Recent questions tagged gate2015-ce-2 / GO Civil

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41

GATE2015-2-26
The probability density function of a random variable, $x$ is $f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{cases}$ The mean $\mu _x$ of the random variable is ______.

The probability density function of a random variable, $x$ is$f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{ca...

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42

GATE2015-2-32
A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick. A vertical load, $P=50$ N is applied at $B$, as shown in the figure. Considering $E=200$ GPa, the force (in N) developed in the spring is ________.

A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick...

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43

GATE2015-2-33
A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load, $P=3$ kN and may occupy any position along the beam. If the beam is an $I$-section having section modulus, $S=16.2 \:cm^3$, the maximum bending stress (in GPa) due to the wheel loads is _______.

A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load...

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44

GATE2015-2-34
According to the concept of Limit State Design as per $IS \: 456:2000$, the probability of failure of a structure is ______.

According to the concept of Limit State Design as per $IS \: 456:2000$, the probability of failure of a structure is ______.

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45

GATE2015-2-35
In a pre-stressed concrete beam section shown in the figure, the net loss is $10 \%$ and the final pre-stressing force applied at $X$ is $750$ kN. The initial fiber stresses (in $N/mm^2$) at the top and bottom of the beam were: $4.166$ and $20.833$ $ – 4.166$ and $ – 20.833$ $4.166$ and $ – 20.833$ $ – 4.166$ and $20.833$

In a pre-stressed concrete beam section shown in the figure, the net loss is $10 \%$ and the final pre-stressing force applied at $X$ is $750$ kN. The initial fiber stres...

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46

GATE2015-2-36
A fixed end beam is subjected to a load, W at $1/3$ rd span from the left support as shown in the figure. The collapse load of the beam is: $16.5 M_p/L$ $15.5 M_p/L$ $15.0 M_p/L$ $16.0 M_p/L$

A fixed end beam is subjected to a load, W at $1/3$ rd span from the left support as shown in the figure. The collapse load of the beam is:$16.5 M_p/L$$15.5 M_p/L$$15.0 M...

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47

GATE2015-2-37
A $588 \: cm^3$ volume of moist sand weighs $1010$ gm. Its dry weight is $918$ gm and specific gravity of solids, $G$ is $2.67$. Assuming density of water as $1 \: gm/cm^3$, the void ratio is _________.

A $588 \: cm^3$ volume of moist sand weighs $1010$ gm. Its dry weight is $918$ gm and specific gravity of solids, $G$ is $2.67$. Assuming density of water as $1 \: gm/cm^...

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48

GATE2015-2-38
A $4$ m thick layer of normally consolidated clay has an average void ratio of $1.30$. Its compression index is $0.6$ and coefficient of consolidation is $1 \: m^2/yr$. If the increase in vertical pressure due to foundation load on the clay layer is equal to the existing effective overburden pressure, the change in the thickness of the clay layer is _______ mm.

A $4$ m thick layer of normally consolidated clay has an average void ratio of $1.30$. Its compression index is $0.6$ and coefficient of consolidation is $1 \: m^2/yr$. I...

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49

GATE2015-2-39
A pile of diameter $0.4$ m is fully embedded in a clay stratum having $5$ layers, each $5$ m thick as shown in the figure below. Assume a constant unit weight of soil as $18 \: kN/m^3$ for all the layers. Using $\lambda$-method. ($ \lambda = 0.15$ for $25$ m embedment length) and neglecting the end bearing component the ultimate pile capacity (in kN) is ___________.

A pile of diameter $0.4$ m is fully embedded in a clay stratum having $5$ layers, each $5$ m thick as shown in the figure below. Assume a constant unit weight of soil as ...

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50

GATE2015-2-40
Stress path equation for tri-axial test upon application of deviatoric stress is, $q=10 \sqrt{3}+0.5p$. The respective values of cohesion, $c$ (in kPa) and angle of internal friction, $\phi$ are: $20$ and $20^{\circ}$ $20$ and $30^{\circ}$ $30$ and $30^{\circ}$ $30$ and $20^{\circ}$

Stress path equation for tri-axial test upon application of deviatoric stress is, $q=10 \sqrt{3}+0.5p$. The respective values of cohesion, $c$ (in kPa) and angle of inter...

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51

GATE2015-2-41
A $6$ m high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top $3$ m thick layer of the backfill is sand having an angle of internal friction. $\phi = 30^{\circ}$ while the bottom layer is $3$ m thick clay with cohesion, $c=20$ ... $150$ $216$ $156$ $196$

A $6$ m high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top $3$ m thick layer of the backfill is sand having an angle of int...

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52

GATE2015-2-42
A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor period of $18$ days, kor depth of $12$ cm, while wheat has a kor period of $18$ ... cm. The discharge (in $m^3/s$) required in the filed channel to supply water to the commanded area during the kor period is ________.

A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor peri...

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53

GATE2015-2-43
A triangular gate with a base width of $2$ m and a height of $1.5$ m lies in a vertical plane. The top vertex of the gate is $1.5$ m below the surface of a tank which contains oil of specific gravity $0.8$. Considering the density of water and acceleration due ... $9.81 m/s^2$ respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________.

A triangular gate with a base width of $2$ m and a height of $1.5$ m lies in a vertical plane. The top vertex of the gate is $1.5$ m below the surface of a tank which con...

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54

GATE2015-2-44
The velocity components of a two dimensional plane motion of a fluid are $:u=\dfrac{y^3}{3}+2x—x^2y$ and $v=xy^2-2y-\dfrac{x^3}{3}$. The correct statement is: Fluid is incompressible and flow is irrotational Fluid is incompressible and flow is rotational Fluid is compressible and flow is irrotational Fluid is compressible and flow is rotational

The velocity components of a two dimensional plane motion of a fluid are $:u=\dfrac{y^3}{3}+2x—x^2y$ and $v=xy^2-2y-\dfrac{x^3}{3}$. The correct statement is:Fluid is i...

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55

GATE2015-2-45
The average surface area of a reservoir in the month of June is $20 \: km^2$. In the same month, the average rate of inflow is $10 \: m^3/s$, outflow rate is $15 \: m^3/s$, monthly rainfall is $10$ cm, monthly seepage loss is $1.8$ cm and the storage change is $16 \: million \: m^3$. The evaporation (in cm) in that month is: $46.8$ $136.0$ $13.6$ $23.4$

The average surface area of a reservoir in the month of June is $20 \: km^2$. In the same month, the average rate of inflow is $10 \: m^3/s$, outflow rate is $15 \: m^3/s...

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56

GATE2015-2-46
A pipe of $0.7$ m diameter has a length of $6$ km and connects two reservoirs A and B. The water level in reservoir A is at an elevation $30$ m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied ... to gravity as $9.81 \: m/s^2$ and neglecting minor losses, the discharge (in $m^3/s$) into the reservoir B is _______.

A pipe of $0.7$ m diameter has a length of $6$ km and connects two reservoirs A and B. The water level in reservoir A is at an elevation $30$ m above the water level in r...

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57

GATE2015-2-47
A landfill is to be designed to serve a population of $200000$ for a period of $25$ years. The solid waste (SW) generation is $2$ kg/person/day. The density of the un-compacted SW is $100 \: kg/m^3$ and a compaction ratio of $4$ is suggested. The ratio of compacted fill (i.e., SW+cover) to compacted SW is $1.5$. The landfill volume (in $million \: m^3$) required is _________.

A landfill is to be designed to serve a population of $200000$ for a period of $25$ years. The solid waste (SW) generation is $2$ kg/person/day. The density of the un-com...

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58

GATE2015-2-48
A water treatment plant of capacity, $1 \: m^3/s$ has filter boxed of dimensions $6 \; m \times 10 \: m$. Loading rate to the filters is $120 \: m^3/day/m^2$. When two of the filters are out of service for back washing, the loading rate (in $m^3/day/m^2$) is _________.

A water treatment plant of capacity, $1 \: m^3/s$ has filter boxed of dimensions $6 \; m \times 10 \: m$. Loading rate to the filters is $120 \: m^3/day/m^2$. When two of...

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59

GATE2015-2-49
Ultimate BOD of a river water sample is $20$ mg/L. BOD rate constant (natural log) is $0.15 \: day^{-1}$. The respective values of BOD (in $\%$) exerted and remaining after $7$ days are: $45$ and $55$ $55$ and $45$ $65$ and $35$ $75$ and $25$

Ultimate BOD of a river water sample is $20$ mg/L. BOD rate constant (natural log) is $0.15 \: day^{-1}$. The respective values of BOD (in $\%$) exerted and remaining aft...

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60

GATE2015-2-50
In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of $32.5 \: m^3/day/m^2$ is $32.5$ m long, $8.0$ m wide and liquid depth of $2.25$ m. If the length of the weir is $75$ m, the weir loading rate (in $m^3/day/m$) is ______.

In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of $32.5 \: m^3/day/m^2$ is $32.5$ m long, $8.0$ m wide and liquid depth of...

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61

GATE2015-2-51
The relation between speed $u$ (in km/h) and density $k$ (number of vehicles/km) for a traffic stream on a road is $u=70-0.7k$. The capacity on this road is _________ vph (vehicles/hour).

The relation between speed $u$ (in km/h) and density $k$ (number of vehicles/km) for a traffic stream on a road is $u=70-0.7k$. The capacity on this road is _________ vph...

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62

GATE2015-2-52
Match the information related to tests on aggregates given in Group - I with that in Group - II. ... $P - 4; Q - 1; R - 3; S - 2;$ $P - 3; Q - 4; R - 2; S - 1;$

Match the information related to tests on aggregates given in Group – I with that in Group – II.$\begin{array}{ll} \text{Group – I} & \text{Group – II} \\ P. \tex...

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63

GATE2015-2-53
In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity $2.60, 2.70, 2.65$ and $1.01$, are mixed in the relative proportions ($\%$ by weight) of $55.0, \: 35.8, \: 3.7$ and $5.5$ respectively. The ... the mix respectively are: $2.42$ and $2.63$ $2.42$ and $2.78$ $2.42$ and $2.93$ $2.64$ and $2.78$

In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity $2.60, 2.70, 2.65$ and $1.01$, are ...

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64

GATE2015-2-54
The bearings of two inaccessible stations, $S_1$ (Easting $500$ m, Northing $500$ m) and $S_2$ (Easting $600$ m, Northing $450$ m) from a station $S_3$ were observed as $225^{\circ}$ and $153^{\circ}\: 26’$ respectively. The independent Easting (in m) of station $S_3$ is: $450.000$ $570.710$ $550.000$ $650.000$

The bearings of two inaccessible stations, $S_1$ (Easting $500$ m, Northing $500$ m) and $S_2$ (Easting $600$ m, Northing $450$ m) from a station $S_3$ were observed as $...

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65

GATE2015-2-55
Two Pegs A and B were fixed on opposite banks of a $50$ m wide river. The level was set up at A and the staff readings on Pegs A and B were observed as $1.350$ m and $1.550$ m, respectively. Thereafter the instrument was shifted and set up at B. The staff reading on Pegs B and ... m and $0.550$ m, respectively. If the R.L. of Peg A is $100.200$ m, the R.L. (in m) of Peg B is _______.

Two Pegs A and B were fixed on opposite banks of a $50$ m wide river. The level was set up at A and the staff readings on Pegs A and B were observed as $1.350$ m and $1.5...

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