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Recent questions tagged numerical-answers
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81
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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82
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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83
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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84
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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85
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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86
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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87
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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88
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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89
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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90
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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91
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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92
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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93
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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94
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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95
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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96
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 ______________
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
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Mar 1, 2021
Calculus
gatecivil-2021-set2
numerical-answers
calculus
definite-integral
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97
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 __________________________
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 materi...
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Solid Mechanics
gatecivil-2021-set2
numerical-answers
torsion
shear-stress
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98
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 ___________
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 vert...
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Structural Analysis
gatecivil-2021-set2
numerical-answers
analysis-of-beams
cantilever-beam
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99
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 ________________
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 (...
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Mar 1, 2021
Foundation Engineering
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numerical-answers
standard-and-cone-penetration-test
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100
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 _____________
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...
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Hydrology
gatecivil-2021-set2
numerical-answers
surface-runoff-models
rainfall
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101
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 ___________________
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...
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Mar 1, 2021
Fluid Mechanics
gatecivil-2021-set2
numerical-answers
momentum-and-energy-equations
fluid-statics
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102
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 _______________
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 th...
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5.3k
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Mar 1, 2021
Traffic Engineering
gatecivil-2021-set2
numerical-answers
traffic-signal
design-by-websters-method
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answers
103
GATE Civil 2021 Set 2 | Question: 25
A horizontal angle $\theta$ ... $\theta$ ( in degree, $\textit{round off to two decimal places}$is _________________
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&\tex...
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Geomatics Engineering
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numerical-answers
distance-angle-measurement
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104
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 _________
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,...
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Mar 1, 2021
Calculus
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numerical-answers
calculus
directional-derivatives
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answers
105
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 ________________________
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 diam...
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5.3k
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Mar 1, 2021
Solid Mechanics
gatecivil-2021-set2
numerical-answers
buckling-of-column
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0
answers
106
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 ______________
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 flexu...
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Mar 1, 2021
Structural Analysis
gatecivil-2021-set2
numerical-answers
stiffness-and-flexibility-methods
structural-analysis
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votes
1
answer
107
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 ________________________
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 ...
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Structural Analysis
gatecivil-2021-set2
numerical-answers
analysis-of-cables
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answers
108
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 __________
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 even...
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Fluid Mechanics
gatecivil-2021-set2
numerical-answers
properties-of-fluids
fluid-statics
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0
votes
0
answers
109
GATE Civil 2021 Set 2 | Question: 41
A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is $\text{16 mm}$. The values of modulus of elasticity of concrete and steel are $2.0 \times 10^{4} \text{ MPa}$ ... $\text{(x)}$ for the uncracked section (in $\text{mm}, \textit{round off to one decimal place}$) is ______________
A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is $\text{16 mm}$. The values of modulus of elastic...
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Mar 1, 2021
Concrete Structures
gatecivil-2021-set2
numerical-answers
prestressed-concrete-beams
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0
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0
answers
110
GATE Civil 2021 Set 2 | Question: 42
The activity details for a small project are given in the Table. ... $\text{days}, \textit{in integer}$) for project completion is __________________________
The activity details for a small project are given in the Table.$$\begin{array}{|cl|cI|cI|}\hline&\textbf{Activity} & \textbf{Duration (days)} & \textbf{Depends on} \\ \h...
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Construction Materials and Management
gatecivil-2021-set2
numerical-answers
construction-management
project-planning
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0
answers
111
GATE Civil 2021 Set 2 | Question: 43
An equipment has been purchased at an initial cost of $₹ 160000$ and has an estimated salvage value of $₹ 10000$. The equipment has an estimated life of $5$ years. The difference between the book values (in ₹, $\textit{in integer}$) ... at the end of $4^{\text{th}}$ year using straight line method and sum of years digit method of depreciation is______________
An equipment has been purchased at an initial cost of $₹ 160000$ and has an estimated salvage value of $₹ 10000$. The equipment has an estimated life of $5$ years. Th...
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Mar 1, 2021
Construction Materials and Management
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numerical-answers
cost-estimation
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votes
0
answers
112
GATE Civil 2021 Set 2 | Question: 44
A rectangular footing of size $\text{2.8 m}$ $\times$ $\text{3.5 m}$ is embedded in a clay layer and a vertical load is placed with an eccentricity of $\text{0.8 m}$ as shown in the figure (not to scale). Take Bearing ... $2.5$ is ________________________
A rectangular footing of size $\text{2.8 m}$ $\times$ $\text{3.5 m}$ is embedded in a clay layer and a vertical load is placed with an eccentricity of $\text{0.8 m}$ as s...
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5.3k
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Mar 1, 2021
Foundation Engineering
gatecivil-2021-set2
numerical-answers
shallow-foundation
meyerhoffs-bearing-capacity-theories
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0
votes
0
answers
113
GATE Civil 2021 Set 2 | Question: 45
The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table $\text{(GWT)}$ is located at the surface of the clay layer, and the ... $\text{m}$, $\textit{round off to two decimal places}$) of the clay layer resulting from this loading will be _____________________
The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table $\text{(GWT...
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Mar 1, 2021
Foundation Engineering
gatecivil-2021-set2
numerical-answers
settlement-analysis-in-clays
effect-of-water-table
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0
votes
0
answers
114
GATE Civil 2021 Set 2 | Question: 46
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \textit{round off to two decimal places}$) obtained is ________________
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \te...
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5.3k
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Mar 1, 2021
Numerical Methods
gatecivil-2021-set2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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0
votes
0
answers
115
GATE Civil 2021 Set 2 | Question: 47
The void ratio of a clay soil sample $\text{M}$ decreased from $0.575$ to $0.510$ when the applied pressure is increased from $\text{120 kPa}$ to $\text{180 kPa}$. For the same increment in pressure, the void ratio of another clay ... of consolidation of sample $\text{M}$ to sample $\text{N } (\textit{round off to three decimal places}$) is __________________
The void ratio of a clay soil sample $\text{M}$ decreased from $0.575$ to $0.510$ when the applied pressure is increased from $\text{120 kPa}$ to $\text{180 kPa}$. For th...
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5.3k
points
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Mar 1, 2021
Soil Mechanics
gatecivil-2021-set2
numerical-answers
time-rate-of-consolidation
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0
votes
0
answers
116
GATE Civil 2021 Set 2 | Question: 48
The hyetograph in the figure corresponds to a rainfall event of $\text{3 cm}$. If the rainfall event has produced a direct runoff of $\text{1.6 cm}$, the $\phi$-index of the event (in $\text{mm/hour},\textit{round off to one decimal place}$) would be
The hyetograph in the figure corresponds to a rainfall event of $\text{3 cm}$.If the rainfall event has produced a direct runoff of $\text{1.6 cm}$, the $\phi$-index of t...
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5.3k
points
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Mar 1, 2021
Hydrology
gatecivil-2021-set2
numerical-answers
surface-runoff-models
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–
0
votes
0
answers
117
GATE Civil 2021 Set 2 | Question: 49
A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of $\text{20 cm}$ diameter. Assume $g=9.8\text{ m/s}^{2}$ ... $\text{lps}$, round off to two decimal places) considering no loss in the venturimeter is ______________________
A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of $\text{20 cm}$ diameter.Assume $g=9.8\text{ m/s}^{2}$...
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5.3k
points
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Mar 1, 2021
Fluid Mechanics
gatecivil-2021-set2
numerical-answers
flow-in-pipes
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0
votes
0
answers
118
GATE Civil 2021 Set 2 | Question: 50
A reservoir with a live storage of $300$ million cubic metre irrigates $40000$ hectares ( $1$ hectare= $10^{4}\text{ m}^{2}$) of a crop with two fillings of the reservoir. If the base period of the crop is $120$ days, the duty for this crop (in hectares per cumec, $\textit{round off to integer}$) will then be _________
A reservoir with a live storage of $300$ million cubic metre irrigates $40000$ hectares ( $1$ hectare= $10^{4}\text{ m}^{2}$) of a crop with two fillings of the reservoir...
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Irrigation
gatecivil-2021-set2
numerical-answers
canals
canals-irrigation-system
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0
votes
0
answers
119
GATE Civil 2021 Set 2 | Question: 51
An activated sludge process $\text{(ASP)}$ is designed for secondary treatment of $7500\:m^{3}/$day of municipal wastewater. After primary clarifier, the ultimate $\text{BOD}$ of the influent, which enters into $\text{ASP}$ ... underflow volume (in $m^{3}$/day, $\textit{round off to one decimal place}$) of sludge wastage is _______________________
An activated sludge process $\text{(ASP)}$ is designed for secondary treatment of $7500\:m^{3}/$day of municipal wastewater. After primary clarifier, the ultimate $\text{...
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Mar 1, 2021
Water and Waste Water Quality and Treatment
gatecivil-2021-set2
numerical-answers
sludge-disposal
activated-sludge-process
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0
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0
answers
120
GATE Civil 2021 Set 2 | Question: 52
A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of $\text{0.25 mm}$ and specific gravity of $2.70$. The terminal settling velocity of the particles is estimated as $\text{2.5 cm/s}$. The ... the chamber (in $\text{m}, \textit{in integer}$) to remove $\text{0.25 mm}$ particles completely is ____________________
A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of $\text{0.25 mm}$ and specific gravity of $2.70$. The terminal settling ...
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Mar 1, 2021
Municipal Solid Wastes
gatecivil-2021-set2
numerical-answers
engineered-system-for-solid-waste-management
treatment-and-disposal
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