid and Hazardous Waste Management→Integrated Solid Waste Management & Municipal Waste
Q58
NAT[2 Marks]
Food waste, paper waste and plastic waste have typical densities of 280 kg/m3280\text{ kg/m}^3, 80 kg/m380\text{ kg/m}^3, and 50 kg/m350\text{ kg/m}^3, respectively. The mixed waste is composed of 70%70\% food waste, 20%20\% paper waste and 10%10\% plastic waste. The density of the mixed waste is _____ kg/m3\text{kg/m}^3 (rounded off to 2 decimal places).
GATE→2024→Solid and Hazardous Waste Management→Integrated Solid Waste Management & Municipal Waste
Q59
NAT[2 Marks]
For a biodegradable waste with a chemical formula C50H100O40NC_{50}H_{100}O_{40}N, the maximum theoretical methane production per ton of waste is _____ kg (rounded off to 2 decimal places). (Assume 100%100\% anaerobic conversion; Atomic weights: C=12,H=1,O=16,N=14C=12, H=1, O=16, N=14)

Global and Regional Environmental Issues

1 Question
GATE→2024→Global and Regional Environmental Issues→Global Effects of Air Pollution & Climate Change
Q60
MCQ[1 Mark]
Which one of the following is NOT a greenhouse gas?

Environmental Management and Sustainable Development

5 Questions
GATE→2024→Environmental Management and Sustainable Development→Sustainable Development and Economics
Q61
MCQ[1 Mark]
As per the United Nations agenda for sustainable development adopted in September 2015, the number of Sustainable Development Goals (SDGs) are _____ and the proposed target year to achieve them is _____
GATE→2024→Environmental Management and Sustainable Development→Environmental Management Systems & Impact Assessment
Q62
MSQ[2 Marks]
Based on the ISO 14040 methodology for Life Cycle Assessment, match the terms with the descriptions in the table: - (a) Goal and Scope -> (ii) The problem is described, and the objective of the study are defined - (b) Functional Unit -> (i) Based on the product or system, the comparative unit must be carefully defined and be same for all scenarios - (c) Life Cycle Inventory -> (iv) Process based approach and input-output approach - (d) Impact Assessment -> (iii) Evaluates the environmental implications due to the inventorized emissions The correct match(es) is/are
GATE→2024→Environmental Management and Sustainable Development→Environmental Management Systems & Impact Assessment
Q63
NAT[2 Marks]
A person consumes 2.5 liters2.5\text{ liters} of water per day. The water quality test indicated that the supplied water has a Pb concentration of 0.6 mg/L0.6\text{ mg/L}. If the weight of the person is 75 kg75\text{ kg}, the exposure level for Pb for this person from this drinking water source is _____ mg/kg/day (rounded off to 2 decimal places).
GATE→2024→Environmental Management and Sustainable Development→Energy and Environment
Q64
NAT[2 Marks]
In a region, total annual consumption of gasoline is 30.6 million tons30.6\text{ million tons}. The land required for growing sugarcane to produce enough bioethanol to replace the gasoline completely is _____ km2\text{km}^2 (an integer value). (Ethanol energy equivalent is 67%67\% of gasoline, gasoline density is 850 kg/m3850\text{ kg/m}^3, yield of bioethanol from sugarcane is 3750 L/hectare3750\text{ L/hectare}, 1 km2=100 hectares1\text{ km}^2 = 100\text{ hectares})
GATE→2024→Environmental Management and Sustainable Development→Environmental Management Systems & Impact Assessment
Q65
NAT[2 Marks]
Initially a bottle contained 400 g400\text{ g} of ethanol. Half of ethanol was used by a student for preparing the stock solution in an environmental chemistry laboratory just before summer vacation of 90 days90\text{ days}. After completing the procedure, the student left the bottle uncorked. If the unsealed bottle loses ethanol at a rate of 0.5 g/day0.5\text{ g/day}, the ethanol that will be left in the bottle at the end of the summer vacation is _____ g (an integer value).