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81

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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82

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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83

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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84

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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85

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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86

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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87

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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88

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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89

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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90

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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91

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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92

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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93

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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94

GATE Civil 2024 Set 1 | Question: 27
A vector field $\vec{p}$ and a scalar field $r$ are given by \[ \begin{aligned} \vec{p} & =\left(2 x^{2}-3 x y+z^{2}\right) \hat{\imath}+\left(2 y^{2}-3 y z+x^{2}\right) \hat{\jmath}+\left(2 z^{2}-3 x z+x^{2}\right) \ ... $\text{P}$ is TRUE and $\text{Q}$ is FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE Both $\mathrm{P}$ and $\mathrm{Q}$ are TRUE

A vector field $\vec{p}$ and a scalar field $r$ are given by\[\begin{aligned}\vec{p} & =\left(2 x^{2}-3 x y+z^{2}\right) \hat{\imath}+\left(2 y^{2}-3 y z+x...

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95

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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96

GATE Civil 2024 Set 2 | Question: 14
The following figure shows a plot between shear stress and velocity gradient for materials/fluids $\text{P, Q, R, S}$, and $\text{T}$. Which one of the following options is CORRECT? $\mathrm{P} \rightarrow$ ... ; $\mathrm{Q} \rightarrow$ Newtonian fluid $\mathrm{R} \rightarrow$ Ideal Bingham plastic; $\mathrm{T} \rightarrow$ Ideal Fluid

The following figure shows a plot between shear stress and velocity gradient for materials/fluids $\text{P, Q, R, S}$, and $\text{T}$.Which one of the followi...

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97

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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98

GATE Civil 2024 Set 1 | Question: 29
The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports $\text{A}$ and $\text{B}$ ... $\mathrm{RA}=\frac{q l}{2} ; \mathrm{RB}=q l ; \mathrm{RC}=\frac{q l}{2}$

The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports $\text{A}$ and $\text{B}$.Considering ...

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99

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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100

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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101

GATE Civil 2024 Set 2 | Question: 21
What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them? \begin{array}{|l|l|} \hline \text{Instruments/Parts of instruments} & \text{Operations} \\ \hline \text{P - Bubble tube} & \text{i - ... $\text{P-i, Q-iii, R-ii, S-iv}$ $\text{P-iii, Q-iv, R-i, S-ii}$

What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them?\begin{array}{|l|...

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102

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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103

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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104

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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105

GATE Civil 2024 Set 1 | Question: 28
Find the correct match between the plane stress states and the Mohr's circles. $\text{(P)-(III); (Q)-(IV); (R)-(I); (S)-(II)}$ $\text{(P)-(III); (Q)-(II); (R)-(I); (S)-(IV)}$ $\text{(P)-(I); (Q)-(IV); (R)-(III); (S)-(II)}$ $\text{(P)-(I); (Q)-(II); (R)-(III); (S)-(IV)}$

Find the correct match between the plane stress states and the Mohr's circles.$\text{(P)-(III); (Q)-(IV); (R)-(I); (S)-(II)}$$\text{(P)-(III); (Q)-(II); (R...

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106

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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107

GATE Civil 2024 Set 1 | Question: 10
The number of degrees of freedom for a natural open channel flow with a mobile bed is $2$ $3$ $4$ $5$

The number of degrees of freedom for a natural open channel flow with a mobile bed is$2$$3$$4$$5$

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108

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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109

GATE Civil 2024 Set 1 | Question: 52
The number of trains and their corresponding speeds for a curved Broad Gauge section with $437 \mathrm{~m}$ radius, are $20$ trains travel at a speed of $40 \mathrm{~km} / \mathrm{hr}$ $15$ ... the required equilibrium cant (in $\mathrm{mm}$ ) will be $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

The number of trains and their corresponding speeds for a curved Broad Gauge section with $437 \mathrm{~m}$ radius, are$20$ trains travel at a speed of $40 \mathrm{~km} /...

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110

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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111

GATE Civil 2024 Set 1 | Question: 35
A map is prepared with a scale of $1: 1000$ and a contour interval of $1 \mathrm{~m}$. If the distance between two adjacent contours on the map is $10 \mathrm{~mm}$, the slope of the ground between the adjacent contours is $30 \%$ $10 \%$ $35 \%$ $40 \%$

A map is prepared with a scale of $1: 1000$ and a contour interval of $1 \mathrm{~m}$. If the distance between two adjacent contours on the map is $10 \...

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112

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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113

GATE Civil 2024 Set 1 | Question: 17
Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT? The line of collimation must be perpendicular to the horizontal axis at its intersection with the vertical axis. The axis of altitude level ... to the vertical axis. The Vernier of vertical circle must read zero when the line of collimation is vertical.

Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT?The line of collimation must be perpendicular to the horizonta...

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114

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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115

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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116

GATE Civil 2024 Set 1 | Question: 13
As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by $x(\%)$ for every $y(\mathrm{~m})$ raise in elevation from the Mean Sea Level (MSL). The values of $x$ and $y$, respectively, are $7 \%$ and $300 \mathrm{~m}$ $5 \%$ and $200 \mathrm{~m}$ $4 \%$ and $500 \mathrm{~m}$ $10 \%$ and $1000 \mathrm{~m}$

As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by $x(\%)$ for every $y(\mathrm{~m})$ raise in elevation ...

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117

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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118

GATE Civil 2024 Set 1 | Question: 26
What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ? $1,2,5$ $1,3,4$ $-5,1,2$ $-5,-1,2$

What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ?$1,2,5$$1,3,4$$-5,1,2$$-5,-1,2$

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119

GATE Civil 2024 Set 1 | Question: 51
A water treatment plant treats $25 \mathrm{MLD}$ water with a natural alkalinity of $4.0 \mathrm{mg} / \mathrm{L}$ (as $\mathrm{CaCO}_{3}$ ). It is estimated that, during coagulation of this water, $450 \mathrm{~kg} /$ ... $\mathrm{kg}$ ) required for this process per day is $\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

A water treatment plant treats $25 \mathrm{MLD}$ water with a natural alkalinity of $4.0 \mathrm{mg} / \mathrm{L}$ (as $\mathrm{CaCO}_{3}$ ). It is estimated that, during...

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120

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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