Recent questions tagged gate2020-ce-1 / GO Civil

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41

GATE2020-CE-1-26
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $-5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $-10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$

For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the s...

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42

GATE2020-CE-1-32
The relationship between traffic flow rate (q) and density (D) is shown in the figure The shock wave condition is depicted by flow with respect to point $1\:(q_1=q_{max})$ flow changing from point $2$ to point $6\:(q_2>q_6)$ flow changing from point $3$ to point $7\:(q_3<q_7)$ flow with respect to point $4$ and point $5\:(q_4=q_5)$

The relationship between traffic flow rate (q) and density (D) is shown in the figure The shock wave condition is depicted byflow with respect to point $1\:(q_1=q_{max})$...

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43

GATE2020-CE-1-33
The appropriate design length of a clearway is calculated on the basis of ‘Normal Take-off’ condition. Which one of the following options correctly depicts the length of the clearway? (Note: None of the options are drawn to scale)

The appropriate design length of a clearway is calculated on the basis of ‘Normal Take-off’ condition. Which one of the following options correctly depicts the length...

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44

GATE2020-CE-1-34
The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below ... $OP-III, OQ-II, OR-I, OS-IV$ $OP-I, OQ-III, OR-II, OS-IV$

The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below $\begin{...

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45

GATE2020-CE-1-35
The soil profile at a site up to a depth of $10\:m$ is shown in the figure ( not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of $70\:kN/m^2$ at the ground level. The water table is at a depth of $3\:m$ below ground level. The soil unit weight ... $kPa$) at points $P$ and $Q$, respectively, are $124$ and $204$ $36$ and $ 90$ $36$ and $126$ $54$ and $95$

The soil profile at a site up to a depth of $10\:m$ is shown in the figure ( not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of $70\:kN/m^2$ a...

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46

GATE2020-CE-1-36
Water flows at the rate of $12\:m^3/s$ in a $6\:m$ wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is $30\:cm$ (just before the jump). Considering acceleration due to gravity as $9.81\:m/s^2$ and density of water as $1000\:kg/m^3$, the energy loss in the jump is $114.2\:kW$ $114.2\:MW$ $141.2\:h.p.$ $141.2\:J/s$

Water flows at the rate of $12\:m^3/s$ in a $6\:m$ wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is $30\:cm$ (ju...

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47

GATE2020-CE-1-37
A water supply scheme transports $10\:MLD$ (MIllion Litres per Day) water through a $450\:mm$ diameter pipeline for a distance of $2.5\:km$. A chlorine dose of $3.50\:mg/litre$ is applied at the starting point of the pipeline to attain a certain level of disinfection at ... the chlorine dose (in $mg/litre$) to be applied at the starting point should be $3.95$ $4.40$ $4.75$ $5.55$

A water supply scheme transports $10\:MLD$ (MIllion Litres per Day) water through a $450\:mm$ diameter pipeline for a distance of $2.5\:km$. A chlorine dose of $3.50\:mg/...

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48

GATE2020-CE-1-38
An open traverse PQRST is surveyed using theodolite and the consecutive coordinates obtained are given in the table If the independent coordinates (Northing, Easting) of station $P$ are $(400\:m,200\:m)$, the independent coordinates (in $m$) of station $T$, are $194.7,370.1$ $205.3,429.9$ $394.7,170.1$ $405.3,229.9$

An open traverse PQRST is surveyed using theodolite and the consecutive coordinates obtained are given in the tableIf the independent coordinates (Northing, Easting) of s...

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49

GATE2020-CE-1-39
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______

If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral$$\int_C [(y+z)dx+(x...

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50

GATE2020-CE-1-40
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.

Consider the system of equations$$\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 ...

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51

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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52

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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53

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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54

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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55

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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56

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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57

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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58

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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59

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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60

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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61

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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62

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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63

GATE2020-CE-1-53
A gaseous chemical has a concentration of $41.6\:\mu mol/m^3$ in air at $1$ atm pressure and temperature $293\:K$. The universal gas constant $R$ is $82.05\times10^{-6}\;(m^3\:atm)/(mol\:K)$. Assuming that ideal gas law is valid , the concentration of the gaseous chemical (in ppm, round off to one decimal place), is ______.

A gaseous chemical has a concentration of $41.6\:\mu mol/m^3$ in air at $1$ atm pressure and temperature $293\:K$. The universal gas constant $R$ is $82.05\times10^{-6}\;...

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64

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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65

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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