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121
GATE Civil 2024 Set 1 | Question: 39
The plane truss shown in the figure has $13$ joints and $22$ members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. A to $\mathrm{M}$ indicate the joints of the truss. The truss has pin supports at ... $\mathrm{L}$ is $\_\_\_\_\_\_$ (rounded off to $1$ decimal place).
The plane truss shown in the figure has $13$ joints and $22$ members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical...
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GATE Civil 2024 Set 1 | Question: 8
A $2 \mathrm{~m}$ wide strip footing is founded at a depth of $1.5 \mathrm{~m}$ below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of $40 \mathrm{kPa}$. Due to seasonal ... peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi's theory, will remain the same decrease increase become zero
A $2 \mathrm{~m}$ wide strip footing is founded at a depth of $1.5 \mathrm{~m}$ below the ground level in a homogeneous pure clay bed. The clay bed has uni...
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123
GATE Civil 2024 Set 1 | Question: 37
The return period of a large earthquake for a given region is $200$ years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceeded at least once in $50$ years is $\_\_\_\_\_\_$ $\%$ (rounded off to the nearest integer).
The return period of a large earthquake for a given region is $200$ years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it wil...
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GATE Civil 2024 Set 1 | Question: 14
Which one of the following statements related to bitumen is FALSE? Kinematic viscosity is a measure of resistance to the flow of molten bitumen under gravity. Softer grade bitumen possesses higher softening point than hard grade bitumen. ... specified test conditions. Ductility test is carried out on bitumen to test its adhesive property and ability to stretch.
Which one of the following statements related to bitumen is FALSE?Kinematic viscosity is a measure of resistance to the flow of molten bitumen under gravity.Softer grade ...
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125
GATE Civil 2024 Set 1 | Question: 2
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as \[ \frac{\partial^{2} u}{\partial x^{2}}=2 \] Assuming $g: g(x), f: f(y)$, and $h: h(y)$, the general solution of the above differential equation is $u=x^{2}+f(y)+g(x)$ $u=x^{2}+x f(y)+h(y)$ $u=x^{2}+x f(y)+g(x)$ $u=x^{2}+f(y)+y g(x)$
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as\[\frac{\partial^{2} u}{\partial x^{2}}=2\]Assuming $g: g(x), f: f(...
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126
GATE Civil 2024 Set 1 | Question: 12
A car is travelling at a speed of $60 \mathrm{~km} / \mathrm{hr}$ on a section of a National Highway having a downward gradient of $2 \%$. The driver of the car suddenly observes a stopped vehicle on the car path at a distance $130 \mathrm{~m}$ ahead, and applies ... the car to a safe stop lies in the range $126$ to $130$ $41$ to $45$ $33$ to $37$ $75$ to $79$
A car is travelling at a speed of $60 \mathrm{~km} / \mathrm{hr}$ on a section of a National Highway having a downward gradient of $2 \%$. The driver of the car suddenly ...
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127
GATE Civil 2024 Set 1 | Question: 16
A surveyor observes a zenith angle of $93^{\circ} 00^{\prime} 00^{\prime \prime}$ during a theodolite survey. The corresponding vertical angle is $-03^{\circ} 00^{\prime} 00^{\prime \prime}$ $+03^{\circ} 00^{\prime} 00^{\prime \prime}$ $-87^{\circ} 00^{\prime} 00^{\prime \prime}$ $+87^{\circ} 00^{\prime} 00^{\prime \prime}$
A surveyor observes a zenith angle of $93^{\circ} 00^{\prime} 00^{\prime \prime}$ during a theodolite survey. The corresponding vertical angle is$-03^{\circ} 00^{\prime} ...
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128
GATE Civil 2024 Set 2 | Question: 50
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of $10$ million liters/day. Assume a detention period of $2.0$ hours and surface loading rate of $40000$ liters $/ \mathrm{m}^{2} /$ day. The height (in meters) of the water column in the tank is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of $10$ million liters/day. Assume a detention period of $2.0$ hours and surface...
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129
GATE Civil 2024 Set 1 | Question: 33
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on $11 \%$ Oxygen) for $\mathrm{HCl}$ ... is lesser than the emission standard. No compliance, as the Oxygen is greater than $11 \%$ in the flue gas.
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air...
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130
GATE Civil 2024 Set 1 | Question: 45
A soil sample was consolidated at a cell pressure of $20 \mathrm{kPa}$ and a back pressure of $10 \mathrm{kPa}$ for $24$ hours during a consolidated undrained $\text{(CU)}$ triaxial test. The cell pressure was increased to $30 \mathrm{kPa}$ on the next ... s pore pressure parameter $B$ for the soil sample is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
A soil sample was consolidated at a cell pressure of $20 \mathrm{kPa}$ and a back pressure of $10 \mathrm{kPa}$ for $24$ hours during a consolidated undrained $\text{(CU)...
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131
GATE Civil 2023 Set 2 | Question: 50
For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil $1$ and Soil $2,$ are $10 \mathrm{~mm} / \mathrm{s}$ and $1 \mathrm{~mm} / \mathrm{s}$, respectively. Assume ... total head (in $\mathrm{m}$, rounded off to two decimal places) at any point located at the junction of the two samples? _____________
For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil $1$ and Soil $2,$ are $10 \mathrm{~mm} / \mathrm{s}$ and...
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132
GATE Civil 2023 Set 2 | Question: 12
In the context of Municipal Solid Waste Management, 'Haul' in 'Hauled Container System operated in conventional mode' includes the __________. time spent by the transport truck at the disposal site time spent by the transport truck in ... at a pickup point time spent by the transport truck in driving from the depot to the first pickup point
In the context of Municipal Solid Waste Management, 'Haul' in 'Hauled Container System operated in conventional mode' includes the __________.time spent by the transport ...
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GATE Civil 2023 Set 2 | Question: 8
A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with $50 \%$ efficiency. The recorded SPT value at a particular depth is $28.$ If an automatic hammer dropping system with $70 \%$ efficiency is used at the same location, the recorded SPT value will be ____________. $28$ $20$ $40$ $25$
A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with $50 \%$ efficiency. The recorded SPT value at a p...
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134
GATE Civil 2023 Set 2 | Question: 54
The theoretical aerobic oxidation of biomass $\left(\mathrm{C}_5 \mathrm{H}_7 \mathrm{O}_2 \mathrm{~N}\right)$ ... $14 \mathrm{~g} / \mathrm{mol}$, respectively]
The theoretical aerobic oxidation of biomass $\left(\mathrm{C}_5 \mathrm{H}_7 \mathrm{O}_2 \mathrm{~N}\right)$ is given below:$\mathrm{C}_5 \mathrm{H}_7 \mathrm{O}_2 \mat...
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135
GATE Civil 2023 Set 2 | Question: 16
In the frame shown in the figure (not to scale), all four members $\text{(AB, } \mathrm{BC}, \mathrm{CD}$, and $\mathrm{AD})$ have the same length and same constant flexural rigidity. All the joints $\text{A, B}$, $\mathrm{C}$, and $\mathrm{D}$ are ... $\mathrm{F}$ are zero Slopes at $\mathrm{E}, \mathrm{F}, \mathrm{G}$, and $\mathrm{H}$ are zero
In the frame shown in the figure (not to scale), all four members $\text{(AB, } \mathrm{BC}, \mathrm{CD}$, and $\mathrm{AD})$ have the same length and same constant flexu...
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136
GATE Civil 2023 Set 2 | Question: 18
The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are: Variation of friction angle along the width of the footing Variation of soil ... Variation of friction angle along the depth of the footing Variation of soil stiffness along the depth of the footing
The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are:Variation o...
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GATE Civil 2023 Set 2 | Question: 3
A remote village has exactly $1000$ vehicles with sequential registration numbers starting from $ 1000.$ Out of the total vehicles, $ 30 \% $ are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on ... date, the number of vehicles expected without pollution clearance certificate is ___________. $15$ $30$ $50$ $70$
A remote village has exactly $1000$ vehicles with sequential registration numbers starting from $ 1000.$ Out of the total vehicles, $ 30 \% $ are without pollution clear...
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138
GATE Civil 2023 Set 2 | Question: 15
For the matrix $[A]=\left[\begin{array}{ccc} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{array}\right]$ which of the following statements is/are TRUE? $[A]\{x\}=\{b\}$ has a unique solution $[A]\{x\}=\{b\}$ does not have a unique solution $[A]$ has three linearly independent eigenvectors $[A]$ is a positive definite matrix
For the matrix$[A]=\left[\begin{array}{ccc}1 & -1 & 0 \\-1 & 2 & -1 \\0 & -1 & 1\end{array}\right]$which of the following statements is/are TRUE?$[A]\{x\}=\{b\}$ has a un...
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139
GATE Civil 2023 Set 2 | Question: 28
Cholesky decomposition is carried out on the following square matrix $[A]$. $[A]=\left[\begin{array}{cc} 8 & -5 \\ -5 & a_{22} \end{array}\right]$ Let $l_{\mathrm{ij}}$ and $a_{\mathrm{ij}}$ ... $[L]$ is $1.968,$ what is the value (rounded off to the nearest integer) of the element $a_{22}$? $5$ $7$ $9$ $11$
Cholesky decomposition is carried out on the following square matrix $[A]$.$$[A]=\left[\begin{array}{cc}8 & -5 \\-5 & a_{22}\end{array}\right]$$Let $l_{\mathrm{ij}}$ and ...
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GATE Civil 2023 Set 2 | Question: 19
Which of the following is/are NOT active disinfectant(s) in water treatment? $\cdot \mathrm{OH}$ (hydroxyl radical) $\mathrm{O}_{3}$ (ozone) $\mathrm{OCl}^{-}$(hypochlorite ion) $\mathrm{Cl}^{-}$(chloride ion)
Which of the following is/are NOT active disinfectant(s) in water treatment? $\cdot \mathrm{OH}$ (hydroxyl radical)$\mathrm{O}_{3}$ (ozone) $\mathrm{OCl}^{-}$(hypochlorit...
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141
GATE Civil 2023 Set 2 | Question: 20
As per the Indian Roads Congress guidelines $\text{(IRC 86: 2018),}$ extra widening depends on which of the following parameters? Horizontal curve radius Superelevation Number of lanes Longitudinal gradient
As per the Indian Roads Congress guidelines $\text{(IRC 86: 2018),}$ extra widening depends on which of the following parameters? Horizontal curve radius Superelevation N...
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GATE Civil 2023 Set 2 | Question: 2
Which of the following probability distribution functions (PDFs) has the mean greater than the median? Function $1$ Function $2$ Function $3$ Function $4$
Which of the following probability distribution functions (PDFs) has the mean greater than the median?Function $1$Function $2$Function $3$Function $4$
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GATE Civil 2023 Set 2 | Question: 25
If the size of the ground area is $6 \mathrm{~km} \times 3 \mathrm{~km}$ and the corresponding photo size in the aerial photograph is $30 \mathrm{~cm} \times 15 \mathrm{~cm}$, then the scale of the photograph is $1 :$ ____________ (in integer).
If the size of the ground area is $6 \mathrm{~km} \times 3 \mathrm{~km}$ and the corresponding photo size in the aerial photograph is $30 \mathrm{~cm} \times 15 \mathrm{~...
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GATE Civil 2023 Set 2 | Question: 6
When a simply-supported elastic beam of span $L$ and flexural rigidity $E I$ ( $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded with a uniformly distributed load $w$ per unit length, the deflection at ... to a value less than $\Delta_0 / 2$ reduces to a value greater than $\Delta_0 / 2$ remains unchanged at $\Delta_0$
When a simply-supported elastic beam of span $L$ and flexural rigidity $E I$ ( $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded...
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GATE Civil 2023 Set 2 | Question: 5
$\text{M20}$ concrete as per $\mathrm{IS~} 456: 2000$ refers to concrete with a design mix having ____________ an average cube strength of $20~ \mathrm{MPa}$ an average cylinder strength of $20~ \mathrm{MPa}$ a $5$-percentile cube strength of $20~ \mathrm{MPa}$ a $5$-percentile cylinder strength of $20~ \mathrm{MPa}$
$\text{M20}$ concrete as per $\mathrm{IS~} 456: 2000$ refers to concrete with a design mix having ____________an average cube strength of $20~ \mathrm{MPa}$an average cyl...
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GATE Civil 2023 Set 2 | Question: 46
A $2\text{D}$ thin plate with modulus of elasticity, $E=1.0 \mathrm{~N} / \mathrm{m}^{2}$, and Poisson's ratio, $\mu=0.5$, is in plane stress condition. The displacement field in the plate is given by $u=C x^{2} y$ and $v=0$ ... $\alpha$ (in $\mathrm{N} / \mathrm{m}^{4}$, in integer)?________________
A $2\text{D}$ thin plate with modulus of elasticity, $E=1.0 \mathrm{~N} / \mathrm{m}^{2}$, and Poisson's ratio, $\mu=0.5$, is in plane stress condition. The displacement ...
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GATE Civil 2023 Set 2 | Question: 29
In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of $\text{PQ, QR,}$ and $\text{RP}$ are $4, 3,$ and $5$ units, respectively. The principal stresses are ___________ . (round off to one ... $\sigma_{\mathrm{x}}=16.0 \mathrm{~MPa}, \sigma_y=138.5 \mathrm{~MPa}$
In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of $\text{PQ, QR,}$ and $\text{RP}$ are $4, 3,$ and $5$ ...
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GATE Civil 2023 Set 2 | Question: 14
The magnetic bearing of the sun for a location at noon is $ 183^{\circ} \; 30^{\prime}$. If the sun is exactly on the geographic meridian at noon, the magnetic declination of the location is ____________. $3^{\circ} \; 30^{\prime} ~ \mathrm{W}$ ... $93^{\circ} \; 30^{\prime} ~ \mathrm{W}$ $93^{\circ} \; 30^{\prime} ~ \mathrm{E}$
The magnetic bearing of the sun for a location at noon is $ 183^{\circ} \; 30^{\prime}$. If the sun is exactly on the geographic meridian at noon, the magnetic declinatio...
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GATE Civil 2023 Set 2 | Question: 23
The pressure in a pipe at $\mathrm{X}$ is to be measured by an open manometer as shown in figure. Fluid $\mathrm{A}$ is oil with a specific gravity of 0.8 and Fluid $\mathrm{B}$ is mercury with a specific gravity of $13.6.$ ... as $9.81 \mathrm{~m} / \mathrm{s}^2$ and atmospheric pressure as $101.3 ~ \mathrm{kN} / \mathrm{m}^2$ ]
The pressure in a pipe at $\mathrm{X}$ is to be measured by an open manometer as shown in figure. Fluid $\mathrm{A}$ is oil with a specific gravity of 0.8 and Fluid $\mat...
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GATE Civil 2023 Set 2 | Question: 13
Which of the following is equal to the stopping sight distance? (braking distance required to come to stop) $+$ (distance travelled during the perception-reaction time) (braking distance required to come to stop) $-$ (distance ... the perception-reaction time) (braking distance required to come to stop) (distance travelled during the perception-reaction time)
Which of the following is equal to the stopping sight distance?(braking distance required to come to stop) $+$ (distance travelled during the perception-reaction time) (b...
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GATE Civil 2023 Set 2 | Question: 22
An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of $76 ~ \mathrm{kPa}$. The undrained cohesion (in $\mathrm{kPa}$, in integer) of the soil is ______________.
An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of $76 ~ \mathrm{kPa}$. The undrained cohesion (in $...
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GATE Civil 2023 Set 2 | Question: 24
For the elevation and temperature data given in the table, the existing lapse rate in the environment is _______________ $\text{C}^{\circ} / 100 \mathrm{~m}$ ...
For the elevation and temperature data given in the table, the existing lapse rate in the environment is _______________ $\text{C}^{\circ} / 100 \mathrm{~m}$ (round off t...
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GATE Civil 2023 Set 2 | Question: 55
A system of seven river segments is shown in the schematic diagram. The $\mathrm{R}_{\mathrm{i}}$ 's, $\mathrm{Q}_{\mathrm{i}}$ 's, and $\mathrm{C}_{\mathrm{i}}$ 's $(\mathrm{i}=1$ to 7) are the river ... concentration (in $\mathrm{kg} / \mathrm{m}^3$, rounded off to two decimal place) of the pollutant in the river segment $7?$ ___________
A system of seven river segments is shown in the schematic diagram. The $\mathrm{R}_{\mathrm{i}}$ 's, $\mathrm{Q}_{\mathrm{i}}$ 's, and $\mathrm{C}_{\mathrm{i}}$ 's $(\ma...
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GATE Civil 2023 Set 2 | Question: 7
Muller-Breslau principle is used in analysis of structures for ___________. drawing an influence line diagram for any force response in the structure writing the virtual work expression to get the equilibrium equation superposing the load ... response in the structure relating the deflection between two points in a member with the curvature diagram in-between
Muller-Breslau principle is used in analysis of structures for ___________.drawing an influence line diagram for any force response in the structure writing the virtual w...
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GATE Civil 2023 Set 1 | Question: 8
A possible slope failure is shown in the figure. Three soil samples are taken from different locations $\text{(I, II}$ and $\text{III)}$ of the potential failure plane. Which is the most appropriate shear strength test for each of the sample to identify the failure mechanism? Identify the ... $\text{I-S, II-Q, III-R}$ $\text{I-P, II-R, III-Q}$
A possible slope failure is shown in the figure. Three soil samples are taken from different locations $\text{(I, II}$ and $\text{III)}$ of the potential failure plane. W...
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GATE Civil 2023 Set 2 | Question: 21
The steady-state temperature distribution in a square plate $\mathrm{ABCD}$ is governed by the $2$-dimensional Laplace equation. The side $\mathrm{AB}$ is kept at a temperature of $100{ }^{\circ} \mathrm{C}$ and the other three sides ... $T_{0}$ is _____________ (rounded off to two decimal places).
The steady-state temperature distribution in a square plate $\mathrm{ABCD}$ is governed by the $2$-dimensional Laplace equation. The side $\mathrm{AB}$ is kept at a tempe...
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GATE Civil 2023 Set 1 | Question: 4
A singly reinforced concrete beam of balanced section is made of $\text{M20}$ grade concrete and $\text{Fe 415}$ ... $0.0038 $ $0.0020$ and $0.0018$ $0.0035$ and $0.0041$ $0.0020$ and $0.0031$
A singly reinforced concrete beam of balanced section is made of $\text{M20}$ grade concrete and $\text{Fe 415}$ grade steel bars. The magnitudes of the maximum compressi...
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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 2 | Question: 4
A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. A torque $T=100 \mathrm{~kN}$ ... $\text{Statement i)}$ is wrong, but $\text{Statement ii)}$ is correct Both the statements are wrong
A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. A torque $T=100 \mathrm{~kN}$.m is applied at the free end. The shear modu...
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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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