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Recent questions tagged gatecivil-2023-set1
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41
GATE Civil 2023 Set 1 | Question: 31
Consider that a force $\text{P}$ is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress $\left(\sigma_{z}\right)$ at any point $(r, z)$, within the half-space is given as, \[\sigma_{z}=\frac{3 P}{2 \pi} \frac{z^{3}}{\left(r^{2 ... $z^{3}=\frac{3}{2} r^{2}$ $z^{2}=\frac{5}{2} r^{2}$ $z^{3}=\frac{5}{2} r^{2}$
Consider that a force $\text{P}$ is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress $\left(\sigma_{z}\right)$ at any ...
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GATE Civil 2023 Set 1 | Question: 32
A square footing of size $2.5 \mathrm{~m} \times 2.5 \mathrm{~m}$ is placed $1.0 \mathrm{~m}$ below the ground surface on a cohesionless homogeneous soil stratum. Considering that the groundwater table is located at the base of the footing, the unit weights ... is the ultimate bearing capacity (in $\mathrm{kPa}$ ) of the plate? $110.16$ $61.20$ $204.00$ $163.20$
A square footing of size $2.5 \mathrm{~m} \times 2.5 \mathrm{~m}$ is placed $1.0 \mathrm{~m}$ below the ground surface on a cohesionless homogeneous soil stratum. Conside...
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43
GATE Civil 2023 Set 1 | Question: 33
A very wide rectangular channel carries a discharge (Q) of $70 \mathrm{~m}^3 / \mathrm{s}$ per meter width. Its bed slope changes from $0.0001$ to $0.0009$ at a point $\mathrm{P}$, as shown in the figure (not to scale). The Manning's roughness ... ? $\mathrm{M}_2$ and $\mathrm{S}_2$ $\mathrm{M}_2$ only $\mathrm{S}_2$ only $\mathrm{S}_2$ and hydraulic jump
A very wide rectangular channel carries a discharge (Q) of $70 \mathrm{~m}^3 / \mathrm{s}$ per meter width. Its bed slope changes from $0.0001$ to $0.0009$ at a point $\m...
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44
GATE Civil 2023 Set 1 | Question: 34
A jet of water having a velocity of $20 \mathrm{~m} / \mathrm{s}$ strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at $15 \mathrm{~m} / \mathrm{s}.$ What is the percentage efficiency of the plates? (round off to one decimal place) $37.5 $ $66.7$ $50.0$ $88.9$
A jet of water having a velocity of $20 \mathrm{~m} / \mathrm{s}$ strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at $15 \...
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45
GATE Civil 2023 Set 1 | Question: 35
In the following table, identify the correct set of associations between the entries in Column-$1$ and Column-$2.$ ... $\text{Q-III, R-II, S-IV}$ $\text{P-IV, R-I, S-II}$ $\text{P-III, Q-I, R-IV}$
In the following table, identify the correct set of associations between the entries in Column-$1$ and Column-$2.$$$\begin{array}{|l|l|}\hline {\qquad \text{Column-1} } &...
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GATE Civil 2023 Set 1 | Question: 36
A plot of speed-density relationship (linear) of two roads (Road $\mathrm{A}$ and Road $\mathrm{B}$) is shown in the figure. If the capacity of Road $\mathrm{A}$ is $C_A$ and the capacity of Road $\mathrm{B}$ is $C_B$, what is $\frac{C_A}{C_B}$? $\frac{k_A}{k_B}$ $\frac{u_A}{u_B}$ $\frac{k_A u_A}{k_B u_B}$ $\frac{k_A u_B}{k_B u_A}$
A plot of speed-density relationship (linear) of two roads (Road $\mathrm{A}$ and Road $\mathrm{B}$) is shown in the figure.If the capacity of Road $\mathrm{A}$ is $C_A$ ...
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47
GATE Civil 2023 Set 1 | Question: 37
For the matrix $[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$ which of the following statements is/are TRUE? The eigenvalues of $[A]^{T}$ are same as the eigenvalues of $[A]$ The ... $[A]^{T}$ are same as the eigenvectors of $[A]$ The eigenvectors of $[A]^{-1}$ are same as the eigenvectors of $[A]$
For the matrix$$[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$$which of the following statements is/are TRUE?The eigenvalues of $[A]^{T}...
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48
GATE Civil 2023 Set 1 | Question: 38
For the function $f(x)=e^{x}|\sin x|; x \in \mathbb{R},$ which of the following statements is/are TRUE? The function is continuous at all $x$ The function is differentiable at all $x$ The function is periodic The function is bounded
For the function $f(x)=e^{x}|\sin x|; x \in \mathbb{R},$ which of the following statements is/are TRUE? The function is continuous at all $x$The function is differentiabl...
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GATE Civil 2023 Set 1 | Question: 39
Consider the beam shown in the figure (not to scale), on a hinge support at end $\mathrm{A}$ and a roller support at end $\mathrm{B}$. The beam has a constant flexural rigidity, and is subjected to the external ... statements is/are TRUE? Support reactions are zero Shear force is zero everywhere Bending moment is zero everywhere Deflection is zero everywhere
Consider the beam shown in the figure (not to scale), on a hinge support at end $\mathrm{A}$ and a roller support at end $\mathrm{B}$. The beam has a constant flexural ri...
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GATE Civil 2023 Set 1 | Question: 40
Which of the following statements is/are TRUE in relation to the Maximum Mixing Depth (or Height) $\mathrm{D}_{\max }$' in the atmosphere? $\mathrm{D}_{\max }$ is always equal to the height of the layer of ... smaller air pollution potential if other meteorological conditions remain same Vertical dispersion of pollutants occurs up to $\mathrm{D}_{\max }$
Which of the following statements is/are TRUE in relation to the Maximum Mixing Depth (or Height) ‘$\mathrm{D}_{\max }$’ in the atmosphere?$\mathrm{D}_{\max }$ is alw...
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51
GATE Civil 2023 Set 1 | Question: 41
Which of the following options match the test reporting conventions with the given material tests in the table? ... $\text{(P) - (VI); (Q) - (III); (R) - (IV); (S) - (VII)}$
Which of the following options match the test reporting conventions with the given material tests in the table?$$\begin{array}{|l|l|}\hline \textbf{Test reporting convent...
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GATE Civil 2023 Set 1 | Question: 42
The differential equation, $\frac{\mathrm{d} u}{\mathrm{~d} t}+2 t u^2=1,$ is solved by employing a backward difference scheme within the finite difference framework. The value of $u$ at the $(n-1)^{\text {th }}$ time-step, for some $n$, ... $0.01 \mathrm{~s}$ long. Then, the value of $\left(u_n-u_{n-1}\right)$ is__________ (round off to three decimal places).
The differential equation,$$\frac{\mathrm{d} u}{\mathrm{~d} t}+2 t u^2=1,$$is solved by employing a backward difference scheme within the finite difference framework. The...
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53
GATE Civil 2023 Set 1 | Question: 43
The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in $\mathrm{N} / \mathrm{mm}^{2}$, in integer) at the point? _____________
The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (i...
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GATE Civil 2023 Set 1 | Question: 44
An idealised bridge truss is shown in the figure. The force in Member $U_2 L_3$ is $\mathrm{kN}$__________ (round off to one decimal place).
An idealised bridge truss is shown in the figure. The force in Member $U_2 L_3$ is $\mathrm{kN}$__________ (round off to one decimal place).
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GATE Civil 2023 Set 1 | Question: 45
The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis $(Y-Y).$ The moment of inertia of the section about the horizontal axis $(X-X)$ passing through the centroid is _________ (round off to nearest integer).
The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis $(Y-Y).$ The moment of inertia of the section about th...
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56
GATE Civil 2023 Set 1 | Question: 46
A soil having the average properties, bulk unit weight $=19 \mathrm{~kN} / \mathrm{m}^3$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{~kPa}$ ... to one decimal place). [Assume the soil is being formed parallel to the rock bedding plane and there is no ground water effect.]
A soil having the average properties, bulk unit weight $=19 \mathrm{~kN} / \mathrm{m}^3$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{~kPa}$, is be...
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GATE Civil 2023 Set 1 | Question: 47
A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is ______________ $\mathrm{kPa}$ (round off to one decimal place).
A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at th...
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GATE Civil 2023 Set 1 | Question: 48
A vertical trench is excavated in a clayey soil deposit having a surcharge load of $30 \mathrm{~kPa}$. A fluid of unit weight $12 \mathrm{~kN} / \mathrm{m}^3$ is poured in the trench to prevent collapse as the excavation proceeds. ... $\mathrm{m}$, rounded off to two decimal places)?________________
A vertical trench is excavated in a clayey soil deposit having a surcharge load of $30 \mathrm{~kPa}$. A fluid of unit weight $12 \mathrm{~kN} / \mathrm{m}^3$ is poured i...
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GATE Civil 2023 Set 1 | Question: 49
A $12$-hour storm occurs over a catchment and results in a direct runoff depth of $100 \mathrm{~mm}.$ The time-distribution of the rainfall intensity is shown in the figure (not to scale). The $\phi \text {-index}$ of the storm is (in $\mathrm{mm}$, rounded off to two decimal places) ___________________.
A $12$-hour storm occurs over a catchment and results in a direct runoff depth of $100 \mathrm{~mm}.$ The time-distribution of the rainfall intensity is shown in the figu...
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GATE Civil 2023 Set 1 | Question: 50
A hydraulic jump occurs in a $1.0 \mathrm{~m}$ wide horizontal, frictionless, rectangular channel, with a pre-jump depth of $0.2 \mathrm{~m}$ and a post-jump depth of $1.0 \mathrm{~m}$. The value of $g$ ... at the pre-jump and post-jump sections are same and are equal to (in $\mathrm{m}^3$, rounded off to two decimal places)_______________.
A hydraulic jump occurs in a $1.0 \mathrm{~m}$ wide horizontal, frictionless, rectangular channel, with a pre-jump depth of $0.2 \mathrm{~m}$ and a post-jump depth of $1....
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GATE Civil 2023 Set 1 | Question: 51
In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is $10 \mathrm{~mm} / \mathrm{h}$; final infiltration capacity is $5 \mathrm{~mm} / \mathrm{h}$ ... $\mathrm{mm}$ ) from a uniform storm of duration $12 \mathrm{~h}$ is___________. (round off to one decimal place)
In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is $10 \mathrm{~mm} / \mathrm{h}$; final infiltration capacity is $5 \m...
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GATE Civil 2023 Set 1 | Question: 52
The composition and energy content of a representative solid waste sample are given in the table. If the moisture content of the waste is $26 \%$, the energy content of the solid waste on dry-weight basis is ___________$\mathrm{MJ} / \mathrm{kg}$ (round off to ...
The composition and energy content of a representative solid waste sample are given in the table. If the moisture content of the waste is $26 \%$, the energy content of t...
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GATE Civil 2023 Set 1 | Question: 53
A flocculator tank has a volume of $2800 \mathrm{~m}^{3 .}$ The temperature of water in the tank is $15^{\circ} \mathrm{C}$, and the average velocity gradient maintained in the tank is $100 / \mathrm{s}$ ... $1.518 \times 10^{-3} \mathrm{~N}-\mathrm{s} / \mathrm{m}^2$, respectively]
A flocculator tank has a volume of $2800 \mathrm{~m}^{3 .}$ The temperature of water in the tank is $15^{\circ} \mathrm{C}$, and the average velocity gradient maintained ...
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GATE Civil 2023 Set 1 | Question: 54
The wastewater inflow to an activated sludge plant is $0.5 \mathrm{~m}^3 / \mathrm{s}$, and the plant is to be operated with a food to microorganism ratio of $0.2 \mathrm{~mg} / \mathrm{mg}-\mathrm{d}$. The concentration of ... organic matter in the tank, the volume of aeration tank (in $\mathrm{m}^3$, in integer) required for the plant is____________.
The wastewater inflow to an activated sludge plant is $0.5 \mathrm{~m}^3 / \mathrm{s}$, and the plant is to be operated with a food to microorganism ratio of $0.2 \mathrm...
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GATE Civil 2023 Set 1 | Question: 55
Trigonometric levelling was carried out from two stations $\mathrm{P}$ and $\mathrm{Q}$ to find the reduced level ($\text{R. L.}$) of the top of hillock, as shown in the table. The distance between Stations $\mathrm{P}$ and $\mathrm{Q}$ is $55 \mathrm{~m}$. ...
Trigonometric levelling was carried out from two stations $\mathrm{P}$ and $\mathrm{Q}$ to find the reduced level ($\text{R. L.}$) of the top of hillock, as shown in the ...
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