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1

GATE Civil 2022 Set 2 | Question: 1
The function $f(x,y)$ satisfies the Laplace equation $\bigtriangledown^{2}f(x,y) = 0$ on a circular domain of radius $r=1$ with its center at point $P$ with coordinates $x=0, y=0.$ The value of this function on the circular boundary of this domain is equal to $3.$ The numerical value of $f(0,0)$ is: $0$ $2$ $3$ $1$

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2

GATE Civil 2022 Set 2 | Question: 2
$\displaystyle{}\int \left( x-\frac{x^{2}}{2} + \frac{x^{3}}{3} – \frac{x^{4}}{4} + \dots \right) dx$ is equal to $\frac{1}{1+x} + $ Constant $\frac{1}{1+x^{2}} + $ Constant $-\frac{1}{1-x} + $ Constant $-\frac{1}{1-x^{2}} + $ Constant

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3

GATE Civil 2022 Set 2 | Question: 3
For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity $(E)$, Poisson’s ratio $(\nu),$ and shear modulus $(G)$ is $G= \frac{E}{2(1+\nu)}$ $G= \frac{E}{(1+2\nu)}$ $E= \frac{G}{2(1+\nu)}$ $E= \frac{G}{(1+2\nu)}$

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4

GATE Civil 2022 Set 2 | Question: 4
Read the following statements relating to flexure of reinforced concrete beams: In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain in steel. In under-reinforced sections, steel reaches yielding at a load lower than the load at which ... $\text{I(False), II(True), III(True), IV(False)}$

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5

GATE Civil 2022 Set 2 | Question: 5
Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties): ... $\text{(i) - (T), (ii) - (S), (iii) - (P) and (Q)}$

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6

GATE Civil 2022 Set 2 | Question: 6
Consider a beam $\text{PQ}$ fixed at $\text{P},$ hinged at $\text{Q},$ and subjected to a load $F$ as shown in figure (not drawn to scale). The static and kinematic degrees of indeterminacy, respectively, are $2$ and $1$ $2$ and $0$ $1$ and $2$ $2$ and $2$

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7

GATE Civil 2022 Set 2 | Question: 7
Read the following statements: While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity. For slope stability of an earthen dam, sudden drawdown is never a critical condition. In a sandy sea beach, quicksand condition ... $\text{(P)-False, (Q)-True, (R)-False, (S)-False}$

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8

GATE Civil 2022 Set 2 | Question: 8
Stresses acting on an infinitesimal soil element are shown in the figure (with $\sigma_{z} > \sigma_{x}$). The major and minor principal stresses are $\sigma_{1}$ and $\sigma_{3},$ respectively. Considering the compressive stresses as positive, which one of the following ... $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{1} + \sigma_{3}} \right)$

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9

GATE Civil 2022 Set 2 | Question: 9
Match $\textbf{Column X}$ and $\textbf{Column Y}:$ ... $\text{(P)-(III), (Q)-(IV), (R)-(I), (S)-(V), (T)-(II)}$

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10

GATE Civil 2022 Set 2 | Question: 10
In a certain month, the reference crop evapotranspiration at a location is $6 \; \text{mm/day.}$ If the crop coefficient and soil coefficient are $1.2$ and $0.8,$ respectively, the actual evapotranspiration in $\text{mm/day}$ is $5.76$ $7.20$ $6.80$ $8.00$

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11

GATE Civil 2022 Set 2 | Question: 11
The dimension of dynamic viscosity is: $\text{ML}^{-1} \text{T}^{-1}$ $\text{ML}^{-1} \text{T}^{-2}$ $\text{ML}^{-2} \text{T}^{-2}$ $\text{ML}^{0} \text{T}^{-1}$

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12

GATE Civil 2022 Set 2 | Question: 12
A process equipment emits $5 \; \text{kg/h}$ of volatile organic compounds $\text{(VOCs)}$. If a hood placed over the process equipment captures $95\%$ of the $\text{VOCs},$ then the fugitive emission in $\text{kg/h}$ is $0.25$ $4.75$ $2.50$ $0.48$

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13

GATE Civil 2022 Set 2 | Question: 13
Match the following attributes of a city with the appropriate scale of measurements. ... $\text{(P)-(I), (Q)-(II), (R)-(III), (S)-(IV)}$

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14

GATE Civil 2022 Set 2 | Question: 14
If the magnetic bearing of the Sun at a place at noon is $\text{S} \; 2^{\circ} \; \text{E},$ the magnetic declination (in $\textbf{degrees}$) at that place is $2^{\circ} \; \text{E}$ $2^{\circ} \; \text{W}$ $4^{\circ} \; \text{E}$ $4^{\circ} \; \text{W}$

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15

GATE Civil 2022 Set 2 | Question: 15
$\text{P}$ and $\text{Q}$ are two square matrices of the same order. Which of the following statement(s) is/are correct? If $\text{P}$ and $\text{Q}$ are invertible, then $\text{[PQ]}^{-1} = \text{Q}^{-1} \text{P}^{-1}.$ If $\text{P}$ and $\text{Q}$ are ... $\text{P}$ and $\text{Q}$ are not invertible, then $\text{[PQ]}^{-1} = \text{Q}^{-1} \text{P}^{-1}.$

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16

GATE Civil 2022 Set 2 | Question: 16
In a solid waste handling facility, the moisture contents $\text{(MC)}$ of food waste, paper waste, and glass waste were found to be $\text{MCf, MCp},$ and $\text{MCg,}$ respectively. Similarly, the energy contents $\text{(EC)}$ of plastic waste, food waste and ... $\text{ECpp > ECf > ECg}$ $\text{MCf < MCp < MCg}$ $\text{ECpp < ECf < ECg}$

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17

GATE Civil 2022 Set 2 | Question: 17
To design an optimum municipal solid waste collection route, which of the following is/are $\text{NOT}$ desired: Collection vehicle should not travel twice down the same street in a day. Waste collection on congested roads should not occur ... uphill direction. The last collection point on a route should be as close as possible to the waste disposal facility.

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18

GATE Civil 2022 Set 2 | Question: 18
For a traffic stream, $v$ is the space mean speed, $k$ is the density, $q$ is the flow, $\nu_{f}$ is the free flow speed, and $k_{j}$ ... $q =k_{j}v - \left( \frac{k_{j}}{v_{f}} \right) v^{2}$

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19

GATE Civil 2022 Set 2 | Question: 19
The error in measuring the radius of a $5 \; \text{cm}$ circular rod was $0.2 \%.$ If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is ____________. (round off to two decimal places)

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20

GATE Civil 2022 Set 2 | Question: 20
The components of pure shear strain in a sheared material are given in the matrix form: $ \varepsilon = \begin{bmatrix} 1 & 1 \\ 1 & – 1 \end{bmatrix}$ Here, $\text{Trace}(\varepsilon) = 0.$ Given, $ P = \text{Trace}(\varepsilon^{8})$ and $Q = \text{Trace}(\varepsilon^{11}).$ The numerical value of $(P + Q)$ is _____________. (in integer)

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21

GATE Civil 2022 Set 2 | Question: 21
The inside diameter of a sample tube is $50 \; \text{mm}.$ The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio $\text{(ICR)}$ is $1.0 \%$ to minimize the friction on the sample as the sampler tube enters into the soil. The inside diameter (in $\text{mm}$) of the cutting edge is _______________. (round off to two decimal places)

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22

GATE Civil 2022 Set 2 | Question: 22
A concentrically loaded isolated square footing of size $2 \; \text{m} \times 2 \; \text{m}$ carries a concentrated vertical load of $1000 \; \text{kN}.$ Considering Boussinesq's theory of stress distributed, the maximum depth (in ... pressure bulb corresponding to $10 \%$ of the vertical load intensity will be ____________. (round off to two decimal places)

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23

GATE Civil 2022 Set 2 | Question: 23
In a triaxial unconsolidated undrained $\text{(UU)}$ test on a saturated clay sample, the cell pressure was $100 \; \text{kPa}.$ If the deviatoric stress at failure was $150 \; \text{kPa},$ then the undrained shear strength of the soil is ___________ $\text{kPa}.$ (in integer)

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24

GATE Civil 2022 Set 2 | Question: 24
A flood control structure having an expected life of $n$ years is designed by considering a flood of return period $T$ years. When $T = n,$ and $n \rightarrow \infty,$ the structure’s hydrologic risk of failure in percentage is _______________. (round off to one decimal place)

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25

GATE Civil 2022 Set 2 | Question: 25
The base length of the runway at the mean sea level $\text{(MSL)}$ is $1500 \; \text{m}.$ If the runway is located at an altitude of $300 \; \text{m}$ above the $\text{(MSL)},$ the actual length (in $\text{m}$) of the runway to be provided is ____________. (round off to the nearest integer)

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26

GATE Civil 2022 Set 2 | Question: 26
Consider the polynomial $f(x) = x^{3} - 6x^{2} + 11x - 6$ on the domain $S$ given by $1 \leq x \leq 3.$ The first and second derivatives are $f'(x)$ and $f''(x).$ Consider the following statements: The given polynomial is zero at ... $\text{I}$ and $\text{IV}$ are correct. Only statements $\text{II}$ and $\text{IV}$ are correct.

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27

GATE Civil 2022 Set 2 | Question: 27
An undamped spring-mass system with mass $m$ and spring stiffness $k$ is shown in the figure. The natural frequency and natural period of this system are $\omega \; \text{rad/s}$ and $T \; \text{s},$ respectively. If the stiffness of the spring is doubled and the mass is ... $T/4 \; \text{s}$ $ \omega \; \text{rad/s}$ and $T \; \text{s}$

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28

GATE Civil 2022 Set 2 | Question: 28
For the square steel beam cross-section shown in the figure, the shape factor about $z - z$ axis is $S$ and the plastic moment capacity is $M_{p}.$ Consider yield stress $f_{y} = 250 \; \text{MPa}$ and $a = 100 \; \text{mm}.$ The values of $S$ and $M_{p}$ (rounded-off to one ... $S = 1.5, M_{p} = 58.9 \; \text{kN-m}$ $S = 1.5, M_{p} = 100.2 \; \text{kN-m}$

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29

GATE Civil 2022 Set 2 | Question: 29
A post-tensioned concrete member of span $15 \; \text(m)$ and cross-section of $450 \; \text{mm} \times 450 \; \text{mm}$ is prestressed with three steel tendons, each of cross-sectional area $200 \; \text{mm}^{2}.$ The tendons are tensioned one after another to a ... is $14.16 \; \text{MPa}$ $7.08 \; \text{MPa}$ $28.32 \; \text{MPa}$ $42.48 \; \text{MPa}$

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30

GATE Civil 2022 Set 2 | Question: 30
Match the following in $\textbf{Column X}$ with $\textbf{Column Y}:$ ... $\text{(P)-(I), (Q)-(II), (R)-(V), (S)-(VI)}$

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31

GATE Civil 2022 Set 2 | Question: 31
A soil sample is underlying a water column of height $h_{1},$ as shown in the figure. The vertical effective stresses at points $\text{A, B,}$ and $\text{C}$ are $\sigma'_{A}, \sigma'_{B},$ and $\sigma'_{C},$ respectively. Let $\gamma_{\text{sat}}$ ... $(h_{1} + h_{2} + h_{3})\gamma_{\text{sat}}$

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32

GATE Civil 2022 Set 2 | Question: 32
A $100 \; \text{mg}$ of $\text{HNO}_{3}$ (strong acid) is added to water, bringing the final volume to $1.0 \; \text{liter}.$ Consider the atomic weights of $\text{H, N,}$ and $\text{O,}$ ... $\text{pH}$ of this water is (Ignore the dissociation of water.) $2.8$ $6.5$ $3.8$ $8.5$

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33

GATE Civil 2022 Set 2 | Question: 33
In a city, the chemical formula of biodegradable fraction of municipal solid waste $\text{(MSW)}$ is $\text{C}_{100} \text{H}_{250} \text{O}_{80} \text{N}.$ The waste has to be treated by forced-aeration composting process for which air requirement has to ... (in $\text{m}^{3}/\text{tonne}$) will be (round off to the nearest integer) $4749$ $8025$ $1418$ $1092$

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34

GATE Civil 2022 Set 2 | Question: 34
A single-lane highway has a traffic density of $40 \; \text{vehicle/km}.$ If the time-mean speed and space-mean speed are $40 \; \text{kmph}$ and $30 \; \text{kmph},$ respectively, the average headway $\text{(in seconds)}$ between the vehicles is $3.00$ $2.25$ $8.33 \times 10^{-4}$ $6.25 \times 10^{-4}$

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35

GATE Civil 2022 Set 2 | Question: 35
Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$ $yy^{T}$ is a symmetric matrix. $y^{T}y$ is an eigenvalue of $yy^{T}.$ $yy^{T}$ has a rank of $2022.$ $yy^{T}$ is invertible.

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36

GATE Civil 2022 Set 2 | Question: 36
Which of the following statements(s) is/are correct? If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that ... loaded by the $\text{M/EI}$ diagram of the real beam is equal to the corresponding deflection of the real beam.

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37

GATE Civil 2022 Set 2 | Question: 37
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section ... . In choked condition, $y_{1}$ increases if the flow is supercritical and decreases if the flow is subcritical.

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38

GATE Civil 2022 Set 2 | Question: 38
The concentrations $s(x,t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation $\frac{\partial s (x,t)}{\partial t} = D \frac{\partial^{2}s (x,t)}{\partial x^{2}}$ ... $x=\dfrac{L}{2}$ of the reservoir (in $\mu \text{mol/m}$) is ______________. (in integer)

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39

GATE Civil 2022 Set 2 | Question: 39
A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals $4$ in exactly two of the three attempts is _______. (round off to three decimal places)

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40

GATE Civil 2022 Set 2 | Question: 40
Consider two linear elastic rods $HI$ and $IJ$, each of length $b$, as shown in the figure. The rods are co-linear, and confined between two fixed supports at $H$ and $J.$ Both the rods are initially stress free. The coefficient of linear thermal ... to zero, the value of the external force $P$ (in $\text{N}$) is ____________ . (round off to the nearest integer)

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