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Recent questions tagged numerical-answers

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GATE2018 CE-2: 42
A cable PQ of length $25$ m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is $20$ m. A point load of $15...
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GATE2018 CE-2: 40
A prismatic propped cantilever beam of span $L$ and plastic moment capacity $M_p$ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is...
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GATE2018 CE-2: 38
An $8$ m long simply-supported elastic beam of rectangular cross-section ($100$ mm $\times 200 $mm) is subjected to a uniformly distributed load of $10$ kN/m over its ent...
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GATE2018 CE-2: 39
A prismatic beam P-Q-R of flexural rigidity $EI = 1 \times 10^4 kNm^2$ is subjected to a momemnt of $180 kNm$ at Q as shown in the figureThe rotation at Q (in rad. up to ...
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GATE2018 CE-2: 37
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r...
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GATE2018 CE-2: 43
The compression curve (void ratio $e$ vs. effective stress, $\sigma_v^{\text{'}}$ for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes th...
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GATE2018 CE-2: 44
The total horizontal and vertical stresses at a point X in a saturated sandy medium are $170$ kPa and $300$ kPa, respectively. The static pore-water pressure is $30$ kPa....
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GATE2018 CE-2: 45
A group of nine piles in a $ 3 \times 3$ square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. ...
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GATE2018 CE-2: 20
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using New...
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GATE2018 CE-2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
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GATE2018 CE-2: 25
A culvert is designed for a flood frequency of $100$ years and a useful life of $20$ years. The risk involved in the design of the culvert (in percentage, up to two decim...
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GATE2018 CE-2: 21
As per $\text{IS }456:2000$, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section...
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GATE2018 CE-2: 22
A reinforced-concrete slab with effective depth of $80$ mm is simply supported at two opposite ends on $230$ mm thick masonry walls. The centre-to-centre distance between...
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GATE2018 CE-2: 23
A fillet weld is simultaneously subjected to factored normal and shear stresses of $120$ MPa and $50$ MPa, respectively. As per $\text{ IS }800:2007$, the equivalent stre...
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GATE2018 CE-2: 24
The intensity of irrigation for the $\textit{kharif}$ season is $50 \%$ for an irrigation project with culturable command area of $50,000 $ hectares. The duty for the $\t...
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GATE2018 CE-1: 52
The ultimate BOD $(L_0)$ of a wastewater sample is estimated as $87 \%$ of COD. The COD of this wastewater is $300$ mg/L. Considering first order BOD reaction rate consta...
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GATE2018 CE-1: 47
A rigid smooth retaining wall of height $7$ m with vertical backface retains saturated clay ass backfill. The saturated unit weight and undrained cohesion of the backfill...
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GATE2018 CE-1: 51
A water sample analysis data is given below,$$\begin{array}{|c|c|} \hline \textbf{Ion} & \textbf{Concentration, mg/L} & \textbf{Atomic Weight} \\ \hline Ca^{2+} & 60 & 40...
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GATE2018 CE-1: 48
Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below$$\begin{array}{|c|c|} \hline\textbf{Rain Gaug...
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GATE2018 CE-1: 49
The infiltration rate $f$ in a basin under ponding condition is given by $f = 30+10e^{-2t}$ where, $f$ is in mm/h and $t$ is time in hour. Total depth of infiltration (in...
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GATE2018 CE-1: 53
A waste activated sludge (WAS) is to be blended with green waste (GW). The carbon (C) and nitrogen (N) contents, per kg of WAS and GW, on dry basis are given in the table...
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GATE2018 CE-1: 50
In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are $\text{0.05}$ $m^{3}/s$ and $\text{0.25}$ $m...
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GATE2018 CE-1: 54
Given the following data: design life $n=15$ years, lane distribution factor $D=0.75$, annual rate of growth of commercial vehicles $r=6 \%$, vehicle damage factor $F=4$ ...
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GATE2018 CE-1: 55
An aircraft approaches the threshold of a runway strip at a speed of $200$ km/h. The pilot decelerates the aircraft at a rate of $1.697 \: m/s^2$ and takes $18 \: s$ to e...
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GATE2018 CE-1: 40
An RCC short column (with lateral ties) of rectangular cross section of $250 \: mm \times 300 \: mm$ is reinforced with four numbers of $16$ mm diameter longitudinal bars...
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GATE2018 CE-1: 39
Variation of water depth $(y)$ in a gradually varied open channel flow is given by the first order differential equation$$ \dfrac{dy}{dx} = \dfrac{1-e^{-\frac{10}{3} \ln(...
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GATE2018 CE-1: 41
An RCC beam of rectangular cross section has factored shear of $200$ kN at its critical section. Its width $b$ is $250$ mm and effective depth $d$ is $350$ mm. Assume des...
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GATE2018 CE-1: 45
A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of $200$ kPa. The deviator str...
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GATE2018 CE-1: 43
Consider the deformable pin-joined truss with loading, geometry and section properties as shown in the figure.Given that $E = 2 \times 10^{11} N/m^2, \: A=10 mm^2, L=1 m$...
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GATE2018 CE-1: 42
The dimensions of a symmetrical welded I-section are shown in the figure.The plastic section modulus about the weaker axis (in $cm^3$, up to decimal place) is _____
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GATE2018 CE-1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ a...
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GATE2018 CE-1: 44
At a construction site, a contractor plans to make an excavation as shown in the figure.The water level in the adjacent river is at an elevation of $+20.0$ m. Unit weight...
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GATE2018 CE-1: 46
The void ratio of a soil is $0.55$ at an effective normal stress of $140$ kPa. The compression index of the soil is $0.25$. In order to reduce the void ratio to $0.4$, an...
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GATE2018 CE-1: 25
A city generates $40 \times 10^6$ kg of municipal solid waste (MSW) per year, out of which only $10\%$ is recovered/recycled and the rest goes to landfill. The landfill h...
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GATE2018 CE-1: 23
A $10$ m wide rectangular channel carries a discharge of $20 \: m^3/s$ under critical condition. Using $g=9.81 m/s^2$, the specific energy (in m, up to two decimal places...
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GATE2018 CE-1: 24
For routing of flood in a given channel using the Muskingum method, two of the routing coefficients are estimated as $C_0=-0.25$ and $C_1=0.55$. The value of the third co...
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GATE2018 CE-1: 21
A core cutter of $130$ mm height has inner and outer diameters of $100$ mm and $106$ mm, respectively. The area ratio of the core cutter (in $\%$, up to two decimal place...
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GATE2018 CE-1: 22
A $1:50$ model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is $1000 \: m^3/s$. The corresponding discharge (in $m^3/s$, up to...
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GATE2018 CE-1: 19
In a fillet weld, the direct shear stress and bending tensile stress are $50$ MPa and $150$ MPa, respectively. As per $\text{IS }800:2007$, the equivalent stress (in MPa,...
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GATE2018 CE-1: 20
In a shrinkage limit test, the volume and mass of a dry soil pat are found to be $50 cm^3$ and $88$ g, respectively. The specific gravity of the soil solids is $2.71$ and...
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