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241

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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242

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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243

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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244

GATE Civil 2024 Set 1 | Question: 22
Consider the data of $f(x)$ given in the table. \begin{array}{|c|c|c|c|} \hline i & 0 & 1 & 2 \\ \hline x_{i} & 1 & 2 & 3 \\ \hline f\left(x_{i}\right) & 0 & 0.3010 & 0.4771 \\ \hline ... value of $f(1.5)$ estimated using second-order Newton's interpolation formula is $\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

Consider the data of $f(x)$ given in the table.\begin{array}{|c|c|c|c|}\hline i & 0 & 1 & 2 \\\hline x_{i} & 1 & 2 & 3 \\\hline f\left(x_{i}\right) & 0 & 0.3010 & 0.4771 ...

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245

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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246

GATE Civil 2022 Set 1 | Question: 46
A two-hour duration storm event with uniform excess rainfall of $3\:cm$ ... the peak flow ordinate (in $m^{3}/s$) of one-hour unit hydrograph for the watershed is _________________. (in integer)

A two-hour duration storm event with uniform excess rainfall of $3\:cm$ occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are give...

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247

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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248

GATE Civil 2024 Set 1 | Question: 21
The primary air pollutant(s) is/are Sulfur dioxide Lead Ozone Sulphuric acid

The primary air pollutant(s) is/areSulfur dioxideLeadOzoneSulphuric acid

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249

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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250

GATE Civil 2023 Set 2 | Question: 38
In the context of water and wastewater treatments, the correct statements are: particulate matter may shield microorganisms during disinfection ammonia decreases chlorine demand phosphorous stimulates algal and aquatic growth calcium and magnesium increase hardness and total dissolved solids

In the context of water and wastewater treatments, the correct statements are:particulate matter may shield microorganisms during disinfectionammonia decreases chlorine d...

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251

GATE Civil 2023 Set 2 | Question: 48
A square footing is to be designed to carry a column load of $500~ \mathrm{kN}$ which is resting on a soil stratum having the following average properties: bulk unit weight $=19 ~\mathrm{kN} / \mathrm{m}^3$; angle of internal ... (round off to one decimal place) [Assume the applicable shape and depth factor values as unity; ground water level at greater depth.]

A square footing is to be designed to carry a column load of $500~ \mathrm{kN}$ which is resting on a soil stratum having the following average properties: bulk unit weig...

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252

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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253

GATE Civil 2024 Set 2 | Question: 39
For the $6 \mathrm{~m}$ long horizontal cantilever beam $\mathrm{PQR}$ shown in the figure, $\mathrm{Q}$ is the midpoint. Segment $\mathrm{PQ}$ of the beam has flexural rigidity $\mathrm{EI}=2 \times 10^{5} \mathrm{kN. \textrm {m } ^ { 2 }}$ whereas the ... (in $\mathrm{mm}$ ) at point $\mathrm{Q}$ is $\_\_\_\_\_\_\_$ (rounded off to $3$ decimal places).

For the $6 \mathrm{~m}$ long horizontal cantilever beam $\mathrm{PQR}$ shown in the figure, $\mathrm{Q}$ is the midpoint. Segment $\mathrm{PQ}$ of the beam has flexural r...

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254

GATE Civil 2024 Set 2 | Question: 51
An organic waste is represented as $\mathrm{C}_{240} \mathrm{O}_{200} \mathrm{H}_{180} \mathrm{~N}_{5} \mathrm{~S}$. (Atomic weights: $\mathrm{S}-32, \mathrm{H}-1, \mathrm{C}-12, \mathrm{O}-16, \mathrm{~N}-14$ ... $\mathrm{kg}$ of this waste is $\_\_\_\_\_\_\_$ (rounded off to $1$ decimal place).

An organic waste is represented as $\mathrm{C}_{240} \mathrm{O}_{200} \mathrm{H}_{180} \mathrm{~N}_{5} \mathrm{~S}$.(Atomic weights: $\mathrm{S}-32, \mathrm{H}-1, \mathrm...

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255

GATE Civil 2024 Set 2 | Question: 54
A child walks on a level surface from point $\text{P}$ to point $\text{Q}$ at a bearing of $30^{\circ}$, from point $\mathrm{Q}$ to point $\mathrm{R}$ at a bearing of $90^{\circ}$ ... degrees, the straight-line path length $\text{RP}$ (in meters) is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

A child walks on a level surface from point $\text{P}$ to point $\text{Q}$ at a bearing of $30^{\circ}$, from point $\mathrm{Q}$ to point $\mathrm{R}$ at a bearing of $90...

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256

GATE Civil 2024 Set 1 | Question: 32
A flow velocity field $\vec{V}: \vec{V}(x, y)$ for a fluid is represented by \[ \vec{V}=3 \hat{\imath}+(5 x) \hat{\jmath} \] In the context of the fluid and the flow, which one of the following ... fluid is incompressible and the flow is irrotational. The fluid is compressible and the flow is rotational The fluid is compressible and the flow is irrotational.

A flow velocity field $\vec{V}: \vec{V}(x, y)$ for a fluid is represented by\[\vec{V}=3 \hat{\imath}+(5 x) \hat{\jmath}\]In the context of the fluid and the f...

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257

GATE Civil 2023 Set 1 | Question: 30
With reference to the compaction test conducted on soils, which of the following is $\text { INCORRECT?}$ Peak point of the compaction curve gives the maximum dry unit weight and optimum moisture content With increase in the ... With increase in the compaction effort, the optimum moisture content decreases Compaction curve crosses the zero-air-voids curve

With reference to the compaction test conducted on soils, which of the following is $\text { INCORRECT?}$Peak point of the compaction curve gives the maximum dry unit wei...

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258

GATE Civil 2024 Set 1 | Question: 34
The free mean speed is $60 \mathrm{~km} / \mathrm{hr}$ on a given road. The average space headway at jam density on this road is $8 \mathrm{~m}$. For a linear speed-density relationship, the maximum flow (in veh/hr/lane) expected on the road is $1875$ $938$ $2075$ $1038$

The free mean speed is $60 \mathrm{~km} / \mathrm{hr}$ on a given road. The average space headway at jam density on this road is $8 \mathrm{~m}$. For a linear speed-densi...

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259

GATE Civil 2023 Set 1 | Question: 27
Consider a doubly reinforced RCC beam with the option of using either $\text{Fe250}$ plain bars or $\text{Fe500}$ ... $\text{Fe500}$ deformed bars Neither $\text{Fe250}$ plain bars nor $\text{Fe500}$ deformed bars

Consider a doubly reinforced RCC beam with the option of using either $\text{Fe250}$ plain bars or $\text{Fe500}$ deformed bars in the compression zone. The modulus of el...

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260

GATE Civil 2023 Set 1 | Question: 13
A student is scanning his $10 \text { inch } \times 10 \text { inch}$ certificate at $ 600 \text { dots per inch (dpi)}$ to convert it to raster. What is the percentage reduction in number of pixels if the same certificate is scanned at $300 \text { dpi? }$ $62$ $88$ $75$ $50$

A student is scanning his $10 \text { inch } \times 10 \text { inch}$ certificate at $ 600 \text { dots per inch (dpi)}$ to convert it to raster. What is the percentage r...

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261

GATE Civil 2022 Set 1 | Question: 13
An aerial photograph is taken from a flight at a height of $3.5$ $\text{km}$ above mean sea level, using a camera of focal length $152$ $\text{mm}$. If the average ground elevation is $460 \:m$ above mean sea level, then the scale of the photograph is $1 : 20000$ $1 : 20$ $1 : 100000$ $1 : 2800$

An aerial photograph is taken from a flight at a height of $3.5$ $\text{km}$ above mean sea level, using a camera of focal length $152$ $\text{mm}$. If the average ground...

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262

GATE Civil 2023 Set 2 | Question: 33
A compound symmetrical open channel section as shown in the figure has a maximum of ______________ critical depth(s). $3$ $2$ $1$ $4$

A compound symmetrical open channel section as shown in the figure has a maximum of ______________ critical depth(s).$3$$2$$1$$4$

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263

GATE Civil 2022 Set 1 | Question: 4
In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of Young's modulus of elasticity of reinforcement material to Young's modulus of elasticity of concrete. Young's modulus of ... shear modulus of concrete. Young's modulus of elasticity of reinforcement material to the shear modulus of concrete.

In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio ofYoung's modulus of elasticity of reinforcement material to Young's mo...

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264

GATE Civil 2022 Set 1 | Question: 29
The project activities are given in the following table along with the duration and dependency. ... $20$ days, Critical path is $\text{P} \rightarrow \text{R}$

The project activities are given in the following table along with the duration and dependency.$$\begin{array}{|c|c|} \hline \textbf{Activities} & \textbf{Duration (days...

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265

GATE Civil 2022 Set 1 | Question: 43
A reinforced concrete beam with rectangular cross section (width = $300$ $\text{mm}$, effective depth = $580$ $\text{mm}$) is made of $M30$ grade concrete. It has $1\%$ longitudinal tension reinforcement of $\text{Fe}$ $415$ grade steel ... diameter vertical stirrups of $\text{Fe}$ $415$ grade steel is ____________ $\text{mm}$. (round off to the nearest integer)

A reinforced concrete beam with rectangular cross section (width = $300$ $\text{mm}$, effective depth = $580$ $\text{mm}$) is made of $M30$ grade concrete. It has $1\%$ l...

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266

GATE Civil 2024 Set 1 | Question: 50
Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics. At a reaction rate of $0.38 /$ day, the time (in days) required to remove the pollutant by $95 \%$ is $\_\_\_\_\_\_\_$. (rounded off to $1$ decimal place).

Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics.At a reaction rate of $0.38 /$ day, t...

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267

GATE Civil 2024 Set 1 | Question: 31
A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of $30^{\circ}$. The inclinations of failure planes with respect to the major principal plane for Rankine's active and passive earth pressure conditions, ... $30^{\circ}$ and $60^{\circ}$ $60^{\circ}$ and $30^{\circ}$

A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of $30^{\circ}$. The inclinations of failure...

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268

GATE Civil 2024 Set 2 | Question: 23
The steel angle section shown in the figure has elastic section modulus of $150.92 \mathrm{~cm}^{3}$ about the horizontal $\mathrm{X}-\mathrm{X}$ axis, which passes through the centroid of the section. The shape factor of the section is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

The steel angle section shown in the figure has elastic section modulus of $150.92 \mathrm{~cm}^{3}$ about the horizontal $\mathrm{X}-\mathrm{X}$ axis, which passes throu...

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269

GATE Civil 2024 Set 2 | Question: 47
A $500 \mathrm{~m}$ long water distribution pipeline $\text{P}$ with diameter $1.0 \mathrm{~m}$, is used to convey $0.1 \mathrm{~m}^{3} / \mathrm{s}$ of flow. A new pipeline $\text{Q}$ ... respectively. The diameter of the pipeline $\text{Q}$ (in meters) is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A $500 \mathrm{~m}$ long water distribution pipeline $\text{P}$ with diameter $1.0 \mathrm{~m}$, is used to convey $0.1 \mathrm{~m}^{3} / \mathrm{s}$ of flow. A new pipel...

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270

GATE Civil 2024 Set 1 | Question: 36
Which of the following statement(s) is/are CORRECT? Swell potential of soil decreases with an increase in the shrinkage limit. Both loose and dense sands with different initial void ratios can attain similar void ... other corrections. In electrical resistivity tomography, the depth of current penetration is half of the spacing between the electrodes.

Which of the following statement(s) is/are CORRECT?Swell potential of soil decreases with an increase in the shrinkage limit.Both loose and dense sands ...

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271

GATE Civil 2023 Set 1 | Question: 31
Consider that a force $\text{P}$ is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress $\left(\sigma_{z}\right)$ at any point $(r, z)$, within the half-space is given as, \[\sigma_{z}=\frac{3 P}{2 \pi} \frac{z^{3}}{\left(r^{2 ... $z^{3}=\frac{3}{2} r^{2}$ $z^{2}=\frac{5}{2} r^{2}$ $z^{3}=\frac{5}{2} r^{2}$

Consider that a force $\text{P}$ is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress $\left(\sigma_{z}\right)$ at any ...

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272

GATE Civil 2024 Set 2 | Question: 41
A concrete column section of size $300 \mathrm{~mm} \times 500 \mathrm{~mm}$ as shown in the figure is subjected to both axial compression and bending along the major axis. The depth of the neutral axis $\left(x_{u}\right)$ is $1.1$ times the depth of the ... tension in the section, is $\_\_\_\_\_\_\_$ $\times 10^{-3}$ (rounded off to $2$ decimal places).

A concrete column section of size $300 \mathrm{~mm} \times 500 \mathrm{~mm}$ as shown in the figure is subjected to both axial compression and bending along the major axi...

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273

GATE Civil 2024 Set 1 | Question: 24
An embankment is constructed with soil by maintaining the degree of saturation as $75 \%$ during compaction. The specific gravity of soil is 2.68 and the moisture content is $17 \%$ ... $\_\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

An embankment is constructed with soil by maintaining the degree of saturation as $75 \%$ during compaction. The specific gravity of soil is 2.68 and the moisture content...

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274

GATE Civil 2024 Set 1 | Question: 47
A standard round bottom triangular canal section as shown in the figure has a bed slope of $1$ in $200$. Consider the Chezy's coefficient as $150 \mathrm{~m}^{1 / 2} / \mathrm{s}$. The normal depth of flow, $y$ (in meters) for carrying a discharge of $20 \mathrm{~m}^{3} / \mathrm{s}$ is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A standard round bottom triangular canal section as shown in the figure has a bed slope of $1$ in $200$. Consider the Chezy's coefficient as $150 \mathrm{~m}^{1 / 2} / \m...

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275

GATE Civil 2023 Set 2 | Question: 42
A $5 \mathrm{~cm}$ long metal rod $\mathrm{AB}$ was initially at a uniform temperature of $T_0{ }^{\circ} \mathrm{C}$. Thereafter, temperature at both the ends are maintained at $0{ }^{\circ} \mathrm{C}$. Neglecting the heat transfer from the ... $\beta$ (in $\mathrm{s}^{-1}$, rounded off to three decimal places) is__________________.

A $5 \mathrm{~cm}$ long metal rod $\mathrm{AB}$ was initially at a uniform temperature of $T_0{ }^{\circ} \mathrm{C}$. Thereafter, temperature at both the ends are mainta...

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276

GATE Civil 2023 Set 1 | Question: 2
A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress ... $15.0$ $25.0$ $35.0$ $45.0$

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the ...

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277

GATE Civil 2022 Set 1 | Question: 52
A two-phase signalized intersection is designed with a cycle time of $100\:s$. The amber and red times for each phase are $4\:s$ and $50\:s$, respectively. If the total lost time per phase due to start-up and clearance is $2\:s$, the effective green time of each phase is __________________ $s$. (in integer)

A two-phase signalized intersection is designed with a cycle time of $100\:s$. The amber and red times for each phase are $4\:s$ and $50\:s$, respectively. If the total l...

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278

GATE Civil 2024 Set 1 | Question: 18
For the following partial differential equation, \[ x \frac{\partial^{2} f}{\partial x^{2}}+y \frac{\partial^{2} f}{\partial y^{2}}=\frac{x^{2}+y^{2}}{2} \] which of the following option(s) is/are CORRECT? elliptic for $x>0$ and $y>0$ parabolic for $x>0$ and $y>0$ elliptic for $x=0$ and $y>0$ hyperbolic for $x<0$ and $y>0$

For the following partial differential equation,\[x \frac{\partial^{2} f}{\partial x^{2}}+y \frac{\partial^{2} f}{\partial y^{2}}=\frac{x^{2}+y^{2}}{2}\...

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279

GATE Civil 2023 Set 1 | Question: 16
consider the following three structures: Which of the following statements is/are TRUE? Structure I is unstable Structure II is unstable Structure III is unstable All three structures are stable

consider the following three structures:Which of the following statements is/are TRUE?Structure I is unstableStructure II is unstableStructure III is unstableAll three st...

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280

GATE Civil 2022 Set 1 | Question: 26
The Cartesian coordinates of a point $P$ in a right-handed coordinate system are $(1, 1, 1)$. The transformed coordinates of $P$ due to a $45^{\circ}$ clockwise rotation of the coordinates system about the positive $x$-axis are $\left ( 1, 0, \sqrt{2} \right )$ ... $\left ( -1, 0, \sqrt{2} \right )$ $\left ( -1, 0, -\sqrt{2} \right )$

The Cartesian coordinates of a point $P$ in a right-handed coordinate system are $(1, 1, 1)$. The transformed coordinates of $P$ due to a $45^{\circ}$ clockwise rotation ...

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