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GATE Civil 2023 Set 1 | Question: 23
A canal supplies water to an area growing wheat over $100$ hectares. The duration between the first and last watering is $120$ days, and the total depth of water required by the crop is $35 \mathrm{~cm}$. The most intense watering is required ... , rounded off to three decimal places) in the canal to satisfy the crop requirement is __________.

A canal supplies water to an area growing wheat over $100$ hectares. The duration between the first and last watering is $120$ days, and the total depth of water required...

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322

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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323

GATE Civil 2023 Set 1 | Question: 39
Consider the beam shown in the figure (not to scale), on a hinge support at end $\mathrm{A}$ and a roller support at end $\mathrm{B}$. The beam has a constant flexural rigidity, and is subjected to the external ... statements is/are TRUE? Support reactions are zero Shear force is zero everywhere Bending moment is zero everywhere Deflection is zero everywhere

Consider the beam shown in the figure (not to scale), on a hinge support at end $\mathrm{A}$ and a roller support at end $\mathrm{B}$. The beam has a constant flexural ri...

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324

GATE Civil 2023 Set 1 | Question: 41
Which of the following options match the test reporting conventions with the given material tests in the table? ... $\text{(P) - (VI); (Q) - (III); (R) - (IV); (S) - (VII)}$

Which of the following options match the test reporting conventions with the given material tests in the table?$$\begin{array}{|l|l|}\hline \textbf{Test reporting convent...

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325

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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326

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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327

GATE Civil 2023 Set 1 | Question: 37
For the matrix $[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$ which of the following statements is/are TRUE? The eigenvalues of $[A]^{T}$ are same as the eigenvalues of $[A]$ The ... $[A]^{T}$ are same as the eigenvectors of $[A]$ The eigenvectors of $[A]^{-1}$ are same as the eigenvectors of $[A]$

For the matrix$$[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$$which of the following statements is/are TRUE?The eigenvalues of $[A]^{T}...

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328

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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329

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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330

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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331

GATE Civil 2023 Set 1 | Question: 42
The differential equation, $\frac{\mathrm{d} u}{\mathrm{~d} t}+2 t u^2=1,$ is solved by employing a backward difference scheme within the finite difference framework. The value of $u$ at the $(n-1)^{\text {th }}$ time-step, for some $n$, ... $0.01 \mathrm{~s}$ long. Then, the value of $\left(u_n-u_{n-1}\right)$ is__________ (round off to three decimal places).

The differential equation,$$\frac{\mathrm{d} u}{\mathrm{~d} t}+2 t u^2=1,$$is solved by employing a backward difference scheme within the finite difference framework. The...

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332

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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333

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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334

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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335

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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336

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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337

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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338

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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339

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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340

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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341

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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342

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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343

GATE Civil 2024 Set 1 | Question: 8
A $2 \mathrm{~m}$ wide strip footing is founded at a depth of $1.5 \mathrm{~m}$ below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of $40 \mathrm{kPa}$. Due to seasonal ... peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi's theory, will remain the same decrease increase become zero

A $2 \mathrm{~m}$ wide strip footing is founded at a depth of $1.5 \mathrm{~m}$ below the ground level in a homogeneous pure clay bed. The clay bed has uni...

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344

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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345

GATE Civil 2024 Set 1 | Question: 14
Which one of the following statements related to bitumen is FALSE? Kinematic viscosity is a measure of resistance to the flow of molten bitumen under gravity. Softer grade bitumen possesses higher softening point than hard grade bitumen. ... specified test conditions. Ductility test is carried out on bitumen to test its adhesive property and ability to stretch.

Which one of the following statements related to bitumen is FALSE?Kinematic viscosity is a measure of resistance to the flow of molten bitumen under gravity.Softer grade ...

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346

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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347

GATE Civil 2024 Set 1 | Question: 16
A surveyor observes a zenith angle of $93^{\circ} 00^{\prime} 00^{\prime \prime}$ during a theodolite survey. The corresponding vertical angle is $-03^{\circ} 00^{\prime} 00^{\prime \prime}$ $+03^{\circ} 00^{\prime} 00^{\prime \prime}$ $-87^{\circ} 00^{\prime} 00^{\prime \prime}$ $+87^{\circ} 00^{\prime} 00^{\prime \prime}$

A surveyor observes a zenith angle of $93^{\circ} 00^{\prime} 00^{\prime \prime}$ during a theodolite survey. The corresponding vertical angle is$-03^{\circ} 00^{\prime} ...

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348

GATE Civil 2024 Set 1 | Question: 12
A car is travelling at a speed of $60 \mathrm{~km} / \mathrm{hr}$ on a section of a National Highway having a downward gradient of $2 \%$. The driver of the car suddenly observes a stopped vehicle on the car path at a distance $130 \mathrm{~m}$ ahead, and applies ... the car to a safe stop lies in the range $126$ to $130$ $41$ to $45$ $33$ to $37$ $75$ to $79$

A car is travelling at a speed of $60 \mathrm{~km} / \mathrm{hr}$ on a section of a National Highway having a downward gradient of $2 \%$. The driver of the car suddenly ...

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349

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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350

GATE Civil 2024 Set 1 | Question: 33
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on $11 \%$ Oxygen) for $\mathrm{HCl}$ ... is lesser than the emission standard. No compliance, as the Oxygen is greater than $11 \%$ in the flue gas.

For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air...

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351

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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