Recent questions tagged numerical-answers / GO Civil

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161

GATE2020-CE-1-41
A rigid, uniform, weightless, horizontal bar is connected to three vertical members P , Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of $10\:kN/mm$ . The lower ends of bars $P$ and $R$ rest ... $W$ (in $kN$, round off to the nearest integer), is ______.

A rigid, uniform, weightless, horizontal bar is connected to three vertical members P , Q and R as shown in the figure (not drawn to the scale). All three members have id...

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162

GATE2020-CE-1-42
The flange and web plates of the doubly symmetric built-up section are connected by continuous $10\:mm$ thick fillet welds as shown in figure (not drawn to the scale). The moment of inertia of the section about its principal axis $X-X$ ... welds. The maximum shear force (in $kN$ , round off to one decimal place ) that can be carried by the section, is ______.

The flange and web plates of the doubly symmetric built-up section are connected by continuous $10\:mm$ thick fillet welds as shown in figure (not drawn to the scale). Th...

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163

GATE2020-CE-1-43
The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of $M25$ grade concrete and $Fe500$ grade reinforcing steel. The total cross-sectional area of the tension steel is $942\:mm^2$. As per Limit State Design IS $456:2000$, the design moment capacity (in $kN.m$, round off to two decimal places) of the beam section, is __________

The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of $M25$ grade concrete and $Fe500$ grade reinforcing steel. The total cr...

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164

GATE2020-CE-1-44
A simply supported prismatic concrete beam of rectangular cross-section, having a span of $8\:m$, is prestressed with an effective prestressing force of $600\:kN$. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of $e$ at ... at the mid-span, the required value of e (in $mm$, round off to the nearest integer) of the tendon, is ______.

A simply supported prismatic concrete beam of rectangular cross-section, having a span of $8\:m$, is prestressed with an effective prestressing force of $600\:kN$. The ec...

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165

GATE2020-CE-1-45
Traffic volume count has been collected on a $2$-lane road section which needs upgradation due to severe traffic flow condition. Maximum service flow rate per lane is observed as $1280\:veh/h$ ... are Regular Commuters', the number of extra lane(s) (round off to the next higher integer) to be provided, is ______.

Traffic volume count has been collected on a $2$-lane road section which needs upgradation due to severe traffic flow condition. Maximum service flow rate per lane is obs...

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166

GATE2020-CE-1-46
A vertical retaining wall of $5\:m$ height has to support soil having unit weight of $18\:kN/m^3$ , effective cohesion of $12\:kN/m^2$, and effective friction angle of $30^\circ{}$ . As per Rankine's earth pressure theory and assuming that a ... has occurred, the lateral active thrust on the wall per meter length ( in $kN/m$ , round off to two decimal places), is __________

A vertical retaining wall of $5\:m$ height has to support soil having unit weight of $18\:kN/m^3$ , effective cohesion of $12\:kN/m^2$, and effective friction angle of $3...

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167

GATE2020-CE-1-47
Water flows in the upward direction in a tank through $2.5\;m$ thick sand layer as shown in the figure. The void ratio and specific gravity of sand are $0.58$ and $2.7$, respectively. The sand is fully saturated. Unit weight of water is $10\:kN/m^3$. The ... (in $kPa$, round off to two decimal places) at point $\textbf{A}$, located $1\:m$ above the base of tank, is ______.

Water flows in the upward direction in a tank through $2.5\;m$ thick sand layer as shown in the figure. The void ratio and specific gravity of sand are $0.58$ and $2.7$, ...

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168

GATE2020-CE-1-48
A $10\:m$ thick clay layer is resting over a $3\:m$ thick sand layer and is submerged. A fill of $2\:m$ thick sand with unit weight of $20\:kN/m^3$ is placed above the clay layer to accelerate the rate of consolidation of the clay layer. ... settlement (in $mm$, round off to two decimal places) of the clay layer, $10$ years after the construction of the fill, is ______.

A $10\:m$ thick clay layer is resting over a $3\:m$ thick sand layer and is submerged. A fill of $2\:m$ thick sand with unit weight of $20\:kN/m^3$ is placed above the cl...

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169

GATE2020-CE-1-49
Three reservoirs $P,Q$ and $R$ are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction $S$ of the pipes is $100\:m$. Assume acceleration due to gravity as $9.81\:m/s^2$ ... height of water level in the lowermost reservoir $R$ (in $m$, round off to one decimal place) with respect to the datum, is ______.

Three reservoirs $P,Q$ and $R$ are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction $S$ of the pipes is $100\:m$....

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170

GATE2020-CE-1-50
In a homogenous unconfined aquifer of area $3.00\:km^2$, the water table was at an elevation of $102.00\:m$. After a natural recharge of volume $0.90$ million cubic meter $(Mm^3)$, the water table rose to $103.20\:m$. After this recharge,ground ... $Mm^3$ and round off to two decimal places), is ______.

In a homogenous unconfined aquifer of area $3.00\:km^2$, the water table was at an elevation of $102.00\:m$. After a natural recharge of volume $0.90$ million cubic meter...

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171

GATE2020-CE-1-51
A circular water tank of $2\:m$ diameter has a circular orifice of diameter $0.1\:m$ at the bottom. Water enters the tank steadily at a flow rate of $20\:litre/s$ and escapes through the orifice. The coefficient of discharge of the orifice is $0.8$. ... losses. The height of the water level (in $m$, round off to two decimal places) in the tank at the steady state, is ______.

A circular water tank of $2\:m$ diameter has a circular orifice of diameter $0.1\:m$ at the bottom. Water enters the tank steadily at a flow rate of $20\:litre/s$ and esc...

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172

GATE2020-CE-1-52
Surface Overflow Rate (SOR) of a primary settling tank (discrete settling) is $20000\:litre/m^2$ per day. Kinematic viscosity of water in the tank is $1.01\times10^{-2}\:cm^2/s$. Specific gravity of the settling particles is $2.64$. Acceleration due to ... $80\%$ efficiency in the tank, is ______.

Surface Overflow Rate (SOR) of a primary settling tank (discrete settling) is $20000\:litre/m^2$ per day. Kinematic viscosity of water in the tank is $1.01\times10^{-2}\:...

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173

GATE2020-CE-1-54
A stream with a flow rate of $5\:m^3/s$ is having an ultimate BOD of $30\:mg/litre$. A wastewater discharge of $0.20\:m^3/s$ having $BOD_5\:\text{of}\:500\:mg/litre$ joins the stream at a location and instantaneously gets mixed up completely. The ... $e$). The BOD (in mg/litre, round off to two decimal places) remaining at $3\:km$ downstream from the mixing location, is __________

A stream with a flow rate of $5\:m^3/s$ is having an ultimate BOD of $30\:mg/litre$. A wastewater discharge of $0.20\:m^3/s$ having $BOD_5\:\text{of}\:500\:mg/litre$ join...

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174

GATE2020-CE-1-55
The lengths and bearings of a traverse $PQRS$ are: $\begin{array}{|c|c|c|}\hline \text{Segment}&\text{Length}\:(m) &\text{Bearing}\\\hline PQ&40&80^\circ{} \\\hline QR&50&10^\circ{} \\\hline RS&30&210^\circ{}\\\hline\end{array}$ The length of line segment SP (in $m$, round off to two decimal places), is __________

The lengths and bearings of a traverse $PQRS$ are:$$\begin{array}{|c|c|c|}\hline \text{Segment}&\text{Length}\:(m) &\text{Bearing}\\\hline PQ&40&80^\circ{} \\\hline QR&...

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175

GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.

A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.

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176

GATE2020 CE-2-19
The maximum applied load on a cylindrical concrete specimen of diameter $150\: mm$ and length $300\: mm$ tested as per the split tensile strength test guidelines of $IS\:5816:1999$ is $157\: kN$. The split tensile strength (in $MPa,$ round off to one decimal place) of the specimen is _______.

The maximum applied load on a cylindrical concrete specimen of diameter $150\: mm$ and length $300\: mm$ tested as per the split tensile strength test guidelines of $IS\:...

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177

GATE2020 CE-2-20
For an axle load of $15$ tonne on a road, the Vehicle Damage Factor (round off to two decimal places), in terms of the standard axle load of $8$ tonne, is __________.

For an axle load of $15$ tonne on a road, the Vehicle Damage Factor (round off to two decimal places), in terms of the standard axle load of $8$ tonne, is __________.

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178

GATE2020 CE-2-21
$24$-$h$ traffic count at a road section was observed to be $1000$ vehicles on a Tuesday in the month of July. If daily adjustment factor for Tuesday is $1.21$ and monthly adjustment factor for July is $0.913$, the Annual Average Daily Traffic (in veh/day, round off to the nearest integer) is __________.

$24$-$h$ traffic count at a road section was observed to be $1000$ vehicles on a Tuesday in the month of July. If daily adjustment factor for Tuesday is $1.21$ and monthl...

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179

GATE2020 CE-2-22
A soil has dry unit weight of $15.5\: kN/m^3$, specific gravity of $2.65$ and degree of saturation of $72\: %.$ Considering the unit weight of water as $10\: kN/m^3$, the water content of the soil (in $\%$ round off to two decimal places) is __________.

A soil has dry unit weight of $15.5\: kN/m^3$, specific gravity of $2.65$ and degree of saturation of $72\: %.$ Considering the unit weight of water as $10\: kN/m^3$, the...

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180

GATE2020 CE-2-23
A one-dimensional consolidation test is carried out on a standard $19\: mm$ thick clay sample. The oedometer’s deflection gauge indicates a reading of $2.1\: mm$, just before removal of the load, without allowing any swelling. The void ratio is $0.62$ at this stage. The initial void ratio (round off to two decimal places) of the standard specimen is __________.

A one-dimensional consolidation test is carried out on a standard $19\: mm$ thick clay sample. The oedometer’s deflection gauge indicates a reading of $2.1\: mm$, just ...

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181

GATE2020 CE-2-24
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{-1}$, round off to two decimal places) at $y = 0$, is ________.

Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vert...

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182

GATE2020 CE-2-25
Two identically sized primary settling tanks receive water for $\text{Type-I}$ settling (discrete particles in dilute suspension) under laminar flow conditions. The Surface Overflow Rate (SOR) maintained in the two tanks are $30\ m^3/m^2.d$ and $15\: m^3/m^2.d$. ... $d_{15}$ respectively. The ratio, $\large \dfrac{d_{30}}{d_{15}}$ (round off to two decimal places), is ________.

Two identically sized primary settling tanks receive water for $\text{Type-I}$ settling (discrete particles in dilute suspension) under laminar flow conditions. The Surfa...

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183

GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.

The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \si...

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184

GATE2020 CE-2-40
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The absolute error in the computed volume ( in $cm^3$ ,round off to three decimal places), is ________

The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The abso...

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185

GATE2020 CE-2-41
A concrete beam of span $15\: m,\ 150\: mm$ wide and $350\: mm$ ... cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is ________.

A concrete beam of span $15\: m,\ 150\: mm$ wide and $350\: mm$ deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of...

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186

GATE2020 CE-2-42
The plane truss has hinge supports at $P$ and $W$ and is subjected to the horizontal forces as shown in the figure (not drawn to the scale) Representing the tensile force with $’+’$ sign and the compressive force with $’-’$ sign, the force in member $XW$ (in $kN$, round off to the nearest integer), is ________.

The plane truss has hinge supports at $P$ and $W$ and is subjected to the horizontal forces as shown in the figure (not drawn to the scale)Representing the tensile force ...

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187

GATE2020 CE-2-43
The cross-section of the reinforced concrete beam having an effective depth of $500\: mm$ is shown in the figure (not drawn to the scale ). The grades of concrete and steel used are $M35$ and $Fe550$, respectively. The area of tension reinforcement is ... ( in $mm,$ round off to the nearest integer ) of the neutral axis measured from the extreme compression fiber, is ________.

The cross-section of the reinforced concrete beam having an effective depth of $500\: mm$ is shown in the figure (not drawn to the scale ). The grades of concrete and ste...

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188

GATE2020 CE-2-44
Two steel plates are lap jointed in a workshop using $6\ mm$ thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is $410\: MPa.$ As per Limit State Design of $IS\: 800:2007$, the design capacity (in $kN$, round off to three decimal places) of the welded connection, is ________.

Two steel plates are lap jointed in a workshop using $6\ mm$ thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is $410\...

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189

GATE2020 CE-2-45
The design speed of a two-lane two-way road is $60\: km/h$ and the longitudinal coefficient of friction is $0.36$. The reaction time of a driver is $2.5$ seconds. Consider acceleration due to gravity as $9.8 m/s^2$. The intermediate sight distance (in $m,$ round off to the nearest integer) required for the road is ________.

The design speed of a two-lane two-way road is $60\: km/h$ and the longitudinal coefficient of friction is $0.36$. The reaction time of a driver is $2.5$ seconds. Conside...

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190

GATE2020 CE-2-46
A footing of size $2\: m \times 2\: m$ transferring a pressure of $200\: kN/m^2$, is place at a depth of $1.5\: m$ below the ground as shown in the figure (not drawn to the scale ). The clay stratum is normally consolidated. The clay has ... $\gamma_w= 10\: kN/m^3$, the primary consolidation settlement in (in mm, round off to two decimal places) of the clay stratum is ________.

A footing of size $2\: m \times 2\: m$ transferring a pressure of $200\: kN/m^2$, is place at a depth of $1.5\: m$ below the ground as shown in the figure (not drawn to t...

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191

GATE2020 CE-2-47
A constant-head permeability test was conducted on a soil specimen under a hydraulic gradient of $2.5$. The soil specimen has specific gravity of $2.65$ and saturated water content of $20\%.$ If the coefficient of permeability of the soil is $0.1\: cm/s$, the seepage velocity (in $cm/s,$ round off to two decimal places) through the soil specimen is ________.

A constant-head permeability test was conducted on a soil specimen under a hydraulic gradient of $2.5$. The soil specimen has specific gravity of $2.65$ and saturated wat...

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192

GATE2020 CE-2-48
A $5\: m$ high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18\: kN/m^3$ and $20\: kPa$, respectively. The angle of internal friction of clay is zero. In order to prevent development of tension zone, the ... tension zone, the minimum height (in $m$, round off to one decimal place) by which the wall has to be raised, is ________.

A $5\: m$ high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18\: kN/m^3$ and $20\: kPa$, respectively. The angle of in...

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193

GATE2020 CE-2-49
A cast iron pipe of diameter $600\: mm$ and length $400\: m$ carries water from a tank and discharges freely into air at a point $4.5\: m$ below the water surface in the tank. The friction factor of the pipe is $0.018$. Consider acceleration due to gravity as $9.81\: m/s^2$. The velocity of the flow in pipe (in $m/s$, round off to two decimal places) is ________.

A cast iron pipe of diameter $600\: mm$ and length $400\: m$ carries water from a tank and discharges freely into air at a point $4.5\: m$ below the water surface in the ...

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194

GATE2020 CE-2-50
A hydraulic jump occurs in a triangular $\text{(V-shaped)}$ channel with side slopes $1:1$ (vertical to horizontal). The sequent depths are $0.5\: m$ and $1.5\: m$. The flow rate (in $m^3/s$, round off to two decimal places) in the channel is ________.

A hydraulic jump occurs in a triangular $\text{(V-shaped)}$ channel with side slopes $1:1$ (vertical to horizontal). The sequent depths are $0.5\: m$ and $1.5\: m$. The f...

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195

GATE2020 CE-2-51
A concrete dam holds $10\: m$ of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the heel, to zero at the toe of the dam. The coefficient of friction between the dam ... , respectively. For NO sliding condition, the required minimum base width $B$ (in $m$ round off to two decimal places) is ________.

A concrete dam holds $10\: m$ of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the he...

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196

GATE2020 CE-2-52
The ion product of water $(pK_w)$ is $14$. If a rain water sample has a $pH$ of $5.6$, the concentration of $OH^-$ in the sample (in $10^{-9}\: \text{mol/litre}$, round off to one decimal place), is ________.

The ion product of water $(pK_w)$ is $14$. If a rain water sample has a $pH$ of $5.6$, the concentration of $OH^-$ in the sample (in $10^{-9}\: \text{mol/litre}$, round o...

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197

GATE2020 CE-2-53
A waste to energy plant burns dry solid waste of composition: Carbon $= 35\%$, Oxygen $= 26\%$ , Hydrogen $= 10\%$, Sulphur $= 6\%$, Nitrogen $= 3\%$ and Inerts $= 20\%.$ Burning rate is $1000\: $ tonnes/d. Oxygen in air ... The stoichiometric (theoretical) amount of air ( in tonnes/d, round off to the nearest integer) required for complete burning of this waste is ________.

A waste to energy plant burns dry solid waste of composition: Carbon $= 35\%$, Oxygen $= 26\%$ , Hydrogen $= 10\%$, Sulphur $= 6\%$, Nitrogen $= 3\%$ and Inerts $= 20\%.$...

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198

GATE2020 CE-2-54
A sample of water contains an organic compound $C_8H_{16}O_8$ at a concentration of $10^{-3}\: \text{mol/litre}$. Given that the atomic weight of $C = 12\: \text{g/mol}, H = 1\: \text{g/mol}$, and $O = 16\: \text{g/mol}$, the theoretical oxygen demand of water (in $g$ of $O_2$ per litre, round off to two decimal places), is ________.

A sample of water contains an organic compound $C_8H_{16}O_8$ at a concentration of $10^{-3}\: \text{mol/litre}$. Given that the atomic weight of $C = 12\: \text{g/mol}, ...

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199

GATE2020 CE-2-55
A theodolite is set up at station $A$. The $RL$ of instrument axis is $212.250\: m$. The angle of elevation to the top of a $4\: m$ long staff, held vertical at station $B$, is $7^{\circ}$.The horizontal distance between stations $A$ and $B$ ... the errors due to curvature of earth and refraction, the $RL$ (in $m,$ round off to three decimal places) of station $B$ is ________.

A theodolite is set up at station $A$. The $RL$ of instrument axis is $212.250\: m$. The angle of elevation to the top of a $4\: m$ long staff, held vertical at station $...

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200

GATE2017 CE-2-19
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________

The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________

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gatecse asked Aug 7, 2019