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161

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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162

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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163

GATE Civil 2023 Set 2 | Question: 31
In the given figure, Point $\mathrm{O}$ indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path $\text{(OP),}$ which of the following loading conditions is correct? $\sigma_v$ is ... $\sigma_v$ is increasing and $\sigma_h$ is decreasing $\sigma_v$ is decreasing and $\sigma_h$ is increasing

In the given figure, Point $\mathrm{O}$ indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path $\text{(OP),}$ which...

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164

GATE Civil 2023 Set 2 | Question: 32
The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: $P$ as the reaction force between the wall ... that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.

The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces ac...

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165

GATE Civil 2023 Set 2 | Question: 33
A compound symmetrical open channel section as shown in the figure has a maximum of ______________ critical depth(s). $3$ $2$ $1$ $4$

A compound symmetrical open channel section as shown in the figure has a maximum of ______________ critical depth(s).$3$$2$$1$$4$

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166

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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167

GATE Civil 2023 Set 2 | Question: 35
Match the following air pollutants with the most appropriate adverse health effects: ...

Match the following air pollutants with the most appropriate adverse health effects:$$\begin{array}{|l|l|}\hline \textbf{Air pollutant} & \textbf{Health effect to human a...

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168

GATE Civil 2023 Set 2 | Question: 36
A delivery agent is at a location $\mathrm{R}$. To deliver the order, she is instructed to travel to location P along straight-line paths of $\mathrm{RC}, \mathrm{CA}, \mathrm{AB}$ and $\mathrm{BP}$ of $5 \mathrm{~km}$ each. The direction of each path is given in the ... $\mathrm{L}=5.0 ; \mathrm{D}=2.5$ $\mathrm{L}=0.0 ; \mathrm{D}=0.0$

A delivery agent is at a location $\mathrm{R}$. To deliver the order, she is instructed to travel to location P along straight-line paths of $\mathrm{RC}, \mathrm{CA}, \m...

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169

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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170

GATE Civil 2023 Set 2 | Question: 38
In the context of water and wastewater treatments, the correct statements are: particulate matter may shield microorganisms during disinfection ammonia decreases chlorine demand phosphorous stimulates algal and aquatic growth calcium and magnesium increase hardness and total dissolved solids

In the context of water and wastewater treatments, the correct statements are:particulate matter may shield microorganisms during disinfectionammonia decreases chlorine d...

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171

GATE Civil 2023 Set 2 | Question: 39
Which of the following statements is/are TRUE for the aerobic composting of sewage sludge? Bulking agent is added during the composting process to reduce the porosity of the solid mixture Leachate can be generated during composting Actinomycetes are involved in the process In-vessel composting systems cannot be operated in the plug-flow mode

Which of the following statements is/are TRUE for the aerobic composting of sewage sludge?Bulking agent is added during the composting process to reduce the porosity of t...

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172

GATE Civil 2023 Set 2 | Question: 40
The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true? Speed is higher in Region $\mathrm{R}$ than in Region $\mathrm{P}$ Volume is ... $\mathrm{P}$ Density is higher in Region $\mathrm{Q}$ than in Region $\mathrm{R}$

The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements a...

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173

GATE Civil 2023 Set 2 | Question: 41
Consider the Marshall method of mix design for bituminous mix. With the increase in bitumen content, which of the following statements is/are TRUE? the Stability decreases initially and then increases the Flow increases monotonically the air voids $(V A)$ increases initially and then decreases the voids filled with bitumen $(V F B)$ increases monotonically

Consider the Marshall method of mix design for bituminous mix. With the increase in bitumen content, which of the following statements is/are TRUE?the Stability decreases...

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174

GATE Civil 2023 Set 2 | Question: 42
A $5 \mathrm{~cm}$ long metal rod $\mathrm{AB}$ was initially at a uniform temperature of $T_0{ }^{\circ} \mathrm{C}$. Thereafter, temperature at both the ends are maintained at $0{ }^{\circ} \mathrm{C}$. Neglecting the heat transfer from the ... $\beta$ (in $\mathrm{s}^{-1}$, rounded off to three decimal places) is__________________.

A $5 \mathrm{~cm}$ long metal rod $\mathrm{AB}$ was initially at a uniform temperature of $T_0{ }^{\circ} \mathrm{C}$. Thereafter, temperature at both the ends are mainta...

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175

GATE Civil 2023 Set 2 | Question: 43
A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (round off to one decimal place).

A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (...

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176

GATE Civil 2023 Set 2 | Question: 44
For the frame shown in the figure (not to scale), all members $\mathrm{(AB, BC, CD, GB,}$ and $\mathrm{CH}$) have the same length, $L$ and flexural rigidity, $E I$. The joints at $\mathrm{B}$ and $\mathrm{C}$ are rigid joints, and ... magnitude of the moment reaction at $\mathrm{A}$ is $w L^2 / k$. What is the value of $k$ (in integer)? ______________________

For the frame shown in the figure (not to scale), all members $\mathrm{(AB, BC, CD, GB,}$ and $\mathrm{CH}$) have the same length, $L$ and flexural rigidity, $E I$. The j...

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177

GATE Civil 2023 Set 2 | Question: 45
Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure $(M25$ grade concrete, $Fe415$ grade steel). The stress block parameters for the section at ultimate limit state, as per $IS \; 456: 2000$ ... cube strength of concrete, $f_y$ is the yield stress of steel, and $x_u$ is the depth of neutral axis.]

Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure $(M25$ grade concrete, $Fe415$ grade steel). The stress block p...

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178

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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179

GATE Civil 2023 Set 2 | Question: 47
An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member $\mathrm{PQ}$ to the vertical member $\mathrm{RS}$ at $\mathrm{P}$ is ____________ (round off to one decimal place).

An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member $\mathrm{PQ}$ to the vertical memb...

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180

GATE Civil 2023 Set 2 | Question: 48
A square footing is to be designed to carry a column load of $500~ \mathrm{kN}$ which is resting on a soil stratum having the following average properties: bulk unit weight $=19 ~\mathrm{kN} / \mathrm{m}^3$; angle of internal ... (round off to one decimal place) [Assume the applicable shape and depth factor values as unity; ground water level at greater depth.]

A square footing is to be designed to carry a column load of $500~ \mathrm{kN}$ which is resting on a soil stratum having the following average properties: bulk unit weig...

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181

GATE Civil 2023 Set 2 | Question: 49
A circular pile of diameter $0.6 \mathrm{~m}$ and length $8 \mathrm{~m}$ was constructed in a cohesive soil stratum having the following properties: bulk unit weight $=19~ \mathrm{kN} / \mathrm{m}^{3}$; angle of internal friction $=0^{\circ}$ ... (round off to one decimal place). [Adopt: Adhesion factor, $\alpha=1.0$ and Bearing capacity factor, $N_{c}=9.0$ ]

A circular pile of diameter $0.6 \mathrm{~m}$ and length $8 \mathrm{~m}$ was constructed in a cohesive soil stratum having the following properties: bulk unit weight $=19...

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182

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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183

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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184

GATE Civil 2023 Set 2 | Question: 52
A catchment may be idealized as a circle of radius $30 \mathrm{~km}$. There are five rain gauges, one at the center of the catchment and four on the boundary (equi-spaced), as shown in the figure (not to scale). The annual rainfall ... , what is the average rainfall (in $\text{mm,}$ rounded off to two decimal places) over the catchment in that year?___________

A catchment may be idealized as a circle of radius $30 \mathrm{~km}$. There are five rain gauges, one at the center of the catchment and four on the boundary (equi-spaced...

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185

GATE Civil 2023 Set 2 | Question: 53
The cross-section of a small river is sub-divided into seven segments of width $1.5 \mathrm{~m}$ each. The average depth, and velocity at different depths were measured during a field campaign at the middle of each segment width. The discharge computed by the velocity area ...

The cross-section of a small river is sub-divided into seven segments of width $1.5 \mathrm{~m}$ each. The average depth, and velocity at different depths were measured d...

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186

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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187

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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188

GATE Civil 2023 Set 1 | GA Question: 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The figure below consists of $20$ unit squares arranged as shown. In addition to the given black squares, upto $5$ ... is representative) $\text{d}$ $\text{c, d, i}$ $\text{c, i}$ $\text{c, d, i, f, g}$

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.The figure b...

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189

GATE Civil 2023 Set 1 | GA Question: 7
Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), $P(x)$, of a variable $x?$ mean $=$ median $\neq$ mode mean $=$ median $=\operatorname{mode}$ $\operatorname{mean} \neq \operatorname{median}=\operatorname{mode}$ mean $\neq$ mode $=$ median

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), $P(x)$, of a variable $...

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190

GATE Civil 2023 Set 1 | GA Question: 8
The James Webb telescope, recently launched in space, is giving humankind unprecedented access to the depths of time by imaging very old stars formed almost $13$ billion years ago. Astrophysicists and cosmologists believe that this odyssey ... dark matter was known to interact via the strong-interaction, then the epithet "dark" would be justified.

The James Webb telescope, recently launched in space, is giving humankind unprecedented access to the depths of time by imaging very old stars formed almost $13$ billion ...

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191

GATE Civil 2023 Set 1 | GA Question: 9
Let $a=30 !, b=50!,$ and $c=100!.$ Consider the following numbers: $\log _a c, \quad \log _c a, \quad \log _b a, \quad \log _a b$ Which one of the following inequalities is $\text{CORRECT?}$ $\log _c a<\log _b a<\log _a b<\log _a c$ ... $\log _c a<\log _b a<\log _a c<\log _a b$ $\log _b a<\log _c a<\log _a b<\log _a c$

Let $a=30 !, b=50!,$ and $c=100!.$ Consider the following numbers:$$\log _a c, \quad \log _c a, \quad \log _b a, \quad \log _a b$$Which one of the following inequalities ...

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192

GATE Civil 2023 Set 1 | GA Question: 10
A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius $2 \mathrm{~cm}$, as shown. The area of the shaded region is__________$\text{cm}^{2}.$ $8$ $4$ $12$ $10$

A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of...

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193

GATE Civil 2023 Set 1 | Question: 1
For the integral $I=\int_{-1}^{1} \frac{1}{x^{2}} d x$ which of the following statements is $\text{TRUE?}$ $I=0$ $I=2$ $I=-2$ The integral does not converge

For the integral$$I=\int_{-1}^{1} \frac{1}{x^{2}} d x$$which of the following statements is $\text{TRUE?}$ $I=0$ $I=2$$I=-2$ The integral does not converge

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194

GATE Civil 2023 Set 1 | Question: 2
A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress ... $15.0$ $25.0$ $35.0$ $45.0$

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the ...

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195

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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196

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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197

GATE Civil 2023 Set 1 | Question: 5
In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE? Compressive strength decreases but workability increases Compressive strength increases but workability decreases Both compressive strength and workability decrease Both compressive strength and workability increase

In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE? Compressive strength decreases but workability incr...

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198

GATE Civil 2023 Set 1 | Question: 6
The specific gravity of a soil is $2.60$. The soil is at $50 \%$ degree of saturation with water content of $15 \%$. The void ratio of the soil is _______. 0.35 0.78 0.87 1.28

The specific gravity of a soil is $2.60$. The soil is at $50 \%$ degree of saturation with water content of $15 \%$. The void ratio of the soil is _______.0.350.780.871.2...

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199

GATE Civil 2023 Set 1 | Question: 7
A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm{~m} $ ... $ 60 \%$? $0.582$ $0.486$ $0.391$ $ 0.677$

A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm...

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200

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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