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201

GATE Civil 2023 Set 1 | Question: 10
Which one of the following statements is TRUE for Greenhouse Gas $(\mathrm{GHG})$ in the atmosphere? $\mathrm{GHG}$ absorbs the incoming short wavelength solar radiation to the earth surface, and allows the long wavelength radiation ... solar radiation to pass through to the earth surface, and absorbs the long wavelength radiation coming from the earth surface

Which one of the following statements is TRUE for Greenhouse Gas $(\mathrm{GHG})$ in the atmosphere?$\mathrm{GHG}$ absorbs the incoming short wavelength solar radiation t...

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202

GATE Civil 2022 Set 2 | Question: 39
A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals $4$ in exactly two of the three attempts is _______. (round off to three decimal places)

A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals $4$ in exactly two of the three attempts is _______. (round of...

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203

GATE Civil 2022 Set 2 | Question: 40
Consider two linear elastic rods $HI$ and $IJ$, each of length $b$, as shown in the figure. The rods are co-linear, and confined between two fixed supports at $H$ and $J.$ Both the rods are initially stress free. The coefficient of linear thermal ... to zero, the value of the external force $P$ (in $\text{N}$) is ____________ . (round off to the nearest integer)

Consider two linear elastic rods $HI$ and $IJ$, each of length $b$, as shown in the figure. The rods are co-linear, and confined between two fixed supports at $H$ and $J....

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204

GATE Civil 2022 Set 1 | Question: 44
A square concrete pile of $10\: m$ length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is $100$ $\text{kPa}$. ... $N_{c} = 9$; adhesion factor $\alpha = 0.7$)

A square concrete pile of $10\: m$ length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through...

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205

GATE Civil 2024 Set 2 | Question: 53
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, $+3.0 \%$ and $-5.0 \%$. Assume the following: Only large-sized trucks are allowed on this corridor Design speed $=80 \mathrm{kmph}$ Eye height of truck drivers ... ) to accommodate the stopping sight distance is $\_\_\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A vertical summit curve on a freight corridor is formed at the intersection of two gradients, $+3.0 \%$ and $-5.0 \%$.Assume the following:Only large-sized trucks are all...

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206

GATE Civil 2022 Set 2 | Question: 41
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the help of the vertical linear spring constant $k= 20 \; \text{kN/m}.$ The fixed ... $Q$ (in $\text{kN}$) is __________.(round off to the nearest integer)

The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the hel...

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207

GATE Civil 2022 Set 1 | Question: 48
Depth of water flowing in a $3\:m$ wide rectangular channel is $2\:m$. The channel carries a discharge of $12\:m^{3}/s$. Take $g = 9.8\; m/s^{2}$. The bed width (in $m$) at contraction, which just causes the critical flow, is _____________ without changing the upstream water level. (round off to two decimal places)

Depth of water flowing in a $3\:m$ wide rectangular channel is $2\:m$. The channel carries a discharge of $12\:m^{3}/s$. Take $g = 9.8\; m/s^{2}$.The bed width (in $m$) a...

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208

GATE Civil 2023 Set 1 | Question: 20
In the differential equation $\frac{d y}{d x}+\alpha x y=0, \alpha$ is a positive constant. If $y=1.0$ at $x=0.0$, and $y=0.8$ at $x=1.0$, the value of $\alpha$ is____________ (rounded off to three decimal places).

In the differential equation $\frac{d y}{d x}+\alpha x y=0, \alpha$ is a positive constant. If $y=1.0$ at $x=0.0$, and $y=0.8$ at $x=1.0$, the value of $\alpha$ is_______...

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209

GATE Civil 2023 Set 1 | Question: 34
A jet of water having a velocity of $20 \mathrm{~m} / \mathrm{s}$ strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at $15 \mathrm{~m} / \mathrm{s}.$ What is the percentage efficiency of the plates? (round off to one decimal place) $37.5 $ $66.7$ $50.0$ $88.9$

A jet of water having a velocity of $20 \mathrm{~m} / \mathrm{s}$ strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at $15 \...

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210

GATE Civil 2022 Set 2 | Question: 50
A sewage treatment plant receives sewage at a flow rate of $5000 \; \text{m}^{3}\text{/day}.$ The total suspended solids $\text{(TSS)}$ concentration in the sewage at the inlet of primary clarifier is $200 \; \text{mg/L}$. After the ... daily volume of the thickened sludge (in $\text{m}^{3}\text{/day}$) will be ___________.(round off to the nearest integer)

A sewage treatment plant receives sewage at a flow rate of $5000 \; \text{m}^{3}\text{/day}.$ The total suspended solids $\text{(TSS)}$ concentration in the sewage at the...

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211

GATE Civil 2022 Set 1 | Question: 51
A water treatment plant has a sedimentation basin of depth $3\:m$, width $5\:m$, and length $40\:m$. The water inflow rate is $500\:m^{3}/h$. The removal fraction of particles having a settling velocity of $1.0\; m/h$ is __________ (round off to one decimal place) (Consider the particle density as $2650\; kg/m^{3}$ and liquid density as $991\; kg/m^{3})$

A water treatment plant has a sedimentation basin of depth $3\:m$, width $5\:m$, and length $40\:m$. The water inflow rate is $500\:m^{3}/h$. The removal fraction of part...

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212

GATE Civil 2024 Set 2 | Question: 3
The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$. The CORRECT expression for the second derivative is $\frac{1}{12 h^{2}}\left[-f_{i+2}+16 f_{i+1}-30 f_{i}+16 f_{i-1}-f_{i-2}\right]$ ... $\frac{1}{12 h^{2}}\left[-f_{i+2}-16 f_{i+1}+30 f_{i}-16 f_{i-1}-f_{i-2}\right]$

The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$.The CORRECT expression ...

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213

GATE Civil 2022 Set 2 | Question: 33
In a city, the chemical formula of biodegradable fraction of municipal solid waste $\text{(MSW)}$ is $\text{C}_{100} \text{H}_{250} \text{O}_{80} \text{N}.$ The waste has to be treated by forced-aeration composting process for which air requirement has to ... (in $\text{m}^{3}/\text{tonne}$) will be (round off to the nearest integer) $4749$ $8025$ $1418$ $1092$

In a city, the chemical formula of biodegradable fraction of municipal solid waste $\text{(MSW)}$ is $\text{C}_{100} \text{H}_{250} \text{O}_{80} \text{N}.$ The waste has...

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214

GATE Civil 2022 Set 2 | Question: 52
A parabolic vertical crest curve connects two road segments with grades $+1.0 \%$ and $-2.0 \%.$ If a $200 \; \text{m}$ stopping sight distance is needed for a driver at a height of $1.2 \; \text{m}$ to avoid an obstacle of height $0.15 \; \text{m},$ then the minimum curve length should be _________ $\text{m}$. (round off to the nearest integer)

A parabolic vertical crest curve connects two road segments with grades $+1.0 \%$ and $-2.0 \%.$ If a $200 \; \text{m}$ stopping sight distance is needed for a driver at ...

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215

GATE Civil 2022 Set 1 | Question: 14
A line between stations $P$ and $Q$ laid on a slope of $1$ in $5$ was measured as $350\; m$ using a $50\; m$ tape. The tape is known to be shortly by $0.1\; m$. The corrected horizontal length (in $m$) of the line $\text{PQ}$ will be $342.52$ $349.30$ $356.20$ $350.70$

A line between stations $P$ and $Q$ laid on a slope of $1$ in $5$ was measured as $350\; m$ using a $50\; m$ tape. The tape is known to be shortly by $0.1\; m$.The correc...

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216

GATE Civil 2022 Set 1 | Question: 33
In a water sample, the concentrations of $Ca^{2+}, Mg^{2+}$ and $\text{HCO}_{3}^{-}$ are $100$ $\text{mg/L}$, $36$ $\text{mg/L}$ and $122$ $\text{mg/L}$ ... $400$ and $100$, respectively. $400$ and $300$, respectively. $500$ and $100$, respectively. $800$ and $200$, respectively.

In a water sample, the concentrations of $Ca^{2+}, Mg^{2+}$ and $\text{HCO}_{3}^{-}$ are $100$ $\text{mg/L}$, $36$ $\text{mg/L}$ and $122$ $\text{mg/L}$, respectively. Th...

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217

GATE Civil 2024 Set 1 | Question: 38
A $2 \mathrm{~m} \times 2 \mathrm{~m}$ tank of $3 \mathrm{~m}$ height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At $t=0$ ... grams) in the tank at $75 \%$ of its capacity is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A $2 \mathrm{~m} \times 2 \mathrm{~m}$ tank of $3 \mathrm{~m}$ height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. A...

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218

GATE Civil 2022 Set 1 | Question: 9
With respect to fluid flow, match the following in Column $X$ with Column $Y$ ... $\text{(P) - (II), (Q) - (IV), (R) - (III), (S) - (I)}$

With respect to fluid flow, match the following in Column $X$ with Column $Y$:$$\begin{array}{|l|l|} \hline \qquad \textbf{Column X} & \qquad \textbf{Column Y} \\ \hline...

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219

GATE Civil 2022 Set 1 | Question: 18
A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature? Decrease the design speed Increase the superelevation Increase the design speed Restrict vehicles with higher weight from using the facility

A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature?Decrease the design...

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220

GATE Civil 2022 Set 1 | Question: 25
The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)

The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)

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221

GATE Civil 2022 Set 1 | Question: 50
A $2\%$ sewage sample (in distilled water) was incubated for $3$ days at $27^{\circ}C$ temperature. After incubation, a dissolved oxygen depletion of $10\:mg/L$ was recorded. The biochemical oxygen demand $\text{(BOD)}$ ... $\text{BOD}$ (in $mg/L$) of the sewage will be __________________ (round off to the nearest integer)

A $2\%$ sewage sample (in distilled water) was incubated for $3$ days at $27^{\circ}C$ temperature. After incubation, a dissolved oxygen depletion of $10\:mg/L$ was recor...

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222

GATE Civil 2022 Set 1 | Question: 54
The vehicle count obtained in every $10$ ... $\text{(PHF)}$ for $10$ minute sub-interval is ________________. (round off to one decimal place)

The vehicle count obtained in every $10$ minute interval of a traffic volume survey done in peak one hour is given below.$$\begin{array}{|c|c|} \hline \text{Time Interval...

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223

GATE Civil 2024 Set 2 | Question: 24
A reinforced concrete pile of $10 \mathrm{~m}$ length and $0.7 \mathrm{~m}$ diameter is embedded in a saturated pure clay with unit cohesion of $50 \mathrm{kPa}$. If the adhesion factor is $0.5$, the net ultimate uplift pullout capacity (in $\mathrm{kN}$ ) of the pile is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

A reinforced concrete pile of $10 \mathrm{~m}$ length and $0.7 \mathrm{~m}$ diameter is embedded in a saturated pure clay with unit cohesion of $50 \mathrm{kPa}$. If the ...

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224

GATE Civil 2024 Set 1 | Question: 4
The three-dimensional state of stress at a point is given by \[ \sigma=\left(\begin{array}{ccc} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{array}\right) \mathrm{MPa} . \] The maximum shear stress at the point is $20 \mathrm{MPa}$ $15 \mathrm{MPa}$ $5 \mathrm{MPa}$ $25 \mathrm{MPa}$

The three-dimensional state of stress at a point is given by\[\sigma=\left(\begin{array}{ccc}10 & 0 & 0 \\0 & 40 & 0 \\0 & 0 & 0\end{array}\right) \mathrm{MPa} .\]The max...

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225

GATE Civil 2023 Set 1 | Question: 46
A soil having the average properties, bulk unit weight $=19 \mathrm{~kN} / \mathrm{m}^3$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{~kPa}$ ... to one decimal place). [Assume the soil is being formed parallel to the rock bedding plane and there is no ground water effect.]

A soil having the average properties, bulk unit weight $=19 \mathrm{~kN} / \mathrm{m}^3$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{~kPa}$, is be...

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226

GATE Civil 2022 Set 1 | Question: 17
Which of the following process(es) can be used for conversion of salt water into fresh water? Microfiltration Electrodialysis Ultrafiltration Reverse osmosis

Which of the following process(es) can be used for conversion of salt water into fresh water?MicrofiltrationElectrodialysisUltrafiltrationReverse osmosis

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227

GATE Civil 2024 Set 1 | Question: 30
A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the figure. The polar moments of inertia of the portions $\text{PQ}$ and $\text{QR}$ of the shaft with circular ... the ratio of the lengths $\mathrm{L}_{1} / \mathrm{L}_{2}$ is $0.50$ $0.25$ $4.00$ $2.00$

A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the fi...

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228

GATE Civil 2023 Set 1 | Question: 29
Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, $A E$. Members $\mathrm{QR}, \mathrm{RS}$, and $\mathrm{ST}$ have the same length $L$. Angles QBT, RCT, SDT are all $90^{\circ}$ ... $k \frac{P L}{A E}$. What is the value of $k$ ? $1.5$ $4.5$ $3.0$ $9.0$

Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, $A E$. Members $\mathrm{QR}, \mathrm{RS}$, and $\mathrm{ST}$ ...

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229

GATE Civil 2022 Set 1 | Question: 47
Two reservoirs are connected by two parallel pipes of equal length and of diameters $20\:cm$ and $10\:cm$, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is $5\:m$, the ratio ... ) (Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)

Two reservoirs are connected by two parallel pipes of equal length and of diameters $20\:cm$ and $10\:cm$, as shown in the figure (not drawn to scale). When the differenc...

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230

GATE Civil 2024 Set 2 | Question: 25
A $2 \mathrm{~m}$ wide rectangular channel is carrying a discharge of $30 \mathrm{~m}^{3} / \mathrm{s}$ at a bed slope of $1$ in $300$. Assuming the energy correction factor as $1.1$ and acceleration due to gravity as $10 \mathrm{~m} / \mathrm{s}^{2}$, the critical depth of flow (in meters) is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A $2 \mathrm{~m}$ wide rectangular channel is carrying a discharge of $30 \mathrm{~m}^{3} / \mathrm{s}$ at a bed slope of $1$ in $300$. Assuming the energy correction fac...

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231

GATE Civil 2024 Set 2 | Question: 31
A round-bottom triangular lined canal is to be laid at a slope of $1$ in $1500$, to carry a discharge of $25 \mathrm{~m}^{3} / \mathrm{s}$. The side slopes of the canal cross-section are to be kept at $1.25 \mathrm{H}: 1 \mathrm{~V}$. If Manning's roughness ... be in the range of $2.39$ to $2.42$ $1.94$ to $1.97$ $2.24$ to $2.27$ $2.61$ to $2.64$

A round-bottom triangular lined canal is to be laid at a slope of $1$ in $1500$, to carry a discharge of $25 \mathrm{~m}^{3} / \mathrm{s}$. The side slopes of the canal c...

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232

GATE Civil 2023 Set 1 | Question: 19
The probabilities of occurrences of two independent events $\text {A}$ and $\text {B}$ are $0.5$ and $0.8,$ respectively. What is the probability of occurrence of at least $\text {A}$ or $\text {B}$ (rounded off to one decimal place)? _____________

The probabilities of occurrences of two independent events $\text {A}$ and $\text {B}$ are $0.5$ and $0.8,$ respectively. What is the probability of occurrence of at leas...

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233

GATE Civil 2023 Set 1 | Question: 51
In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is $10 \mathrm{~mm} / \mathrm{h}$; final infiltration capacity is $5 \mathrm{~mm} / \mathrm{h}$ ... $\mathrm{mm}$ ) from a uniform storm of duration $12 \mathrm{~h}$ is___________. (round off to one decimal place)

In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is $10 \mathrm{~mm} / \mathrm{h}$; final infiltration capacity is $5 \m...

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234

GATE Civil 2022 Set 2 | Question: 31
A soil sample is underlying a water column of height $h_{1},$ as shown in the figure. The vertical effective stresses at points $\text{A, B,}$ and $\text{C}$ are $\sigma'_{A}, \sigma'_{B},$ and $\sigma'_{C},$ respectively. Let $\gamma_{\text{sat}}$ ... $(h_{1} + h_{2} + h_{3})\gamma_{\text{sat}}$

A soil sample is underlying a water column of height $h_{1},$ as shown in the figure. The vertical effective stresses at points $\text{A, B,}$ and $\text{C}$ are $\sigma�...

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235

GATE Civil 2022 Set 1 | Question: 35
Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 - x,x -1\}$? It is continuous on its domain. It has a local minimum at $x = 2$. It has a local maximum at $x = 2$. It is differentiable on its domain.

Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 -...

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236

GATE Civil 2024 Set 2 | Question: 20
For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of $1: 13000$ using a camera. If the permissible flying height is assumed as $3000 \mathrm{~m}$ above a datum and the average terrain ... above the datum, the required focal length (in $\mathrm{mm}$ ) of the camera is $100$ $150$ $125$ $200$

For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of $1: 13000$ using a camera. If the...

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237

GATE Civil 2024 Set 2 | Question: 15
What is the CORRECT match between the air pollutants and treatment techniques given in the table? \begin{array}{|l|l|} \hline \text{Air pollutants} & \text{Treatment techniques} \\ \hline \mathrm{P}-\mathrm{NO}_{2} & \text{i - Flaring} \\ \mathrm{Q}-\mathrm{SO}_{2} & ... $\text{P-ii, Q-iii, R-iv, S-i}$ $\text{P-iv, Q-iii, R-i, S-ii}$

What is the CORRECT match between the air pollutants and treatment techniques given in the table?\begin{array}{|l|l|}\hline \text{Air pollutants} & \text{Treatment techni...

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238

GATE Civil 2024 Set 1 | Question: 7
The following figure shows the arrangement of formwork for casting a cantilever $\mathrm{RC}$ ...

The following figure shows the arrangement of formwork for casting a cantilever $\mathrm{RC}$ beam.The correct sequence of removing the Shores/Props is$\mathrm{S} 1 \righ...

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239

GATE Civil 2024 Set 1 | Question: 53
The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle. The mean speed (in $\mathrm{km} / \mathrm{hr}$ ) of the vehicles in the entire time-space domain is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle.The mean s...

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240

GATE Civil 2023 Set 2 | Question: 47
An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member $\mathrm{PQ}$ to the vertical member $\mathrm{RS}$ at $\mathrm{P}$ is ____________ (round off to one decimal place).

An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member $\mathrm{PQ}$ to the vertical memb...

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