Recent questions tagged numerical-answers / GO Civil

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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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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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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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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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15

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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16

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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17

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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18

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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19

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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21

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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22

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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23

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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24

GATE Civil 2024 Set 1 | Question: 23
The plane frame shown in the figure has fixed support at joint $\text{A}$, hinge support at joint $\text{F}$, and roller support at joint $\text{I}$. In the figure, $\text{A}$ to $\text{I}$ indicate joints of the frame. If the axial deformations are neglected, the degree of kinematic indeterminacy is $\_\_\_\_\_\_$. (in integer).

The plane frame shown in the figure has fixed support at joint $\text{A}$, hinge support at joint $\text{F}$, and roller support at joint $\text{I}$. In the figure, $\tex...

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25

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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26

GATE Civil 2024 Set 1 | Question: 25
A $30 \mathrm{~cm}$ diameter well fully penetrates an unconfined aquifer of saturated thickness $20 \mathrm{~m}$ with hydraulic conductivity of $10 \mathrm{~m} /$ ... $\_\_\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

A $30 \mathrm{~cm}$ diameter well fully penetrates an unconfined aquifer of saturated thickness $20 \mathrm{~m}$ with hydraulic conductivity of $10 \mathrm{~m} /$ day. Un...

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27

GATE Civil 2024 Set 1 | Question: 37
The return period of a large earthquake for a given region is $200$ years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceeded at least once in $50$ years is $\_\_\_\_\_\_$ $\%$ (rounded off to the nearest integer).

The return period of a large earthquake for a given region is $200$ years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it wil...

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28

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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29

GATE Civil 2024 Set 1 | Question: 39
The plane truss shown in the figure has $13$ joints and $22$ members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. A to $\mathrm{M}$ indicate the joints of the truss. The truss has pin supports at ... $\mathrm{L}$ is $\_\_\_\_\_\_$ (rounded off to $1$ decimal place).

The plane truss shown in the figure has $13$ joints and $22$ members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical...

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30

GATE Civil 2024 Set 1 | Question: 40
An inverted $\mathrm{T}$-shaped concrete beam $\text{(B1)}$ in the figure, with centroidal axis $\mathrm{X}-\mathrm{X}$, is subjected to an effective prestressing force of $1000 \mathrm{kN}$ acting at the bottom kern point of the beam cross-section. Also consider ... $\text{B}2$ is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

An inverted $\mathrm{T}$-shaped concrete beam $\text{(B1)}$ in the figure, with centroidal axis $\mathrm{X}-\mathrm{X}$, is subjected to an effective prestressing force o...

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31

GATE Civil 2024 Set 1 | Question: 41
The initial cost of an equipment is Rs. $1,00,000$. Its salvage value at the end of accounting life of $5$ years is Rs. $10,000$. The difference in depreciation (in Rs.) computed using 'double-declining balance method' and 'straight line method' of depreciation in Year-$2$ is $\_\_\_\_\_\_$ (in positive integer).

The initial cost of an equipment is Rs. $1,00,000$. Its salvage value at the end of accounting life of $5$ years is Rs. $10,000$. The difference in depreciation (in Rs.) ...

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32

GATE Civil 2024 Set 1 | Question: 42
A slab panel with an effective depth of $250 \mathrm{~mm}$ is reinforced with $0.2 \%$ main reinforcement using $8 \mathrm{~mm}$ diameter steel bars. The uniform center-to-center spacing (in $\mathrm{mm}$ ) at which the $8 \mathrm{~mm}$ diameter bars are placed in the slab panel is $\_\_\_\_\_\_$. (rounded off to the nearest integer).

A slab panel with an effective depth of $250 \mathrm{~mm}$ is reinforced with $0.2 \%$ main reinforcement using $8 \mathrm{~mm}$ diameter steel bars. The uniform center-t...

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33

GATE Civil 2024 Set 1 | Question: 43
The total primary consolidation settlement $\left(S_{c}\right)$ of a building constructed on a $10 \mathrm{~m}$ thick saturated clay layer is estimated to be $50 \mathrm{~mm}$. After $300$ days of the construction of the building, primary consolidation settlement was reported ... $50 \%$ of $S_{c}$ will be $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

The total primary consolidation settlement $\left(S_{c}\right)$ of a building constructed on a $10 \mathrm{~m}$ thick saturated clay layer is estimated to be $50 \mathrm{...

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34

GATE Civil 2024 Set 1 | Question: 44
An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is $30^{\circ}$ ... for the critically stable condition of the slope is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is $30^{\circ}$ with respect to horizontal gr...

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35

GATE Civil 2024 Set 1 | Question: 45
A soil sample was consolidated at a cell pressure of $20 \mathrm{kPa}$ and a back pressure of $10 \mathrm{kPa}$ for $24$ hours during a consolidated undrained $\text{(CU)}$ triaxial test. The cell pressure was increased to $30 \mathrm{kPa}$ on the next ... s pore pressure parameter $B$ for the soil sample is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A soil sample was consolidated at a cell pressure of $20 \mathrm{kPa}$ and a back pressure of $10 \mathrm{kPa}$ for $24$ hours during a consolidated undrained $\text{(CU)...

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36

GATE Civil 2024 Set 1 | Question: 46
The ordinates of a $1$-hour unit hydrograph $\text{(UH)}$ are given below. Time (hours) $0$ $1$ $2$ $3$ $4$ $5$ Ordinates of $1$-hour $\mathrm{UH}\left(\mathrm{m}^{3} / \mathrm{s}\right)$ $0$ $13$ $50$ $80$ $95$ $85$ Time (hours) $6$ $7$ ... $3$-hour $\text{UH}$ is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

The ordinates of a $1$-hour unit hydrograph $\text{(UH)}$ are given below.Time (hours)$0$$1$$2$$3$$4$$5$Ordinates of $1$-hour $\mathrm{UH}\left(\mathrm{m}^{3} / \mathrm{s...

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37

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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38

GATE Civil 2024 Set 1 | Question: 48
A spillway has unit discharge of $7.5 \mathrm{~m}^{3} / \mathrm{s} / \mathrm{m}$. The flow depth at the downstream horizontal apron is $0.5 \mathrm{~m}$. The tail water depth (in meters) required to form a hydraulic jump is $\_\_\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

A spillway has unit discharge of $7.5 \mathrm{~m}^{3} / \mathrm{s} / \mathrm{m}$. The flow depth at the downstream horizontal apron is $0.5 \mathrm{~m}$. The tail water d...

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39

GATE Civil 2024 Set 1 | Question: 49
A $5 \mathrm{~m} \times 5 \mathrm{~m}$ closed tank of $10 \mathrm{~m}$ height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use $\gamma_{w}=10 \mathrm{kN} / \mathrm{m}^{3}$ and Specific gravity of oil ... $\_\_\_\_\_\_$. (rounded off to the nearest integer).

A $5 \mathrm{~m} \times 5 \mathrm{~m}$ closed tank of $10 \mathrm{~m}$ height contains water and oil, and is connected to an overhead water reservoir as shown in the figu...

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40

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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