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121

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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122

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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123

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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124

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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125

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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126

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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127

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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128

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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129

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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130

GATE Civil 2024 Set 1 | Question: 54
The following data is obtained from an axle load survey at a site: Average rear axle load $=12000 \mathrm{~kg}$ Number of commercial vehicles $=800$ per day The pavement at this site would be reconstructed over a period of 5 years from the date of survey. The ... $\mathrm{msa}$ ) for the pavement design is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

The following data is obtained from an axle load survey at a site:Average rear axle load $=12000 \mathrm{~kg}$Number of commercial vehicles $=800$ per dayThe pavement at ...

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131

GATE Civil 2024 Set 1 | Question: 55
A bird is resting on a point $\mathrm{P}$ at a height of $8 \mathrm{~m}$ above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point $\mathrm{Q}$ ... the horizontal distance (in meters) between points $\mathrm{P}$ and $\mathrm{Q}$ is $\_\_\_\_\_\_$ (in integer).

A bird is resting on a point $\mathrm{P}$ at a height of $8 \mathrm{~m}$ above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground ...

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132

GATE Civil 2023 Set 2 | Question: 1
Let $\phi$ be a scalar field, and $\boldsymbol{u}$ be a vector field. Which of the following identities is true for $\operatorname{div}(\phi \boldsymbol{u})$ ...

Let $\phi$ be a scalar field, and $\boldsymbol{u}$ be a vector field. Which of the following identities is true for $\operatorname{div}(\phi \boldsymbol{u})$? $\operatorn...

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133

GATE Civil 2023 Set 2 | Question: 2
Which of the following probability distribution functions (PDFs) has the mean greater than the median? Function $1$ Function $2$ Function $3$ Function $4$

Which of the following probability distribution functions (PDFs) has the mean greater than the median?Function $1$Function $2$Function $3$Function $4$

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134

GATE Civil 2023 Set 2 | Question: 3
A remote village has exactly $1000$ vehicles with sequential registration numbers starting from $ 1000.$ Out of the total vehicles, $ 30 \% $ are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on ... date, the number of vehicles expected without pollution clearance certificate is ___________. $15$ $30$ $50$ $70$

A remote village has exactly $1000$ vehicles with sequential registration numbers starting from $ 1000.$ Out of the total vehicles, $ 30 \% $ are without pollution clear...

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135

GATE Civil 2023 Set 2 | Question: 4
A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. A torque $T=100 \mathrm{~kN}$ ... $\text{Statement i)}$ is wrong, but $\text{Statement ii)}$ is correct Both the statements are wrong

A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. A torque $T=100 \mathrm{~kN}$.m is applied at the free end. The shear modu...

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136

GATE Civil 2023 Set 2 | Question: 5
$\text{M20}$ concrete as per $\mathrm{IS~} 456: 2000$ refers to concrete with a design mix having ____________ an average cube strength of $20~ \mathrm{MPa}$ an average cylinder strength of $20~ \mathrm{MPa}$ a $5$-percentile cube strength of $20~ \mathrm{MPa}$ a $5$-percentile cylinder strength of $20~ \mathrm{MPa}$

$\text{M20}$ concrete as per $\mathrm{IS~} 456: 2000$ refers to concrete with a design mix having ____________an average cube strength of $20~ \mathrm{MPa}$an average cyl...

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137

GATE Civil 2023 Set 2 | Question: 6
When a simply-supported elastic beam of span $L$ and flexural rigidity $E I$ ( $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded with a uniformly distributed load $w$ per unit length, the deflection at ... to a value less than $\Delta_0 / 2$ reduces to a value greater than $\Delta_0 / 2$ remains unchanged at $\Delta_0$

When a simply-supported elastic beam of span $L$ and flexural rigidity $E I$ ( $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded...

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138

GATE Civil 2023 Set 2 | Question: 7
Muller-Breslau principle is used in analysis of structures for ___________. drawing an influence line diagram for any force response in the structure writing the virtual work expression to get the equilibrium equation superposing the load ... response in the structure relating the deflection between two points in a member with the curvature diagram in-between

Muller-Breslau principle is used in analysis of structures for ___________.drawing an influence line diagram for any force response in the structure writing the virtual w...

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139

GATE Civil 2023 Set 2 | Question: 8
A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with $50 \%$ efficiency. The recorded SPT value at a particular depth is $28.$ If an automatic hammer dropping system with $70 \%$ efficiency is used at the same location, the recorded SPT value will be ____________. $28$ $20$ $40$ $25$

A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with $50 \%$ efficiency. The recorded SPT value at a p...

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140

GATE Civil 2023 Set 2 | Question: 9
A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_{H}$ and coefficient of vertical permeability, $k_{V}.$ In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of ... $\sqrt{\frac{k_{V}}{k_{H}}}$ $1.0 $ $\frac{k_{H}}{k_{V}}$

A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_{H}$ and coefficient of vertical permeability, $k_{V}.$ I...

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141

GATE Civil 2023 Set 2 | Question: 10
Identify the cross-drainage work in the figure. Super passage Aqueduct Siphon aquedut Level crossing

Identify the cross-drainage work in the figure. Super passage Aqueduct Siphon aquedutLevel crossing

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142

GATE Civil 2023 Set 2 | Question: 11
Which one of the following options provides the correct match of the terms listed in Column-$1$ and Column-$2$ ... $\text{P-III, Q-IV, R-I}$ $\text{P-IV, Q-III, R-II}$ $\text{P-III, Q-I, R-IV}$

Which one of the following options provides the correct match of the terms listed in Column-$1$ and Column-$2$?$$\begin{array}{|l|l|}\hline \qquad \text{Column-1} & \qqua...

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143

GATE Civil 2023 Set 2 | Question: 12
In the context of Municipal Solid Waste Management, 'Haul' in 'Hauled Container System operated in conventional mode' includes the __________. time spent by the transport truck at the disposal site time spent by the transport truck in ... at a pickup point time spent by the transport truck in driving from the depot to the first pickup point

In the context of Municipal Solid Waste Management, 'Haul' in 'Hauled Container System operated in conventional mode' includes the __________.time spent by the transport ...

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144

GATE Civil 2023 Set 2 | Question: 13
Which of the following is equal to the stopping sight distance? (braking distance required to come to stop) $+$ (distance travelled during the perception-reaction time) (braking distance required to come to stop) $-$ (distance ... the perception-reaction time) (braking distance required to come to stop) (distance travelled during the perception-reaction time)

Which of the following is equal to the stopping sight distance?(braking distance required to come to stop) $+$ (distance travelled during the perception-reaction time) (b...

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145

GATE Civil 2023 Set 2 | Question: 14
The magnetic bearing of the sun for a location at noon is $ 183^{\circ} \; 30^{\prime}$. If the sun is exactly on the geographic meridian at noon, the magnetic declination of the location is ____________. $3^{\circ} \; 30^{\prime} ~ \mathrm{W}$ ... $93^{\circ} \; 30^{\prime} ~ \mathrm{W}$ $93^{\circ} \; 30^{\prime} ~ \mathrm{E}$

The magnetic bearing of the sun for a location at noon is $ 183^{\circ} \; 30^{\prime}$. If the sun is exactly on the geographic meridian at noon, the magnetic declinatio...

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146

GATE Civil 2023 Set 2 | Question: 15
For the matrix $[A]=\left[\begin{array}{ccc} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{array}\right]$ which of the following statements is/are TRUE? $[A]\{x\}=\{b\}$ has a unique solution $[A]\{x\}=\{b\}$ does not have a unique solution $[A]$ has three linearly independent eigenvectors $[A]$ is a positive definite matrix

For the matrix$[A]=\left[\begin{array}{ccc}1 & -1 & 0 \\-1 & 2 & -1 \\0 & -1 & 1\end{array}\right]$which of the following statements is/are TRUE?$[A]\{x\}=\{b\}$ has a un...

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147

GATE Civil 2023 Set 2 | Question: 16
In the frame shown in the figure (not to scale), all four members $\text{(AB, } \mathrm{BC}, \mathrm{CD}$, and $\mathrm{AD})$ have the same length and same constant flexural rigidity. All the joints $\text{A, B}$, $\mathrm{C}$, and $\mathrm{D}$ are ... $\mathrm{F}$ are zero Slopes at $\mathrm{E}, \mathrm{F}, \mathrm{G}$, and $\mathrm{H}$ are zero

In the frame shown in the figure (not to scale), all four members $\text{(AB, } \mathrm{BC}, \mathrm{CD}$, and $\mathrm{AD})$ have the same length and same constant flexu...

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148

GATE Civil 2023 Set 2 | Question: 17
With regard to the shear design of RCC beams, which of the following statements is/are TRUE? Excessive shear reinforcement can lead to compression failure in concrete Beams without shear reinforcement, even if adequately designed for flexure, can have ... in the beams of varying depth depends on both the design shear force as well as the design bending moment

With regard to the shear design of RCC beams, which of the following statements is/are TRUE? Excessive shear reinforcement can lead to compression failure in concreteBeam...

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149

GATE Civil 2023 Set 2 | Question: 18
The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are: Variation of friction angle along the width of the footing Variation of soil ... Variation of friction angle along the depth of the footing Variation of soil stiffness along the depth of the footing

The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are:Variation o...

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150

GATE Civil 2023 Set 2 | Question: 19
Which of the following is/are NOT active disinfectant(s) in water treatment? $\cdot \mathrm{OH}$ (hydroxyl radical) $\mathrm{O}_{3}$ (ozone) $\mathrm{OCl}^{-}$(hypochlorite ion) $\mathrm{Cl}^{-}$(chloride ion)

Which of the following is/are NOT active disinfectant(s) in water treatment? $\cdot \mathrm{OH}$ (hydroxyl radical)$\mathrm{O}_{3}$ (ozone) $\mathrm{OCl}^{-}$(hypochlorit...

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151

GATE Civil 2023 Set 2 | Question: 20
As per the Indian Roads Congress guidelines $\text{(IRC 86: 2018),}$ extra widening depends on which of the following parameters? Horizontal curve radius Superelevation Number of lanes Longitudinal gradient

As per the Indian Roads Congress guidelines $\text{(IRC 86: 2018),}$ extra widening depends on which of the following parameters? Horizontal curve radius Superelevation N...

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152

GATE Civil 2023 Set 2 | Question: 21
The steady-state temperature distribution in a square plate $\mathrm{ABCD}$ is governed by the $2$-dimensional Laplace equation. The side $\mathrm{AB}$ is kept at a temperature of $100{ }^{\circ} \mathrm{C}$ and the other three sides ... $T_{0}$ is _____________ (rounded off to two decimal places).

The steady-state temperature distribution in a square plate $\mathrm{ABCD}$ is governed by the $2$-dimensional Laplace equation. The side $\mathrm{AB}$ is kept at a tempe...

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153

GATE Civil 2023 Set 2 | Question: 22
An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of $76 ~ \mathrm{kPa}$. The undrained cohesion (in $\mathrm{kPa}$, in integer) of the soil is ______________.

An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of $76 ~ \mathrm{kPa}$. The undrained cohesion (in $...

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154

GATE Civil 2023 Set 2 | Question: 23
The pressure in a pipe at $\mathrm{X}$ is to be measured by an open manometer as shown in figure. Fluid $\mathrm{A}$ is oil with a specific gravity of 0.8 and Fluid $\mathrm{B}$ is mercury with a specific gravity of $13.6.$ ... as $9.81 \mathrm{~m} / \mathrm{s}^2$ and atmospheric pressure as $101.3 ~ \mathrm{kN} / \mathrm{m}^2$ ]

The pressure in a pipe at $\mathrm{X}$ is to be measured by an open manometer as shown in figure. Fluid $\mathrm{A}$ is oil with a specific gravity of 0.8 and Fluid $\mat...

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155

GATE Civil 2023 Set 2 | Question: 24
For the elevation and temperature data given in the table, the existing lapse rate in the environment is _______________ $\text{C}^{\circ} / 100 \mathrm{~m}$ ...

For the elevation and temperature data given in the table, the existing lapse rate in the environment is _______________ $\text{C}^{\circ} / 100 \mathrm{~m}$ (round off t...

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156

GATE Civil 2023 Set 2 | Question: 25
If the size of the ground area is $6 \mathrm{~km} \times 3 \mathrm{~km}$ and the corresponding photo size in the aerial photograph is $30 \mathrm{~cm} \times 15 \mathrm{~cm}$, then the scale of the photograph is $1 :$ ____________ (in integer).

If the size of the ground area is $6 \mathrm{~km} \times 3 \mathrm{~km}$ and the corresponding photo size in the aerial photograph is $30 \mathrm{~cm} \times 15 \mathrm{~...

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157

GATE Civil 2023 Set 2 | Question: 26
The solution of the differential equation $\frac{d^3 y}{d x^3}-5.5 \frac{d^2 y}{d x^2}+9.5 \frac{d y}{d x}-5 y=0$ is expressed as $y=C_1 e^{2.5 x}+C_2 e^{\alpha x}+C_3 e^{\beta x}$, where $C_1, C_2, C_3, \alpha$, and $\beta$ are constants ... following options is correct for the values of $\alpha$ and $\beta$ ? $1$ and $2$ $-1$ and $-2$ $2$ and $3$ $-2$ and $-3$

The solution of the differential equation$\frac{d^3 y}{d x^3}-5.5 \frac{d^2 y}{d x^2}+9.5 \frac{d y}{d x}-5 y=0$is expressed as $y=C_1 e^{2.5 x}+C_2 e^{\alpha x}+C_3 e^{\...

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158

GATE Civil 2023 Set 2 | Question: 27
Two vectors $\left[\begin{array}{llll}2 & 1 & 0 & 3\end{array}\right]^{T} $ and $\left[\begin{array}{cccc}1 & 0 & 1 & 2\end{array}\right]^{T}$ belong to the null space of a $4 \times 4$ matrix of rank $ 2.$ Which one of ... $\left[\begin{array}{llll}3 & 1 & 1 & 2\end{array}\right]^{T}$

Two vectors $\left[\begin{array}{llll}2 & 1 & 0 & 3\end{array}\right]^{T} $ and $\left[\begin{array}{cccc}1 & 0 & 1 & 2\end{array}\right]^{T}$ belong to the null space of...

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159

GATE Civil 2023 Set 2 | Question: 28
Cholesky decomposition is carried out on the following square matrix $[A]$. $[A]=\left[\begin{array}{cc} 8 & -5 \\ -5 & a_{22} \end{array}\right]$ Let $l_{\mathrm{ij}}$ and $a_{\mathrm{ij}}$ ... $[L]$ is $1.968,$ what is the value (rounded off to the nearest integer) of the element $a_{22}$? $5$ $7$ $9$ $11$

Cholesky decomposition is carried out on the following square matrix $[A]$.$$[A]=\left[\begin{array}{cc}8 & -5 \\-5 & a_{22}\end{array}\right]$$Let $l_{\mathrm{ij}}$ and ...

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160

GATE Civil 2023 Set 2 | Question: 29
In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of $\text{PQ, QR,}$ and $\text{RP}$ are $4, 3,$ and $5$ units, respectively. The principal stresses are ___________ . (round off to one ... $\sigma_{\mathrm{x}}=16.0 \mathrm{~MPa}, \sigma_y=138.5 \mathrm{~MPa}$

In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of $\text{PQ, QR,}$ and $\text{RP}$ are $4, 3,$ and $5$ ...

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