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81

GATE Civil 2023 Set 2 | Question: 26
The solution of the differential equation $\frac{d^3 y}{d x^3}-5.5 \frac{d^2 y}{d x^2}+9.5 \frac{d y}{d x}-5 y=0$ is expressed as $y=C_1 e^{2.5 x}+C_2 e^{\alpha x}+C_3 e^{\beta x}$, where $C_1, C_2, C_3, \alpha$, and $\beta$ are constants ... following options is correct for the values of $\alpha$ and $\beta$ ? $1$ and $2$ $-1$ and $-2$ $2$ and $3$ $-2$ and $-3$

The solution of the differential equation$\frac{d^3 y}{d x^3}-5.5 \frac{d^2 y}{d x^2}+9.5 \frac{d y}{d x}-5 y=0$is expressed as $y=C_1 e^{2.5 x}+C_2 e^{\alpha x}+C_3 e^{\...

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82

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)

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 ...

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83

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 _________ $\text{kmph}$ ...

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 schema...

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84

GATE Civil 2022 Set 1 | Question: 16
For wastewater coming from a wood pulping industry, Chemical Oxygen Demand $\text{(COD)}$ and $5$-day Biochemical Oxygen Demand $\text{(BOD}_{5})$ were determined. For this wastewater, which of the following statement(s) is/are correct? $\text{COD} > \text{BOD}_{5}$ ... $\text{COD} < \text{BOD}_{5}$ $\text{COD} = \text{BOD}_{5}$

For wastewater coming from a wood pulping industry, Chemical Oxygen Demand $\text{(COD)}$ and $5$-day Biochemical Oxygen Demand $\text{(BOD}_{5})$ were determined. For th...

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85

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)

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 maxim...

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86

GATE Civil 2024 Set 2 | GA Question: 5
The ratio of the number of girls to boys in class $\text{VIII}$ is the same as the ratio of the number of boys to girls in class $\text{IX}$. The total number of students (boys and girls) in classes $\text{VIII}$ and $\text{IX}$ is $450$ ... $\text{VIII}$ and $\text{IX}$ is the same, then the number of girls in each class is $150$ $200$ $250$ $175$

The ratio of the number of girls to boys in class $\text{VIII}$ is the same as the ratio of the number of boys to girls in class $\text{IX}$. The total number of students...

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87

GATE Civil 2023 Set 2 | Question: 1
Let $\phi$ be a scalar field, and $\boldsymbol{u}$ be a vector field. Which of the following identities is true for $\operatorname{div}(\phi \boldsymbol{u})$ ...

Let $\phi$ be a scalar field, and $\boldsymbol{u}$ be a vector field. Which of the following identities is true for $\operatorname{div}(\phi \boldsymbol{u})$? $\operatorn...

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88

GATE Civil 2022 Set 1 | Question: 49
A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of $\text{N, H, and O}$ as $14\:g/mol$, $1\:g/mol$, and $16\:g/mol$, respectively. In this wastewater, the ... . The total nitrogen concentration in this wastewater is _____________ milligram nitrogen per liter. (round off to one decimal place)

A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of $\text{N, H, and O}$ as $14\:g/mol$, $1\:g/mol$, and $16\:g/m...

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89

GATE Civil 2022 Set 1 | Question: 55
For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between the wheels, and $d$ is the clear distance between the wheels. ... round off to one decimal place) (Consider the influence angle to be $45^{\circ}$ for the linear dispersion of stress with depth)

For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between th...

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90

GATE Civil 2023 Set 2 | Question: 9
A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_{H}$ and coefficient of vertical permeability, $k_{V}.$ In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of ... $\sqrt{\frac{k_{V}}{k_{H}}}$ $1.0 $ $\frac{k_{H}}{k_{V}}$

A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_{H}$ and coefficient of vertical permeability, $k_{V}.$ I...

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91

GATE Civil 2023 Set 2 | Question: 37
Which of the following statements is/are TRUE? The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the square root of the distance from the leading edge If the streamlines ... it For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow

Which of the following statements is/are TRUE?The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the squar...

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92

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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93

GATE Civil 2022 Set 1 | Question: 42
Consider a simply supported beam $\text{PQ}$ as shown in the figure. A truck having $100$ $\text{kN}$ on the front axle and $200$ $\text{kN}$ on the rear axle, moves from left to right. The spacing between the axles is $3\: m$. The maximum bending moment at point $R$ is _______________ $\text{kNm}$ (in integer)

Consider a simply supported beam $\text{PQ}$ as shown in the figure. A truck having $100$ $\text{kN}$ on the front axle and $200$ $\text{kN}$ on the rear axle, moves from...

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94

GATE Civil 2024 Set 2 | GA Question: 4
If the sum of the first $20$ consecutive positive odd numbers is divided by $20^{2}$, the result is $1$ $20$ $2$ $1 / 2$

If the sum of the first $20$ consecutive positive odd numbers is divided by $20^{2}$, the result is$1$$20$$2$$1 / 2$

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95

GATE Civil 2022 Set 2 | Question: 32
A $100 \; \text{mg}$ of $\text{HNO}_{3}$ (strong acid) is added to water, bringing the final volume to $1.0 \; \text{liter}.$ Consider the atomic weights of $\text{H, N,}$ and $\text{O,}$ ... $\text{pH}$ of this water is (Ignore the dissociation of water.) $2.8$ $6.5$ $3.8$ $8.5$

A $100 \; \text{mg}$ of $\text{HNO}_{3}$ (strong acid) is added to water, bringing the final volume to $1.0 \; \text{liter}.$ Consider the atomic weights of $\text{H, N,}...

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96

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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97

GATE Civil 2022 Set 1 | Question: 1
Consider the following expression: $z = \sin \left ( y + it \right ) + \cos \left ( y - it \right )$ where $\text{z, y}$ and $t$ are variables, and $i = \sqrt{-1}$ is a complex number. The partial differential equation derived from the above expression ... $\frac{\partial z}{\partial t} + i \frac{\partial z}{\partial y} = 0$

Consider the following expression: $$z = \sin \left ( y + it \right ) + \cos \left ( y - it \right )$$ where $\text{z, y}$ and $t$ are variables, and $i = \sqrt{-1}$ is a...

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98

GATE Civil 2022 Set 1 | Question: 2
For the equation $\frac{d^{3}y}{dx^{3}} + x \left ( \frac{dy}{dx} \right )^{\frac{3}{2}}+ x^{2}y=0$ the correct description is an ordinary differential equation of order $3$ and degree $2$ an ordinary differential equation of ... $2$ and degree $3$ an ordinary differential equation of order $3$ and degree $\frac{3}{2}$

For the equation $$\frac{d^{3}y}{dx^{3}} + x \left ( \frac{dy}{dx} \right )^{\frac{3}{2}}+ x^{2}y=0$$ the correct description isan ordinary differential equation of order...

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99

GATE Civil 2023 Set 2 | Question: 27
Two vectors $\left[\begin{array}{llll}2 & 1 & 0 & 3\end{array}\right]^{T} $ and $\left[\begin{array}{cccc}1 & 0 & 1 & 2\end{array}\right]^{T}$ belong to the null space of a $4 \times 4$ matrix of rank $ 2.$ Which one of ... $\left[\begin{array}{llll}3 & 1 & 1 & 2\end{array}\right]^{T}$

Two vectors $\left[\begin{array}{llll}2 & 1 & 0 & 3\end{array}\right]^{T} $ and $\left[\begin{array}{cccc}1 & 0 & 1 & 2\end{array}\right]^{T}$ belong to the null space of...

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100

GATE Civil 2023 Set 1 | Question: 21
Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. The weld size is $8 \mathrm{~mm}$, and the permissible stress in the weld is ... load $\text{P}$ (in $\mathrm{kN}$, rounded off to one decimal place) that can be transmitted by this welded joint?

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. Th...

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101

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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102

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 $10 \; \text{m/s}^{2}$.)

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 dischar...

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103

GATE Civil 2024 Set 2 | Question: 11
The structural design method that DOES NOT take into account the safety factors on the design loads is working stress method. load factor method. ultimate load method. limit state method.

The structural design method that DOES NOT take into account the safety factors on the design loads isworking stress method.load factor method.ultimate load method.limit ...

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104

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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105

GATE Civil 2022 Set 2 | Question: 29
A post-tensioned concrete member of span $15 \; \text(m)$ and cross-section of $450 \; \text{mm} \times 450 \; \text{mm}$ is prestressed with three steel tendons, each of cross-sectional area $200 \; \text{mm}^{2}.$ The tendons are tensioned one after another to a ... is $14.16 \; \text{MPa}$ $7.08 \; \text{MPa}$ $28.32 \; \text{MPa}$ $42.48 \; \text{MPa}$

A post-tensioned concrete member of span $15 \; \text(m)$ and cross-section of $450 \; \text{mm} \times 450 \; \text{mm}$ is prestressed with three steel tendons, each of...

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106

GATE Civil 2022 Set 1 | Question: 27
A semi-circular bar of radius $\text{R m}$, in a vertical plane, is fixed at the end $G$, as shown in the figure. A horizontal load of magnitude $\text{P kN}$ is applied at the end $H$. The magnitude of the axial force, shear force, and bending moment at point $Q$ for ... $\frac{PR}{\sqrt{2}} \:kNm$ $\frac{P}{\sqrt{2}}\:kN,0\:kN$, and $\frac{PR}{\sqrt{2}} \:kNm$

A semi-circular bar of radius $\text{R m}$, in a vertical plane, is fixed at the end $G$, as shown in the figure. A horizontal load of magnitude $\text{P kN}$ is applied ...

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107

GATE Civil 2023 Set 1 | Question: 3
Creep of concrete under compression is defined as the _________. increase in the magnitude of strain under constant stress increase in the magnitude of stress under constant strain decrease in the magnitude of strain under constant stress decrease in the magnitude of stress under constant strain

Creep of concrete under compression is defined as the _________. increase in the magnitude of strain under constant stress increase in the magnitude of stress under const...

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108

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)

A set of observations of independent variable $(x)$ and the corresponding dependent variable $(y)$ is given below.$$\begin{array}{|c|c|} \hline\text{x} & 5 & 2 & 4 & 3 \\...

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109

GATE Civil 2022 Set 1 | Question: 7
Four different soils are classified as $\text{CH, ML, SP, and SW}$, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement in the decreasing order of hydraulic conductivity? $\text{SW, SP, ML, CH}$ $\text{CH, ML, SP, SW}$ $\text{SP, SW, CH, ML}$ $\text{ML, SP, CH, SW}$

Four different soils are classified as $\text{CH, ML, SP, and SW}$, as per the Unified Soil Classification System. Which one of the following options correctly represents...

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110

GATE Civil 2022 Set 1 | Question: 12
The total hardness in raw water is $500$ milligram per liter as $CaCO_{3}$. The total hardness of this raw water, expressed in milligram equivalent per liter, is (Consider the atomic weights of $\text{Ca, C, and O}$ as $40$ $\text{g/mol}$, $12$ $\text{g/mol}$, and $16$ $\text{g/mol}$, respectively.) $10$ $100$ $1$ $5$

The total hardness in raw water is $500$ milligram per liter as $CaCO_{3}$. The total hardness of this raw water, expressed in milligram equivalent per liter, is(Consider...

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111

GATE Civil 2023 Set 2 | Question: 51
A consolidated drained $\text{(CD)}$ triaxial test was carried out on a sand sample with the known effective shear strength parameters, $c^{\prime}=0$ and $\phi^{\prime}=30^{\circ}$. In the test, prior to the failure, when the sample ... is applied in either of the tests, what is the deviatoric stress (in $\mathrm{kPa}$, in integer) at the failure?___________

A consolidated drained $\text{(CD)}$ triaxial test was carried out on a sand sample with the known effective shear strength parameters, $c^{\prime}=0$ and $\phi^{\prime}=...

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112

GATE Civil 2024 Set 1 | GA Question: 2
In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from $301$, while the house-numbers on the other side of the road are consecutive even numbers starting from $302$. The ... of the road is $27$, then the number of houses on each side of the road is $27$ $52$ $54$ $26$

In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from $301$, while th...

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113

GATE Civil 2022 Set 2 | Question: 37
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section ... . In choked condition, $y_{1}$ increases if the flow is supercritical and decreases if the flow is subcritical.

Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to rea...

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114

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)

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...

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115

GATE Civil 2022 Set 1 | Question: 36
A horizontal force of $\text{P kN}$ is applied to a homogeneous body of weight $25$ $\text{kN}$, as shown in the figure. The coefficient of friction between the body and the floor is $0.3$. Which of the following statement(s) is/are correct? ... the body never occurs. No motion occurs for $P\leq 6$ $\text{kN}$. The motion of the body will occur by sliding only

A horizontal force of $\text{P kN}$ is applied to a homogeneous body of weight $25$ $\text{kN}$, as shown in the figure. The coefficient of friction between the body and ...

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116

GATE Civil 2023 Set 2 | Question: 34
The critical flow condition in a channel is given by ____________. [Note: $\alpha$ - kinetic energy correction factor; $Q$ - discharge; $A_c$ - cross-sectional area of flow at critical flow condition; $T_c$ - top width of flow at critical flow condition; $g$ - acceleration due ... $\frac{\alpha Q^2}{g}=\frac{A_c^3}{T_c^2}$ $\frac{\alpha Q}{g}=\frac{A_c^3}{T_c}$

The critical flow condition in a channel is given by ____________.[Note: $\alpha$ - kinetic energy correction factor; $Q$ - discharge; $A_c$ - cross-sectional area of flo...

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117

GATE Civil 2024 Set 2 | Question: 30
Consider the statements $\mathrm{P}$ and $\mathrm{Q}$ related to the analysis/design of retaining walls. $\mathrm{P}$: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobilizes in upward direction along the wall. $\mathrm{Q}$ ... Both $\mathrm{P}$ and $\mathrm{Q}$ are FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE

Consider the statements $\mathrm{P}$ and $\mathrm{Q}$ related to the analysis/design of retaining walls.$\mathrm{P}$: When a rough retaining wall moves toward the backfil...

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118

GATE Civil 2023 Set 2 | Question: 30
Two plates are connected by fillet welds of size $10 \mathrm{~mm}$ and subjected to tension, as shown in the figure. The thickness of each plate is $12 \mathrm{~mm}$. The yield stress and the ultimate stress of steel under tension are $250 \mathrm{~MPa}$ ... each weld to transmit a factored force $\text{P}$ equal to $275 \mathrm{~kN}$? $100$ $105$ $110$ $115$

Two plates are connected by fillet welds of size $10 \mathrm{~mm}$ and subjected to tension, as shown in the figure. The thickness of each plate is $12 \mathrm{~mm}$. The...

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119

GATE Civil 2023 Set 1 | Question: 9
When a supercritical stream enters a mild-sloped $(\mathrm{M})$ channel section, the type of flow profile would become _________. $\mathrm{M}_{1}$ $\mathrm{M}_{2}$ $\mathrm{M}_{3}$ $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$

When a supercritical stream enters a mild-sloped $(\mathrm{M})$ channel section, the type of flow profile would become _________.$\mathrm{M}_{1}$$\mathrm{M}_{2}$ $\mathrm...

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120

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)

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 ...

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Arjun asked Feb 15, 2022

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