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41
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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GATE Civil 2024 Set 2 | Question: 32
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: $1.50$), silica sand (specific gravity: $2.60$), and ilmenite sand (specific gravity: $4.20$), is to be designed for treating water/wastewater. After backwashing, the ... than $0.64 \mathrm{~mm}$ and diameter of ilmenite particles is slightly less than $0.10 \mathrm{~mm}$.
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: $1.50$), silica sand (specific gravity: $2.60$), and ilmenite sand (specific gravi...
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GATE Civil 2024 Set 2 | Question: 33
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table. Speed range $(\mathrm{kmph})$ Number of observations $0-10$ $7$ $10-20$ $31$ $20-30$ $76$ $30-40$ $129$ $40-50$ $104$ $50-60$ $78$ ... $13$ $90-100$ $9$ The "upper speed limit" (in $\mathrm{kmph}$) for the traffic sign is $50$ $55$ $65$ $70$
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.Speed range $(\mathrm{kmph})$Number of observations...
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GATE Civil 2024 Set 2 | Question: 34
Three vectors $\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}$, and $\overrightarrow{\mathrm{r}}$ are given as \[ \begin{array}{c} \overrightarrow{\mathrm{p}}=\hat{\imath}+\hat{\jmath}+\hat{k} \\ \overrightarrow{\mathrm ...
Three vectors $\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}$, and $\overrightarrow{\mathrm{r}}$ are given as\[\begin{array}{c}\overrightarrow{\mathrm{p}}=\hat...
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GATE Civil 2024 Set 2 | Question: 35
Consider the statements $\text{P, Q,}$ and $\text{R}$. $\text{P}$: Compacted fine-grained soils with flocculated structure have isotropic permeability. $\text{Q}$ ... is TRUE $\mathrm{P}$ is TRUE and $\mathrm{R}$ is FALSE Both $\mathrm{Q}$ and $\mathrm{R}$ are FALSE
Consider the statements $\text{P, Q,}$ and $\text{R}$.$\text{P}$: Compacted fine-grained soils with flocculated structure have isotropic permeability.$\tex...
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GATE Civil 2024 Set 2 | Question: 36
In the context of pavement material characterization, the CORRECT statement(s) is/are The load penetration curve of $\text{CBR}$ test may need origin correction due to the non-vertical penetrating plunger of the loading machine. The toughness and hardness of ... total volume of air voids $\left(V_{v}\right)$ and total volume of bitumen $\left(V_{b}\right)$.
In the context of pavement material characterization, the CORRECT statement(s) is/areThe load penetration curve of $\text{CBR}$ test may need origin correctio...
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GATE Civil 2024 Set 2 | Question: 37
The expression for computing the effective interest rate $\left(i_{\text {eff }}\right)$ using continuous compounding for a nominal interest rate of $5 \%$ is \[ i_{\text {eff }}=\lim _{m \rightarrow \infty}\left(1+\frac{0.05}{m}\right)^{m}-1 \] The effective interest rate (in percentage) is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
The expression for computing the effective interest rate $\left(i_{\text {eff }}\right)$ using continuous compounding for a nominal interest rate of $5 \%$ is\[i_{\text {...
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GATE Civil 2024 Set 2 | Question: 38
Consider two matrices $\mathbf{A}=\left[\begin{array}{lll}2 & 1 & 4 \\ 1 & 0 & 3\end{array}\right]$ and $\mathbf{B}=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3 \\ 1 & 4\end{array}\right]$. The determinant of the matrix $\mathbf{AB}$ is $\_\_\_\_\_\_\_$ (in integer).
Consider two matrices $\mathbf{A}=\left[\begin{array}{lll}2 & 1 & 4 \\ 1 & 0 & 3\end{array}\right]$ and $\mathbf{B}=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3 \\ 1 & 4\end{ar...
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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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GATE Civil 2024 Set 2 | Question: 40
The horizontal beam $\mathrm{PQRS}$ shown in the figure has a fixed support at point $\mathrm{P}$, an internal hinge at point $Q$, and a pin support at point $R$. A concentrated vertically downward load $(V)$ of $10 \mathrm{kN}$ can act at any point over the ... $\mathrm{P}$ due to $V$ is $\_\_\_\_\_\_$ (in integer).
The horizontal beam $\mathrm{PQRS}$ shown in the figure has a fixed support at point $\mathrm{P}$, an internal hinge at point $Q$, and a pin support at point $R$. A conce...
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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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GATE Civil 2024 Set 2 | Question: 42
The table shows the activities and their durations and dependencies in a project. \begin{array}{|c|c|c|} \hline \text{Activity} & \text{Duration (Days)} & \text{Depends on} \\ \hline \text{A} & 8 & - \\ \hline \text{B} & 4 & \text{ ... , K} \\ \hline \end{array} The total duration (in days) of the project is $\_\_\_\_\_\_\_$ (in integer).
The table shows the activities and their durations and dependencies in a project.\begin{array}{|c|c|c|}\hline \text{Activity} & \text{Duration (Days)} & \text{Depends on}...
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GATE Civil 2024 Set 2 | Question: 43
A homogeneous earth dam has a maximum water head difference of $15 \mathrm{~m}$ between the upstream and downstream sides. A flownet was drawn with the number of potential drops as 10 and the average length of the element as $3 \mathrm{~m}$. Specific gravity of the ... failure, void ratio of the soil is $\_\_\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A homogeneous earth dam has a maximum water head difference of $15 \mathrm{~m}$ between the upstream and downstream sides. A flownet was drawn with the number of potentia...
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GATE Civil 2024 Set 2 | Question: 44
The in-situ percentage of voids of a sand deposit is $50 \%$. The maximum and minimum densities of sand determined from the laboratory tests are $1.8 \mathrm{~g} / \mathrm{cm}^{3}$ and $1.3 \mathrm{~g} / \mathrm{cm}^{3}$, respectively. Assume the ... $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
The in-situ percentage of voids of a sand deposit is $50 \%$. The maximum and minimum densities of sand determined from the laboratory tests are $1.8 \mathrm{~g} / \mathr...
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GATE Civil 2024 Set 2 | Question: 45
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of $100 \mathrm{kN} / \mathrm{m}^{2}$ ... (in degrees) with respect to horizontal is $\_\_\_\_\_\_\_\_$ (rounded off to the nearest integer).
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value ...
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GATE Civil 2024 Set 2 | Question: 46
A storm with a recorded precipitation of $11.0 \mathrm{~cm}$, as shown in the table, produced a direct run-off of $6.0 \mathrm{~cm}$. Time from start (hours) $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ Recorded cumulative precipitation$(\mathrm{cm})$ $0.5$ ... $\_\_\_\_\_\_\_\_$ $\mathrm{cm} / \mathrm{hr}$ (rounded off to $2$ decimal places).
A storm with a recorded precipitation of $11.0 \mathrm{~cm}$, as shown in the table, produced a direct run-off of $6.0 \mathrm{~cm}$.Time from start (hours)$1$$2$$3$$4$$5...
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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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GATE Civil 2024 Set 2 | Question: 48
A $2 \mathrm{~m} \times 1.5 \mathrm{~m}$ tank of $6 \mathrm{~m}$ height is provided with a $100 \mathrm{~mm}$ diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to $5 \mathrm{~m}$ height. Consider the ... to $3.5 \mathrm{~m}$ under free discharge condition is $\_\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A $2 \mathrm{~m} \times 1.5 \mathrm{~m}$ tank of $6 \mathrm{~m}$ height is provided with a $100 \mathrm{~mm}$ diameter orifice at the center of its base. The orifice is p...
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GATE Civil 2024 Set 2 | Question: 49
A rectangular channel is $4.0 \mathrm{~m}$ wide and carries a discharge of $2.0 \mathrm{~m}^{3} / \mathrm{s}$ with a depth of $0.4 \mathrm{~m}$. The channel transitions to a maximum width contraction at a downstream location, without influencing the ... . The width (in meters) at the maximum contraction is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A rectangular channel is $4.0 \mathrm{~m}$ wide and carries a discharge of $2.0 \mathrm{~m}^{3} / \mathrm{s}$ with a depth of $0.4 \mathrm{~m}$. The channel transitions t...
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GATE Civil 2024 Set 2 | Question: 50
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of $10$ million liters/day. Assume a detention period of $2.0$ hours and surface loading rate of $40000$ liters $/ \mathrm{m}^{2} /$ day. The height (in meters) of the water column in the tank is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of $10$ million liters/day. Assume a detention period of $2.0$ hours and surface...
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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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GATE Civil 2024 Set 2 | Question: 52
A horizontal curve of radius $1080 \mathrm{~m}$ (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of $70 \mathrm{kmph}$. However, a few years after construction, the Railway Authorities ... the express trains running on this track is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).
A horizontal curve of radius $1080 \mathrm{~m}$ (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium spee...
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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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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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GATE Civil 2024 Set 2 | Question: 55
Differential levelling is carried out from point $\text{P(B M}:+200.000 \mathrm{~m})$ to point $\text{R}$. The readings taken are given in the table. Points Staff readings (m) Remarks Back Sight Fore Sight P $(-) 2.050$ BM: $+200.000 \mathrm{~m}$ ... Level (in meters) of the point $\mathrm{R}$ is $\_\_\_\_\_\_\_\_$ (rounded off to $3$ decimal places).
Differential levelling is carried out from point $\text{P(B M}:+200.000 \mathrm{~m})$ to point $\text{R}$. The readings taken are given in the table.PointsStaff readings ...
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GATE Civil 2024 Set 1 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [simmer $\rightarrow$ seethe $\rightarrow$ smolder] is analogous to [break $\rightarrow$ raze $\_\_\_\_\_\_ $ $\rightarrow$ ] Which one of the given options is appropriate to fill the blank? obfuscate obliterate fracture fissure
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [simmer $\rightarrow$ seethe $\rightarrow$ smolder] is analogous ...
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GATE Civil 2024 Set 1 | GA Question: 2
In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from $301$, while the house-numbers on the other side of the road are consecutive even numbers starting from $302$. The ... of the road is $27$, then the number of houses on each side of the road is $27$ $52$ $54$ $26$
In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from $301$, while th...
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GATE Civil 2024 Set 1 | GA Question: 3
For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1,\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}$. Then, $q^{p}=p^{q}$ $q^{p}=p^{2 q}$ $\sqrt{q}=\sqrt{p}$ $\sqrt[p]{q}=\sqrt[q]{p}$
For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1,\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}$. Then,$q^{p}=p^{q}$$q^{p}=p^{2 q}...
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GATE Civil 2024 Set 1 | GA Question: 4
Which one of the given options is a possible value of $x$ in the following sequence? \[ 3,7,15, x, 63,127,255 \] $35$ $40$ $45$ $31$
Which one of the given options is a possible value of $x$ in the following sequence?\[3,7,15, x, 63,127,255\]$35$$40$$45$$31$
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GATE Civil 2024 Set 1 | GA Question: 5
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ hours? $51$ $49$ $50$ $55$
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ ...
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GATE Civil 2024 Set 1 | GA Question: 6
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the ... $\text{(i)}$ holds $\text{(ii)}$ waits $\text{(iii)}$ culminate $\text{(iv)}$ pivots
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.From the ancient Athenian arena to the modern Olympi...
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GATE Civil 2024 Set 1 | GA Question: 7
Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin? $12$ $14$ $10$ $28$
Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined ...
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GATE Civil 2024 Set 1 | GA Question: 8
The chart given below compares the Installed Capacity (MW) of four power generation technologies, $\text{T}1, \text{T}2, \text{T}3$, and $\text{T}4$, and their Electricity Generation (MWh) in a time of $1000$ hours (h). The Capacity Factor of a power ... of the given technologies has the highest Capacity Factor? $\text{T}1$ $\text{T}2$ $\text{T}3$ $\text{T}4$
The chart given below compares the Installed Capacity (MW) of four power generation technologies, $\text{T}1, \text{T}2, \text{T}3$, and $\text{T}4$, and their Electricit...
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GATE Civil 2024 Set 1 | GA Question: 9
In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule. \begin{array}{|l|l|l|l|} \hline 1 & 1 & 2 & \\ \hline 2 & X & 3 ... , right, top, bottom, diagonals). As per this rule, the maximum number of crosses possible in the empty column is $0$ $1$ $2$ $3$
In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule.\begin{array}{|l|l|...
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GATE Civil 2024 Set 1 | GA Question: 10
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of the Earth-Sun and Earth-Moon distances is closest to $328$ $382$ $238$ $283$
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of th...
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GATE Civil 2024 Set 1 | Question: 1
The smallest positive root of the equation \[ x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0 \] lies in the range $0 < x \leq 2$ $2 < x \leq 4$ $6 \leq x \leq 8$ $10 \leq x \leq 100$
The smallest positive root of the equation\[x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0\]lies in the range$0 < x \leq 2$$2 < x \leq 4$$6 \leq x \leq 8$$10 \le...
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GATE Civil 2024 Set 1 | Question: 2
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as \[ \frac{\partial^{2} u}{\partial x^{2}}=2 \] Assuming $g: g(x), f: f(y)$, and $h: h(y)$, the general solution of the above differential equation is $u=x^{2}+f(y)+g(x)$ $u=x^{2}+x f(y)+h(y)$ $u=x^{2}+x f(y)+g(x)$ $u=x^{2}+f(y)+y g(x)$
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as\[\frac{\partial^{2} u}{\partial x^{2}}=2\]Assuming $g: g(x), f: f(...
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GATE Civil 2024 Set 1 | Question: 3
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the ... one of these two subjects is $\frac{17}{18}$ $\frac{11}{18}$ $\frac{14}{18}$ $\frac{1}{18}$
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. Th...
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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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GATE Civil 2024 Set 1 | Question: 5
Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $30 \mathrm{MPa}$ strength should be $35$ $37$ $38$ $39$
Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $...
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