Recent questions tagged numerical-answers

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1

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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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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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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4

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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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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6

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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7

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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8

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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9

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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10

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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11

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)

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12

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)

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13

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)

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14

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)

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15

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)

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16

GATE Civil 2022 Set 2 | Question: 46
A hydraulic jump takes place in a $6 \; \text{m}$ wide rectangular channel at a point where the upstream depth is $0.5 \; \text{m}$ (just before the jump). If the discharge in the channel is $30 \; \text{m}^{3}\text{/s}$ and the ... the jump is ______________. (round off to two decimal places) (Consider the acceleration due to gravity as $10 \; \text{m/s}^{2}$.)

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17

GATE Civil 2022 Set 2 | Question: 47
A pump with an efficiency of $80\%$ is used to draw groundwater from a well for irrigating a flat field of area $108$ hectares. The base period and delta for paddy crop on this field are $120 \; \text{days}$ and $144\; \text{cm},$ respectively. Water application efficiency ... $= 9810 \; \text{N/m}^{3}$)

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18

GATE Civil 2022 Set 2 | Question: 48
Two discrete spherical particles ($\text{P}$ and $\text{Q}$) of equal mass density are independently released in water. Particle $\text{P}$ and particle $\text{Q}$ have diameters of $0.5 \; \text{mm}$ and $1.0 \; \text{mm},$ ... force on partial $\text{Q}$ will be _____________ times the drag force on particle $\text{P}.$ (round off to the nearest integer)

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19

GATE Civil 2022 Set 2 | Question: 49
At a municipal waste handling facility, $30$ metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be $10\%.$ The ideal moisture content for composting this ... water to be added to this mixture to bring its moisture content to the ideal condition is ___________metric ton. (in integer)

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20

GATE Civil 2022 Set 2 | Question: 50
A sewage treatment plant receives sewage at a flow rate of $5000 \; \text{m}^{3}\text{/day}.$ The total suspended solids $\text{(TSS)}$ concentration in the sewage at the inlet of primary clarifier is $200 \; \text{mg/L}$. After the ... daily volume of the thickened sludge (in $\text{m}^{3}\text{/day}$) will be ___________.(round off to the nearest integer)

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21

GATE Civil 2022 Set 2 | Question: 51
A sample of air analyzed at $25 \; ^{\circ}\text{C}$ and $1 \; \text{atm}$ pressure is reported to contain $0.04 \; \text{ppm}$ of $\text{SO}_{2}.$ Atomic mass of $\text{S = 32, O = 16}.$ The equivalent $\text{SO}_{2}$ concentration (in $\mu \text{g/m}^{3}$) will be _________. (round off to the nearest integer)

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22

GATE Civil 2022 Set 2 | Question: 52
A parabolic vertical crest curve connects two road segments with grades $+1.0 \%$ and $-2.0 \%.$ If a $200 \; \text{m}$ stopping sight distance is needed for a driver at a height of $1.2 \; \text{m}$ to avoid an obstacle of height $0.15 \; \text{m},$ then the minimum curve length should be _________ $\text{m}$. (round off to the nearest integer)

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23

GATE Civil 2022 Set 2 | Question: 53
Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams $\text{(P)}$ and $\text{(Q)}$ as shown in the schematic is _________ $\text{kmph}$ ...

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24

GATE Civil 2022 Set 2 | Question: 54
It is given that an aggregate mix has $260 \; \text{grams}$ of coarse aggregates and $240 \; \text{grams}$ of fine aggregates. The specific gravities of the coarse and fine aggregate are $2.6$ and $2.4,$ respectively. The bulk specific gravity of the mix is $2.3.$ The percentage air voids in the mix is _______________. (round off to the nearest integer)

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25

GATE Civil 2022 Set 2 | Question: 55
The lane configuration with lane volumes in vehicles per hour of a four-arm signalized intersection is shown in the figure. There are only two phases: the first phase is for East-West and the West-East through movements, and the second phase is for ... length (in $\text{seconds}$), as per the Webster's method, is ____________.(rounds off to the nearest integer)

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26

GATE Civil 2022 Set 1 | Question: 19
Consider the following recursive iteration scheme for different values of variable $P$ with the initial guess $x_{1} =1$: $x_{n + 1} = \frac{1}{2}\left ( x_{n} + \frac{P}{x_{n}} \right ), \:\:\:n = 1, 2, 3, 4, 5$ For ... $P = 10$, the numerical value of $x_{5}$ is ___________________. (round off to three decimal places)

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27

GATE Civil 2022 Set 1 | Question: 20
The Fourier cosine series of a function is given by : $f\left ( x \right ) = \sum_{n = 0}^{\infty} f_{n} \cos nx$ For $f\left ( x \right ) = \cos^{4} x$, the numerical value of $\left ( f_{4} + f_{5} \right )$ is __________. (round off to three decimal places)

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28

GATE Civil 2022 Set 1 | Question: 21
An uncompacted heap of soil has a volume of $10000\: m^{3}$ and void ratio of $1$. If the soil is compacted to a volume of $7500\: m^{3}$, then the corresponding void ratio of the compacted soil is _________________. (round off to one decimal place)

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29

GATE Civil 2022 Set 1 | Question: 22
A concentrated vertical load of $3000$ $\text{kN}$ is applied on a horizontal ground surface. Points $P$ and $Q$ are at depths $1 \:m$ and $2\: m$ below the ground, respectively, along the line of application of the load. Considering ... the ratio of the increase in vertical stress at $P$ to the increase in vertical stress at $Q$ is _______________. (in integer)

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30

GATE Civil 2022 Set 1 | Question: 23
At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance $q_{c}$ was $1000$ $\text{kPa}$ at a certain depth. The friction ratio $(f_{r})$ was estimated as $1\%$ at the same depth. The value of sleeve (side) friction (in $\text{kPa}$) at that depth was _________________. (in integer)

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31

GATE Civil 2022 Set 1 | Question: 24
During a particular stage of the growth of a crop, the consumptive use of water is $2.8$ $\text{mm}$/day. The amount of water available in the soil is $50\%$ of the maximum depth of available water in the root zone. ... the irrigation efficiency as $70\%$. The interval between irrigation (in days) will be _______________. (round off to the nearest integer)

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32

GATE Civil 2022 Set 1 | Question: 25
The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)

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33

GATE Civil 2022 Set 1 | Question: 38
Consider the differential equation $\frac{\mathrm{dy} }{\mathrm{d} x} = 4 \left ( x + 2 \right ) - y$ For the initial condition $y = 3$ at $x = 1$, the value of $y$ at $x = 1.4$ obtained using Euler’s method with a step-size of $0.2$ is ____________. (round off to one decimal place)

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34

GATE Civil 2022 Set 1 | Question: 39
A set of observations of independent variable $(x)$ and the corresponding dependent variable $(y)$ ... regression model $y = a + bx$ is estimated as $6.1$. The coefficient $b$ is ____________________ (round off to one decimal place)

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35

GATE Civil 2022 Set 1 | Question: 40
The plane truss shown in the figure is subjected to an external force $P$. It is given that $P = 70\; kN$, $a = 2\; m$, and $b = 3\; m$. The magnitude (absolute value) of force (in $kN$) in member $EF$ is ______________. (round off to the nearest integer)

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36

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 $\alpha = 0.7$)

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37

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)

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38

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)

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39

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)

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40

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)

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