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81
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 $2$
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 degre...
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Feb 15, 2022
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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 ... $\text{(P)-False, (Q)-True, (R)-False, (S)-False}$
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 sta...
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Feb 15, 2022
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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 ... $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{1} + \sigma_{3}} \right)$
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 $\si...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 9
Match $\textbf{Column X}$ and $\textbf{Column Y}:$ ... $\text{(P)-(III), (Q)-(IV), (R)-(I), (S)-(V), (T)-(II)}$
Match $\textbf{Column X}$ and $\textbf{Column Y}:$$$\begin{array} {|l|l|} \hline \quad \textbf{Column X} & \qquad \textbf{Column Y} \\\hline \text{(P) Horton equation} ...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 10
In a certain month, the reference crop evapotranspiration at a location is $6 \; \text{mm/day.}$ If the crop coefficient and soil coefficient are $1.2$ and $0.8,$ respectively, the actual evapotranspiration in $\text{mm/day}$ is $5.76$ $7.20$ $6.80$ $8.00$
In a certain month, the reference crop evapotranspiration at a location is $6 \; \text{mm/day.}$ If the crop coefficient and soil coefficient are $1.2$ and $0.8,$ respect...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 11
The dimension of dynamic viscosity is: $\text{ML}^{-1} \text{T}^{-1}$ $\text{ML}^{-1} \text{T}^{-2}$ $\text{ML}^{-2} \text{T}^{-2}$ $\text{ML}^{0} \text{T}^{-1}$
The dimension of dynamic viscosity is:$\text{ML}^{-1} \text{T}^{-1}$$\text{ML}^{-1} \text{T}^{-2}$$\text{ML}^{-2} \text{T}^{-2}$$\text{ML}^{0} \text{T}^{-1}$
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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 $0.25$ $4.75$ $2.50$ $0.48$
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...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 13
Match the following attributes of a city with the appropriate scale of measurements. ... $\text{(P)-(I), (Q)-(II), (R)-(III), (S)-(IV)}$
Match the following attributes of a city with the appropriate scale of measurements.$$\begin{array} {|l|l|} \hline \qquad \qquad \qquad \textbf{Attribute} & \textbf{ Sca...
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Feb 15, 2022
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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}$
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} ...
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Feb 15, 2022
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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}.$
$\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 ...
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Feb 15, 2022
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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}$
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,}$ ...
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Feb 15, 2022
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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.
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 s...
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Feb 15, 2022
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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}$
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}$ is the jam density. Assume that the ...
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Feb 15, 2022
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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)
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 ...
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Feb 15, 2022
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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)
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{Tra...
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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)
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 \%$...
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Feb 15, 2022
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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)
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 Bous...
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Feb 15, 2022
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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)
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 $...
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Feb 15, 2022
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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)
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,$ th...
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Feb 15, 2022
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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)
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{(M...
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Feb 15, 2022
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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.
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)...
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Feb 15, 2022
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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}$
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...
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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}$
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 stres...
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Feb 15, 2022
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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}$
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...
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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)}$
Match the following in $\textbf{Column X}$ with $\textbf{Column Y}:$$\begin{array} {|l|l|} \hline \qquad \qquad \qquad \qquad \qquad \textbf{Column X} & \textbf{Column Y}...
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Feb 15, 2022
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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 $\gamma_{\text{sat}}$ ... $(h_{1} + h_{2} + h_{3})\gamma_{\text{sat}}$
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�...
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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.) $2.8$ $6.5$ $3.8$ $8.5$
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,}...
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Feb 15, 2022
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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) $4749$ $8025$ $1418$ $1092$
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...
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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 $3.00$ $2.25$ $8.33 \times 10^{-4}$ $6.25 \times 10^{-4}$
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 $30 \; \text{kmph},$ res...
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Feb 15, 2022
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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.
Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$$yy^{T}$ is a symmetric matrix.$y^{T}y$ is an eigenvalue of...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 36
Which of the following statements(s) is/are correct? If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that ... loaded by the $\text{M/EI}$ diagram of the real beam is equal to the corresponding deflection of the real beam.
Which of the following statements(s) is/are correct?If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with...
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GATE Civil 2022 Set 2 | Question: 37
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section ... . In choked condition, $y_{1}$ increases if the flow is supercritical and decreases if the flow is subcritical.
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to rea...
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GATE Civil 2022 Set 2 | Question: 38
The concentrations $s(x,t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation $\frac{\partial s (x,t)}{\partial t} = D \frac{\partial^{2}s (x,t)}{\partial x^{2}}$ ... $x=\dfrac{L}{2}$ of the reservoir (in $\mu \text{mol/m}$) is ______________. (in integer)
The concentrations $s(x,t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation$$\frac{\partial s (x,t)}{\partial t...
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Feb 15, 2022
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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)
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 of...
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Feb 15, 2022
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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)
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....
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 41
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the help of the vertical linear spring constant $k= 20 \; \text{kN/m}.$ The fixed ... $Q$ (in $\text{kN}$) is __________.(round off to the nearest integer)
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the hel...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 42
A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given that $w = 10 \; \text{kN}, a = 4 \; \text{m}$ ... of static friction that is required at the point $J$ to hold the rod in equilibrium is _________. (round off to three decimal places)
A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given ...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 43
The activities of a project are given in the following table along with their durations and dependency. ... $\text{E}$ (in $\textbf{days}$) is ___________. (in integer)
The activities of a project are given in the following table along with their durations and dependency.$$ \begin{array} {|c|c|c|} \hline \textbf{Activities}& \textbf{Dura...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 44
A group of total $16$ piles are arranged in a square grid format. The center-to-center spacing $(s)$ between adjacent piles is $3 \; \text{m}.$ The diameter $(d)$ and length of embedment of each pile are $1 \; \text{m}$ and ... value of the pile group capacity (in $\text{kN}$) in the vertical downward direction is _______. (round off to the nearest integer)
A group of total $16$ piles are arranged in a square grid format. The center-to-center spacing $(s)$ between adjacent piles is $3 \; \text{m}.$ The diameter $(d)$ and len...
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Feb 15, 2022
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GATE Civil 2022 Set 2 | Question: 45
A saturated compressible clay layer of thickness $h$ is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point $\text{P},$ which is located at the mid-depth of the clay layer, ... $\text{P}$ is ___________. (in integer)
A saturated compressible clay layer of thickness $h$ is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pr...
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