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Recent questions tagged numerical-answers

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GATE Civil 2026 Set 2 | GA | Question: 7
The table lists the unit selling price of five products $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$, and $\text{T}$. On a particular day, $250$ items were sold with ...
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GATE Civil 2026 Set 2 | Question: 1
Matrix $\text{A}$ has the eigenvalues $1,2$, and $3$. The Trace of $\mathrm{A}^{2}$ is$6$$14$$20$$8$
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GATE Civil 2026 Set 2 | Question: 2
A fifth-degree polynomial in $x$ is defined for $x>0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at ...
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GATE Civil 2026 Set 2 | Question: 9
The Culturable Command Area (CCA) for a canal is $10000$ hectares. The base period for a crop in the CCA is $140$ days. Watering depth for the crop is $40$ cm. The outlet...
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GATE Civil 2026 Set 2 | Question: 12
Information related to foundation design is provided in table below.\[\begin{array}{|l|l|}\hline\text{Column 1} & \text{Column 2} \\\hline\text{(I) Converse-Labarre formu...
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GATE Civil 2026 Set 2 | Question: 13
An incident occurred on one side of a median on a four-lane dual carriageway road section. This incident disrupted the traffic movement in one direction. Traffic police d...
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GATE Civil 2026 Set 2 | Question: 18
One-third of the solid matter in a sludge containing $90 \%$ water is composed of fixed mineral solids with specific gravity $2.5$, and two-third is composed of volatile ...
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GATE Civil 2026 Set 2 | Question: 20
A partial differential equation is given below.\[\frac{\partial^{2} u}{\partial x^{2}}-\frac{\partial^{2} u}{\partial y^{2}}=0\]Possible solution(s) is/are:$(x+y)^{5}$$(x...
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GATE Civil 2026 Set 2 | Question: 21
The eigenvalues of $[A]=\left[\begin{array}{ccc}2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5\end{array}\right]$ are $\lambda_{1}=-1.547, \lambda_{2}=12.330$, and $\lambda_{...
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GATE Civil 2026 Set 2 | Question: 22
The probability (in $\%$) that a storm having return period of $15$ years may occur in the next $10$ years is $\_\_\_\_$ (rounded off to two decimal places).
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GATE Civil 2026 Set 2 | Question: 23
A fully saturated sandy soil deposit has water content $20 ~\%$ and specific gravity $2.65$.The critical hydraulic gradient for seepage through the soil to create the qui...
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GATE Civil 2026 Set 2 | Question: 24
A downgrade of $1$ in $100$ meets an upgrade of $1$ in $125$ on a road. If the rate of change of grade is $0.10 \%$ per $30$ m, the length (in m ) of the vertical curve b...
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GATE Civil 2026 Set 2 | Question: 25
A tourist visiting a city holds a map prepared at a scale of $1: 25000$. The tourist measures the distance between place $\text{A}$ and place $\text{B}$ in the city as $1...
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GATE Civil 2026 Set 2 | Question: 26
Let $f(x)=\left|\begin{array}{ccc}x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^{2} & p^{3}\end{array}\right|$ where $p$ is a constant.The value of $\dfrac{d^{3}}{d x^{3...
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GATE Civil 2026 Set 2 | Question: 29
The plane truss shown in the figure is hinge-supported at $\text{E}$ and $\text{F}$. The truss is subjected to vertical downward force at $\text{R}$ and horizontal force ...
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GATE Civil 2026 Set 2 | Question: 31
For the traverse given below, the benchmark is at ground point $\text{L}$. The Reduced Level (RL) of $\text{L}$ is $150.000$ m. The direction of the traverse is from $\te...
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GATE Civil 2026 Set 2 | Question: 32
The $2.4$ ml of raw sewage is diluted to $240$ ml. The Dissolved Oxygen (DO) of the diluted sample at the beginning of Biochemical Oxygen Demand (BOD) test was $8 \mathrm...
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GATE Civil 2026 Set 2 | Question: 33
Types of flood routing and methods are given in the table below.\[\begin{array}{|l|l|}\hline\begin{array}{l}\text{Column 1}\\\text{Type of Flood Routing}\end{array}&\begi...
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GATE Civil 2026 Set 2 | Question: 36
Consider differential equation $\dfrac{d y}{d x}+x y=x$ with the condition as $y=0$ at $x=0$. The value of $y$ at $x=1.0$ is $\_\_\_\_$ (rounded off to two decimal places...
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GATE Civil 2026 Set 2 | Question: 37
The age (in years) of a population is normally distributed with a mean of $36$ and standard deviation of $12$. The height (in cm) of the same population is also normally ...
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GATE Civil 2026 Set 2 | Question: 38
A $250 \mathrm{~mm}$ wide $\times 600 \mathrm{~mm}$ deep rectangular concrete beam is prestressed by means of $4$ high-tensile tendons, each of $14 \mathrm{~mm}$ diameter...
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GATE Civil 2026 Set 2 | Question: 39
A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length $L$. The frame has a fixed support at one end and a roller support at the ...
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GATE Civil 2026 Set 2 | Question: 40
Linearly elastic, homogeneous, uniform bars $\text{BCD}$ and $\text{FG}$ shown in the figure have fixed supports at $\text{B}$ and $\text{G}$, respectively. For both the ...
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GATE Civil 2026 Set 2 | Question: 41
A simply-supported rectangular reinforced concrete beam has a width $250$ mm and an overall depth $600$ mm . The effective span of the beam is $6.23$ m. The beam carries ...
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GATE Civil 2026 Set 2 | Question: 42
Width (in m) of a rectangular channel required to carry a discharge of $96 \mathrm{~m}^{3} / \mathrm{s}$ at a critical depth of $9.8 \text{ m}$ is $\_\_\_\_$ (rounded off...
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GATE Civil 2026 Set 2 | Question: 43
The cross section of a $0.5$ m wide vertical gate holding water and oil is shown in the figure. The unit weights of water and oil are $10 ~\mathrm{kN} / \mathrm{m}^{3}$ a...
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GATE Civil 2026 Set 2 | Question: 44
A centrifugal pump is delivering water from an underground tank to an overhead reservoir against a static head of $35$ m through a $2$ km long, $250$ mm diameter pipe. Th...
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GATE Civil 2026 Set 2 | Question: 45
The flow depth for a discharge of $10 \mathrm{~m}^{3} / \mathrm{s}$ in a wide rectangular channel is $2.0 \text{ m}$. Assume that the flow is uniform.If the discharge is ...
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GATE Civil 2026 Set 2 | Question: 46
For a clayey soil stratum, the time required for degree of consolidation from $25 \%$ to $50 \%$ is $30$ days.The total time (in days) required for $90 \%$ degree of cons...
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GATE Civil 2026 Set 2 | Question: 47
The ultimate bearing capacity of a $1 \text{ m}$ wide strip footing is $532.80 \text{ kPa}$ , when it is embedded at $1 \text{ m}$ depth in dry cohesionless soil. The soi...
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GATE Civil 2026 Set 2 | Question: 48
A building is proposed in an area having thick deposit of silty clay. The water table is at the ground surface. The saturated unit weight of soil is $18 ~\mathrm{kN} / \m...
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GATE Civil 2026 Set 2 | Question: 49
A soil sample has following properties:Natural water content $=30$ $\%$Plasticity index $=40$ $\%$Liquidity index $=50$ $\%$The estimated plastic limit (in $\%$) of the s...
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GATE Civil 2026 Set 2 | Question: 50
For a given traffic stream, the speed-density relationship is given as:\[v=v_{o} \ln \left(\frac{k_{j}}{k}\right)\]where $v$ is the mean speed (in $\mathrm{km} / \mathrm{...
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GATE Civil 2026 Set 2 | Question: 51
A vertical curve is formed by a descending gradient of $1$ in $40$ meeting an ascending gradient of $1$ in $50$. Consider the following:Stopping Sight Distance $(\mathrm{...
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GATE Civil 2026 Set 2 | Question: 52
Interior angles measured at the locations of a closed traverse $\text{ABCDA}$ are given in table below.\[\begin{array}{|c|c|}\hline\text{Location} & \text{Interior angle}...
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GATE Civil 2026 Set 2 | Question: 53
The analysis of major cations and anions in a water sample collected from a city's water supply is given below. Ions present in minor concentrations are not given.\[\begi...
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GATE Civil 2026 Set 2 | Question: 54
Anaerobic bacteria are being utilized for the destruction of biodegradable organic content of wastewater measured in terms of Chemical Oxygen Demand (COD). The yield coef...
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GATE Civil 2026 Set 2 | Question: 55
In an industry, a cyclone collector with $80 \%$ efficiency is installed for air purification, followed by an electrostatic precipitator with $50 \%$ efficiency. The conc...
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GATE Civil 2026 Set 1 | GA | Question: 10
$P$ and $Q$ are two positive integers such that $P^{2}=Q^{2}+13$.The product of the numbers $P$ and $Q$ is $\_\_\_\_$$13$$26$$39$$42$
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GATE Civil 2026 Set 1 | Question: 6
Two reservoirs having different water levels are connected by two long parallel pipelines of same length and same material but having diameters of $600$ mm and $400$ mm. ...
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