GATE Civil Q&A

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1

GATE Civil 2021 Set 2 | Question: 1
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is $0$ $1.0$ $0.5$ $\infty$

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2

GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$

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3

GATE Civil 2021 Set 2 | Question: 3
The unit normal vector to the surface $X^{2} + Y^{2} + Z^{2} – 48 = 0$ at the point $(4, 4, 4)$ is $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}}$ $\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}}$

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4

GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$

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5

GATE Civil 2021 Set 2 | Question: 5
In general, the $\text{CORRECT}$ sequence of surveying operations is Field observations $\rightarrow$ Reconnaissance $\rightarrow$ Data analysis $\rightarrow$ Map making Data analysis $\rightarrow$ Reconnaissance $\rightarrow$ Field ... $\rightarrow$ Data analysis $\rightarrow$ Field observations $\rightarrow$ Map making

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6

GATE Civil 2021 Set 2 | Question: 6
Strain hardening of structural steel means experiencing higher stress than yield stress with increased deformation strengthening steel member externally for reducing strain experienced strain occurring before plastic flow of steel material decrease in the stress experienced with increasing strain

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7

GATE Civil 2021 Set 2 | Question: 7
A single story building model is shown in the figure. The rigid bar of mass $\text{m}$' is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force $\text{(P)}$ ... $6\sqrt{\frac{6EI}{mL^{3}}}\text{rad/s}$ $\frac{2}{L}\sqrt{\frac{EI}{m}}\text{rad/s}$

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8

GATE Civil 2021 Set 2 | Question: 8
Seasoning of timber for use in construction is done essentially to increase strength and durability smoothen timber surfaces remove knots from timber logs cut timber in right season and geometry

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9

GATE Civil 2021 Set 2 | Question: 9
In case of bids in Two-Envelop System, the correct option is Technical bid is opened first Financial bid is opened first Both (Technical and Financial) bids are opened simultaneously Either of the two (Technical and Financial) bids can be opened first

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10

GATE Civil 2021 Set 2 | Question: 10
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is consolidated drained test unconsolidated undrained test consolidated undrained test unconfined compression test

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11

GATE Civil 2021 Set 2 | Question: 11
As per the Unified Soil Classification System $\text{(USCS)}$, the type of soil represented by $\text{MH}$' is Inorganic silts of high plasticity with liquid limit more than $50\%$ Inorganic silts of low plasticity with liquid limit less ... high plasticity with liquid limit less than $50\%$ Inorganic clays of low plasticity with liquid limit more than $50\%$

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12

GATE Civil 2021 Set 2 | Question: 12
The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe is $\frac{1}{2}$ $\frac{2}{3}$ $1$ $\frac{3}{2}$

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13

GATE Civil 2021 Set 2 | Question: 13
Relationship between traffic speed and density is described using a negatively sloped straight line. If $v_{f}$ is the free flow speed then the speed at which the maximum flow occurs is $0$ $\frac{v_{f}}{4}$ $\frac{v_{f}}{2}$ $v_{f}$

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14

GATE Civil 2021 Set 2 | Question: 14
Determine the correctness or otherwise of the following Assertion $\text{[a]}$ and the Reason $\text{[r]}$. $\text{Assertion [a]}$: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials. $\text{Reason [r]}$: Solid ... Both $\text{[a]}$ and $\text{[r]}$ are false $\text{[a]}$ is true but $\text{[r]}$ is false

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15

GATE Civil 2021 Set 2 | Question: 15
The hardness of a water sample is measured directly by titration with $\text{0.01 M}$ solution of ethylenediamine tetraacetic acid $\text{(EDTA)}$ using eriochrome black $\text{T (EBT)}$ as an indicator. The $\text{EBT}$ reacts ... colour of the solution changes from blue-green to reddish brown blue to colourless reddish brown to pinkish yellow Wine red to blue

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16

GATE Civil 2021 Set 2 | Question: 16
The softening point of bitumen has the same unit as that of distance temperature time viscosity

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17

GATE Civil 2021 Set 2 | Question: 17
Which of the following statement$\text{(s)}$ is/are correct? Increased levels of carbon monoxide in the indoor environment result in the formation of carboxyhemoglobin and the long term exposure becomes a cause of cardiovascular diseases ... in the indoor environment will result in the formation of photochemical smog which is a cause of cardiovascular diseases

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18

GATE Civil 2021 Set 2 | Question: 18
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________

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19

GATE Civil 2021 Set 2 | Question: 19
A solid circular torsional member $\text{OPQ}$ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is $\text{160 MPa}$. The absolute maximum shear stress in the member (in $\text{MPa}$, $\textit{round off to one decimal place}$) is __________________________

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20

GATE Civil 2021 Set 2 | Question: 20
A propped cantilever beam $\text{XY}$, with an internal hinge at the middle, is carrying a uniformly distributed load of $\text{10 kN/m}$, as shown in the figure. The vertical reaction at support $\text{X}$ ( in $\text{kN}$, $\textit{in integer}$) is ___________

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21

GATE Civil 2021 Set 2 | Question: 21
The internal $(d_{i})$ and external $(d_{o})$ diameters of a Shelby sampler are $\text{48 mm}$ and $\text{52 mm}$, respectively. The area ratio $(A_{r})$ of the sampler (in $\%, \textit{round off to two decimal palces}$) is ________________

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22

GATE Civil 2021 Set 2 | Question: 22
A $12$-hour unit hydrograph (of $\text{1 cm}$ excess rainfall) of a catchment is of a triangular shape with a base width of $144$ hour and a peak discharge of $23\text{ m}^3\text{/s}$. The area of the catchment (in $\text{km}^2, \textit{round off to the nearest integer}$) is _____________

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23

GATE Civil 2021 Set 2 | Question: 23
A lake has a maximum depth of $\text{60 m}$. If the mean atmospheric pressure in the lake region is $\text{91 kPa}$ and the unit weight of the lake water is $\text{9790 N/m}^{3}$, the absolute pressure (in $\text{kPa}, \textit{round off to two decimal places}$) at the maximum depth of the lake is ___________________

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24

GATE Civil 2021 Set 2 | Question: 24
In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are $0.18, 0.32$, and $0.22$. The total loss time in each of the phases is $\text{2 s}$. As per Webster's formula, the optimal cycle length (in $\text{s}, \textit{round off to the nearest integer}$) is _______________

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25

GATE Civil 2021 Set 2 | Question: 25
A horizontal angle $\theta$ is measured by four different surveyors multiple times and the values reported are given below. $\begin{array}{|lc|cI|cI|cI|cI|cI|}\hline &\text{Surveyor} & \text{Angle $ ... $\theta$ ( in degree, $\textit{round off to two decimal places}$is _________________

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26

GATE Civil 2021 Set 2 | Question: 26
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$

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27

GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are $1.55$ and $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$ $2.00$ ... and $\begin{Bmatrix} -2.55\\ -0.45 \end{Bmatrix}$ $1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$

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28

GATE Civil 2021 Set 2 | Question: 28
A prismatic steel beam is shown in the figure. The plastic moment, $M_{P}$ calculated for the collapse mechanism using static method and kinematic method is $M_{P,static}> \frac{2PL}{9}=M_{P,kinematic}$ $M_{P,static}= \frac{2PL}{9}\neq M_{P,kinematic}$ $M_{P,static}= \frac{2PL}{9}= M_{P,kinematic}$ $M_{P,static}< \frac{2PL}{9}= M_{P,kinematic}$

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29

GATE Civil 2021 Set 2 | Question: 29
A frame $\text{EFG}$ is shown in the figure. All members are prismatic and have equal flexural rigidity. The member $\text{FG}$ carries a uniformly distributed load $\text{w}$ per unit length. Axial deformation of any member is neglected. Considering the joint $\text{F}$ being ... $\text{0.375 wL}$ $\text{0.453 wL}$ $\text{0.482 wL}$ $\text{0.500 wL}$

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30

GATE Civil 2021 Set 2 | Question: 30
A clay layer of thickness $\text{H}$ has a preconsolidation pressure $p_{c}$ and an initial void ratio $e_{0}$.The initial effective overburden stress at the mid-height of the layer is $p_{0}$. At the same location, the increment in effective stress due to applied external load ...

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31

GATE Civil 2021 Set 2 | Question: 31
A rectangular open channel of $\text{6 m}$ width is carrying a discharge of $20 \text{ m$^{3}$/s}$. Consider the acceleration due to gravity as $9.81 \text{ m/s}^{2}$ and assume water as incompressible and inviscid. The depth of flow in the channel at which the ... the given discharge will then be $\text{0.82 m}$ $\text{1.04 m}$ $\text{2.56 m}$ $\text{3.18 m}$

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32

GATE Civil 2021 Set 2 | Question: 32
Read the statements given below. Value of the wind profile exponent for the 'very unstable' atmosphere is smaller than the wind profile exponent for the 'neutral' atmosphere. Downwind concentration of air pollutants due to an elevated point source will be inversely ... is False and $\text{iii}$ is False $\text{iii}$ is False and $\text{iv}$ is False

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33

GATE Civil 2021 Set 2 | Question: 33
A water filtration unit is made of uniform-size sand particles of $\text{0.4 mm}$ diameter with a shape factor of $0.84$ and specific gravity of $2.55$. The depth of the filter bed is $\text{0.70 m}$ and the porosity is $0.35$. The filter bed is to be expanded to a ... $6.35 \times 10^{-3}\text{ m/s}$ $0.69 \text{ cm/s}$ $0.75 \text{ cm/s}$

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34

GATE Civil 2021 Set 2 | Question: 34
For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to $\text{+2.1 m}$ and the sum of departures is equal to $\text{-2.8 m}$. The length and bearing of the closing error, respectively, are $\text{3.50 m}$ ... $53.13^{\circ}$ $\text{SE}$ $\text{3.50 m}$ and $53.13^{\circ}$ $\text{SE}$

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35

GATE Civil 2021 Set 2 | Question: 35
From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as $60\%, 27\%, 32\%$ and $27$, respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, are $0.15$ and $1.22$ $0.19$ and $6.60$ $1.22$ and $0.15$ $6.60$ and $0.19$

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36

GATE Civil 2021 Set 2 | Question: 36
A function is defined in Cartesian coordinate system as $f(x,y)=xe^{y}$. The value of the directional derivative of the function ($\textit{in integer}$) at the point $(2,0)$ along the direction of the straight line segment from point $(2, 0)$ to point $\left ( \dfrac{1}{2} ,2\right )$ is _________

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37

GATE Civil 2021 Set 2 | Question: 37
An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of $\text{1.5 m}$. It is supported on a solid steel circular column of diameter $\text{75 mm}$ and total height $\text{(L)}$ of $\text{4m}$ ... $\text{(h)}$ of the water permissible (in $\text{m}$, $\textit{round off to one decimal place}$) is ________________________

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38

GATE Civil 2021 Set 2 | Question: 38
A prismatic fixed-fixed beam, modelled with a total lumped-mass of $\text{10 kg}$ as a single degree of freedom $\text{(SDOF)}$ system is shown in the figure. If the flexural stiffness of the beam is $4 \pi ^{2}$ $\text{kN/m}$, its natural frequency of vibration (in $\text{Hz}$, $\textit{in integer}$) in the flexural mode will be ______________

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39

GATE Civil 2021 Set 2 | Question: 39
A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at $\text{F}$ and $\text{G}$ are acting vertically. The magnitude of tension in the cable segment $\text{FG}$ (in $\text{kN}, \textit{round off to two decimal places}$) is ________________________

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40

GATE Civil 2021 Set 2 | Question: 40
A fire hose nozzle directs a steady stream of water of velocity $\text{50 m/s}$ at an angle of $45^{\circ}$ above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and ... ) reached by the stream above the hose nozzle will then be __________

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