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GATE Civil 2022 Set 1 | Question: 25
The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)

The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)

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322

GATE Civil 2022 Set 1 | Question: 26
The Cartesian coordinates of a point $P$ in a right-handed coordinate system are $(1, 1, 1)$. The transformed coordinates of $P$ due to a $45^{\circ}$ clockwise rotation of the coordinates system about the positive $x$-axis are $\left ( 1, 0, \sqrt{2} \right )$ ... $\left ( -1, 0, \sqrt{2} \right )$ $\left ( -1, 0, -\sqrt{2} \right )$

The Cartesian coordinates of a point $P$ in a right-handed coordinate system are $(1, 1, 1)$. The transformed coordinates of $P$ due to a $45^{\circ}$ clockwise rotation ...

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323

GATE Civil 2022 Set 1 | Question: 27
A semi-circular bar of radius $\text{R m}$, in a vertical plane, is fixed at the end $G$, as shown in the figure. A horizontal load of magnitude $\text{P kN}$ is applied at the end $H$. The magnitude of the axial force, shear force, and bending moment at point $Q$ for ... $\frac{PR}{\sqrt{2}} \:kNm$ $\frac{P}{\sqrt{2}}\:kN,0\:kN$, and $\frac{PR}{\sqrt{2}} \:kNm$

A semi-circular bar of radius $\text{R m}$, in a vertical plane, is fixed at the end $G$, as shown in the figure. A horizontal load of magnitude $\text{P kN}$ is applied ...

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324

GATE Civil 2022 Set 1 | Question: 28
A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile load. The permissible stress in the angle is $150$ $\text{MPa}$ and the permissible shear stress ... $\text{mm}$ $380$ $\text{mm}$ and $151$ $\text{mm}$ $151$ $\text{mm}$ and $380$ $\text{mm}$

A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile lo...

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325

GATE Civil 2022 Set 1 | Question: 29
The project activities are given in the following table along with the duration and dependency. ... $20$ days, Critical path is $\text{P} \rightarrow \text{R}$

The project activities are given in the following table along with the duration and dependency.$$\begin{array}{|c|c|} \hline \textbf{Activities} & \textbf{Duration (days...

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326

GATE Civil 2022 Set 1 | Question: 30
The correct match between the physical states of the soils given is Group $\text{I}$ and the governing conditions given in Group $\text{II}$ ... $1-Q, 2-S, 3-P, 4-R$ $1-Q, 2-P, 3-R, 4-S$ $1-S, 2-Q, 3-P, 4-R$

The correct match between the physical states of the soils given is Group $\text{I}$ and the governing conditions given in Group $\text{II}$ is$\begin{array}{|c|c|} \hlin...

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327

GATE Civil 2022 Set 1 | Question: 31
As per Rankine's theory of earth pressure, the inclination of failure planes is $\left ( 45 + \frac{\phi }{2} \right )^{\circ}$ with respect to the direction of the minor principal stress. The above statement is correct ... passive state Only the passive state and not the active state Both active as well as passive states Neither active nor passive state

As per Rankine's theory of earth pressure, the inclination of failure planes is $\left ( 45 + \frac{\phi }{2} \right )^{\circ}$ with respect to the direction of the minor...

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328

GATE Civil 2022 Set 1 | Question: 32
Henry's law constant for transferring $O_{2}$ from air into water, at room temperature, is $1.3 \dfrac{\text{mmol}}{\text{liter-atm}}$. Given that the partial pressure of $O_{2}$ in the atmosphere is $0.21$ ... (Consider the molecular weight of $O_{2}$ as $32$ $\text{g/mol}$) $8.7$ $0.8$ $198.1$ $0.2$

Henry's law constant for transferring $O_{2}$ from air into water, at room temperature, is $1.3 \dfrac{\text{mmol}}{\text{liter-atm}}$. Given that the partial pressure of...

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329

GATE Civil 2022 Set 1 | Question: 33
In a water sample, the concentrations of $Ca^{2+}, Mg^{2+}$ and $\text{HCO}_{3}^{-}$ are $100$ $\text{mg/L}$, $36$ $\text{mg/L}$ and $122$ $\text{mg/L}$ ... $400$ and $100$, respectively. $400$ and $300$, respectively. $500$ and $100$, respectively. $800$ and $200$, respectively.

In a water sample, the concentrations of $Ca^{2+}, Mg^{2+}$ and $\text{HCO}_{3}^{-}$ are $100$ $\text{mg/L}$, $36$ $\text{mg/L}$ and $122$ $\text{mg/L}$, respectively. Th...

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330

GATE Civil 2022 Set 1 | Question: 34
Consider the four points $\text{P, Q, R and S}$ shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_{P}, k_{Q}, k_{R},$ and $k_{S}$ ... $k_{Q} > k_{R} > k_{S} > k_{P}$ $k_{Q} > k_{R} > k_{P} > k_{S}$

Consider the four points $\text{P, Q, R and S}$ shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_{P}, k_{Q}, k...

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331

GATE Civil 2022 Set 1 | Question: 35
Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 - x,x -1\}$? It is continuous on its domain. It has a local minimum at $x = 2$. It has a local maximum at $x = 2$. It is differentiable on its domain.

Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 -...

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332

GATE Civil 2022 Set 1 | Question: 36
A horizontal force of $\text{P kN}$ is applied to a homogeneous body of weight $25$ $\text{kN}$, as shown in the figure. The coefficient of friction between the body and the floor is $0.3$. Which of the following statement(s) is/are correct? ... the body never occurs. No motion occurs for $P\leq 6$ $\text{kN}$. The motion of the body will occur by sliding only

A horizontal force of $\text{P kN}$ is applied to a homogeneous body of weight $25$ $\text{kN}$, as shown in the figure. The coefficient of friction between the body and ...

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333

GATE Civil 2022 Set 1 | Question: 37
In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are In an aqueduct, natural drain water goes under the irrigation canal, ... drain water goes under the irrigation canal. In a canal syphon, natural drain water goes through the irrigation canal.

In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/areIn...

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334

GATE Civil 2022 Set 1 | Question: 38
Consider the differential equation $\frac{\mathrm{dy} }{\mathrm{d} x} = 4 \left ( x + 2 \right ) - y$ For the initial condition $y = 3$ at $x = 1$, the value of $y$ at $x = 1.4$ obtained using Euler’s method with a step-size of $0.2$ is ____________. (round off to one decimal place)

Consider the differential equation $$\frac{\mathrm{dy} }{\mathrm{d} x} = 4 \left ( x + 2 \right ) - y$$ For the initial condition $y = 3$ at $x = 1$, the value of $y$ at ...

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335

GATE Civil 2022 Set 1 | Question: 39
A set of observations of independent variable $(x)$ and the corresponding dependent variable $(y)$ ... regression model $y = a + bx$ is estimated as $6.1$. The coefficient $b$ is ____________________ (round off to one decimal place)

A set of observations of independent variable $(x)$ and the corresponding dependent variable $(y)$ is given below.$$\begin{array}{|c|c|} \hline\text{x} & 5 & 2 & 4 & 3 \\...

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336

GATE Civil 2022 Set 1 | Question: 40
The plane truss shown in the figure is subjected to an external force $P$. It is given that $P = 70\; kN$, $a = 2\; m$, and $b = 3\; m$. The magnitude (absolute value) of force (in $kN$) in member $EF$ is ______________. (round off to the nearest integer)

The plane truss shown in the figure is subjected to an external force $P$. It is given that $P = 70\; kN$, $a = 2\; m$, and $b = 3\; m$.The magnitude (absolute value) of ...

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337

GATE Civil 2022 Set 1 | Question: 41
Consider the linearly elastic plane frame shown in the figure. Members $\text{HF, FK and FG}$ are welded together at joint $F$. Joints $\text{K, G and H}$ are fixed supports. A counter-clockwise moment $M$ ... of the applied moment $\text{M (in kN-m)}$ to maintain static equilibrium is __________________ .(round off to the nearest integer)

Consider the linearly elastic plane frame shown in the figure. Members $\text{HF, FK and FG}$ are welded together at joint $F$. Joints $\text{K, G and H}$ are fixed suppo...

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338

GATE Civil 2022 Set 1 | Question: 42
Consider a simply supported beam $\text{PQ}$ as shown in the figure. A truck having $100$ $\text{kN}$ on the front axle and $200$ $\text{kN}$ on the rear axle, moves from left to right. The spacing between the axles is $3\: m$. The maximum bending moment at point $R$ is _______________ $\text{kNm}$ (in integer)

Consider a simply supported beam $\text{PQ}$ as shown in the figure. A truck having $100$ $\text{kN}$ on the front axle and $200$ $\text{kN}$ on the rear axle, moves from...

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339

GATE Civil 2022 Set 1 | Question: 43
A reinforced concrete beam with rectangular cross section (width = $300$ $\text{mm}$, effective depth = $580$ $\text{mm}$) is made of $M30$ grade concrete. It has $1\%$ longitudinal tension reinforcement of $\text{Fe}$ $415$ grade steel ... diameter vertical stirrups of $\text{Fe}$ $415$ grade steel is ____________ $\text{mm}$. (round off to the nearest integer)

A reinforced concrete beam with rectangular cross section (width = $300$ $\text{mm}$, effective depth = $580$ $\text{mm}$) is made of $M30$ grade concrete. It has $1\%$ l...

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340

GATE Civil 2022 Set 1 | Question: 44
A square concrete pile of $10\: m$ length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is $100$ $\text{kPa}$. ... $N_{c} = 9$; adhesion factor $\alpha = 0.7$)

A square concrete pile of $10\: m$ length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through...

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341

GATE Civil 2022 Set 1 | Question: 45
A raft foundation of $30\:m \times 25\:m$ is proposed to be constructed at a depth of $8\:m$ in a sand layer. A $25\:m$ thick saturated clay layer exists $2 m$ below the base of the raft foundation. Below the clay ... The time (in days) required for $25\%$ consolidation settlement of the raft foundation will be _______________ (round off to the nearest integer)

A raft foundation of $30\:m \times 25\:m$ is proposed to be constructed at a depth of $8\:m$ in a sand layer. A $25\:m$ thick saturated clay layer exists $2 m$ below the ...

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342

GATE Civil 2022 Set 1 | Question: 46
A two-hour duration storm event with uniform excess rainfall of $3\:cm$ ... the peak flow ordinate (in $m^{3}/s$) of one-hour unit hydrograph for the watershed is _________________. (in integer)

A two-hour duration storm event with uniform excess rainfall of $3\:cm$ occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are give...

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343

GATE Civil 2022 Set 1 | Question: 47
Two reservoirs are connected by two parallel pipes of equal length and of diameters $20\:cm$ and $10\:cm$, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is $5\:m$, the ratio ... ) (Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)

Two reservoirs are connected by two parallel pipes of equal length and of diameters $20\:cm$ and $10\:cm$, as shown in the figure (not drawn to scale). When the differenc...

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344

GATE Civil 2022 Set 1 | Question: 48
Depth of water flowing in a $3\:m$ wide rectangular channel is $2\:m$. The channel carries a discharge of $12\:m^{3}/s$. Take $g = 9.8\; m/s^{2}$. The bed width (in $m$) at contraction, which just causes the critical flow, is _____________ without changing the upstream water level. (round off to two decimal places)

Depth of water flowing in a $3\:m$ wide rectangular channel is $2\:m$. The channel carries a discharge of $12\:m^{3}/s$. Take $g = 9.8\; m/s^{2}$.The bed width (in $m$) a...

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345

GATE Civil 2022 Set 1 | Question: 49
A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of $\text{N, H, and O}$ as $14\:g/mol$, $1\:g/mol$, and $16\:g/mol$, respectively. In this wastewater, the ... . The total nitrogen concentration in this wastewater is _____________ milligram nitrogen per liter. (round off to one decimal place)

A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of $\text{N, H, and O}$ as $14\:g/mol$, $1\:g/mol$, and $16\:g/m...

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346

GATE Civil 2022 Set 1 | Question: 50
A $2\%$ sewage sample (in distilled water) was incubated for $3$ days at $27^{\circ}C$ temperature. After incubation, a dissolved oxygen depletion of $10\:mg/L$ was recorded. The biochemical oxygen demand $\text{(BOD)}$ ... $\text{BOD}$ (in $mg/L$) of the sewage will be __________________ (round off to the nearest integer)

A $2\%$ sewage sample (in distilled water) was incubated for $3$ days at $27^{\circ}C$ temperature. After incubation, a dissolved oxygen depletion of $10\:mg/L$ was recor...

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347

GATE Civil 2022 Set 1 | Question: 51
A water treatment plant has a sedimentation basin of depth $3\:m$, width $5\:m$, and length $40\:m$. The water inflow rate is $500\:m^{3}/h$. The removal fraction of particles having a settling velocity of $1.0\; m/h$ is __________ (round off to one decimal place) (Consider the particle density as $2650\; kg/m^{3}$ and liquid density as $991\; kg/m^{3})$

A water treatment plant has a sedimentation basin of depth $3\:m$, width $5\:m$, and length $40\:m$. The water inflow rate is $500\:m^{3}/h$. The removal fraction of part...

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348

GATE Civil 2022 Set 1 | Question: 52
A two-phase signalized intersection is designed with a cycle time of $100\:s$. The amber and red times for each phase are $4\:s$ and $50\:s$, respectively. If the total lost time per phase due to start-up and clearance is $2\:s$, the effective green time of each phase is __________________ $s$. (in integer)

A two-phase signalized intersection is designed with a cycle time of $100\:s$. The amber and red times for each phase are $4\:s$ and $50\:s$, respectively. If the total l...

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349

GATE Civil 2022 Set 1 | Question: 53
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of $4$ vehicles per hour and $2$ vehicles per hour, respectively. The probability of observing at least $2$ vehicles in $30$ minutes is ___________________. (round off to two decimal places)

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of $4$ vehicles per hour and $2$ vehicles per hour...

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350

GATE Civil 2022 Set 1 | Question: 54
The vehicle count obtained in every $10$ ... $\text{(PHF)}$ for $10$ minute sub-interval is ________________. (round off to one decimal place)

The vehicle count obtained in every $10$ minute interval of a traffic volume survey done in peak one hour is given below.$$\begin{array}{|c|c|} \hline \text{Time Interval...

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351

GATE Civil 2022 Set 1 | Question: 55
For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between the wheels, and $d$ is the clear distance between the wheels. ... round off to one decimal place) (Consider the influence angle to be $45^{\circ}$ for the linear dispersion of stress with depth)

For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between th...

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