Recent questions tagged numerical-answers / GO Civil

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441

GATE2014-1-2
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _______

Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _...

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442

GATE2014-1-3
The probability density function of evaporation $E$ on any day during a year in a watershed is given by $f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day} \\ 0 & \text{otherwise} \end{cases}$ The probability that $E$ lies in between $2$ and $4$ mm/day in a day in the watershed is (in decimal) ____________

The probability density function of evaporation $E$ on any day during a year in a watershed is given by$f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day...

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443

GATE Civil 2013 | Question: 51
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight sight ... ; and beam angle $1^{\circ}$. What is the length of valley curve (in m) based on the comfort condition? __________

For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...

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444

GATE Civil 2013 | Question: 50
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight ... $1^{\circ}$. What is the length of valley curve (in m) based on the head light sight distance condition? ___________

For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...

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445

GATE Civil 2013 | Question: 47
A theodolite is set up at station A and a $3$ m long staff is held vertically at station B. The depression angle reading at $2.5$ m marking on the staff is $6^{\circ}10'$. The horizontal distance between A and B is $2200$ m. Height of instrument ... m and R.L. of A is $880.88$ m. Apply the curvature and refraction correction, and determine the RL of B (in m) _______

A theodolite is set up at station A and a $3$ m long staff is held vertically at station B. The depression angle reading at $2.5$ m marking on the staff is $6^{\circ}10�...

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446

GATE Civil 2013 | Question: 48
A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. If load $P=80$ kN, find the reaction $R$ (in kN) correct to $1$-decimal place) using elastic analysis ________

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If load $P=80$ kN, find the reaction $R$ (in kN) correct to...

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447

GATE Civil 2013 | Question: 49
A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. If the magnitude of load $P$ is increased till collapse and the plastic moment carrying capacity of steel beam section is $90$ kNm, determine reaction $R$ (in kN) (correct to $1$-decimal place) using plastic analysis _______

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If the magnitude of load $P$ is increased till collapse and...

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448

GATE Civil 2013 | Question: 43
A student began experiment for determination of $5$-day, $20^{\circ}C$ BOD on Monday. Since the $5$th day fell on Saturday, the final DO readings were taken on next Monday. On calculation, BOD (i.e. $7$ day, $20^{\circ}C$ was found to be $150$ ... )? Assume value of BOD rate constant $(k)$ at standard temperature of $20^{\circ}C$ as $0.23/day$ (base $e$). ___________

A student began experiment for determination of $5$-day, $20^{\circ}C$ BOD on Monday. Since the $5$th day fell on Saturday, the final DO readings were taken on next Monda...

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449

GATE Civil 2013 | Question: 32
A uniform beam $(EI = \textit{constant})PQ$ in the form of a quarter-circle of radius $R$ is fixed at end $P$ and free at the end $Q$, where a load $W$ is applied as shown. The vertical downward displacement, $\delta_q$, at the loaded point $Q$ is ... $\delta_q = \beta \bigg( \dfrac{WR^3}{EI} \bigg)$. Find the value of $\beta$(correct to $4$-decimal places). ______

A uniform beam $(EI = \textit{constant})PQ$ in the form of a quarter-circle of radius $R$ is fixed at end $P$ and free at the end $Q$, where a load $W$ is applied as show...

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450

GATE Civil 2013 | Question: 31
All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $EI$. Find the magnitude of the bending moment at $Q$ (in kNm) due to given loading ________

All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $EI$. Find the magnitude of the bending moment at $Q$ (in kNm) due to give...

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451

GATE Civil 2013 | Question: 30
Laplace equation for water flow in soils is given below. $\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = 0$ Head $H$ does not vary in $y$ and $z$ directions. Boundary conditions are: at $x=0$, $H=5$; and $\dfrac{dH}{dx}=-1$. What is the value of $H$ at $x=1.2$? __________

Laplace equation for water flow in soils is given below. $$\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = ...

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452

GATE Civil 2013 | Question: 29
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______ $f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \leq 2 \\ 0 & \text{otherwise} \end{cases}$

Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______$f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \...

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453

GATE Civil 2013 | Question: 33
A uniform beam weighing $1800 \: N$ is supported at E and F by cable ABCD. Determine the tension (in $N$) in segment AB of this cable (correct to $1$- decimal place). Assume the cables ABCD, BE and CF to be weightless. _______

A uniform beam weighing $1800 \: N$ is supported at E and F by cable ABCD. Determine the tension (in $N$) in segment AB of this cable (correct to $1$- decimal place). Ass...

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454

GATE Civil 2013 | Question: 35
A rectangular concrete beam $250$ mm wide and $600$ mm deep is pre-stressed by means of $16$ high tensile wires, each of $7$ mm diameter, located at $200$ mm from the bottom face of the beamat a given section. If the effective pre- ... beam can with stand without causing tensile stress at the bottom face of of the beam? Neglect the effect of dead load of beam ______

A rectangular concrete beam $250$ mm wide and $600$ mm deep is pre-stressed by means of $16$ high tensile wires, each of $7$ mm diameter, located at $200$ mm from the bot...

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455

GATE Civil 2013 | Question: 27
Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$ _________ $\int_0^4 (x^4+10) dx$

Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$...

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456

GATE Civil 2013 | Question: 23
It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of time headways greater than $5$ seconds in the above observation? ________

It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential...

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457

GATE Civil 2013 | Question: 21
A water treatment plant is designed to treat $1 \: m^3/s$ of raw water. It has $14$ sand filters. Surface area of each filter is $50 \: m^2$. What is the loading rate (in $\dfrac{m^3}{\text{day} \cdot m^2}$) with two filters out of service for routine backwashing? __________

A water treatment plant is designed to treat $1 \: m^3/s$ of raw water. It has $14$ sand filters. Surface area of each filter is $50 \: m^2$. What is the loading rate (in...

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458

GATE Civil 2013 | Question: 11
A symmetric I-section (with width of each flange $=50$ mm, thickness of each flange $=10$ mm, depth of web $=100$ mm, and thickness of web $=10$ mm) of steel is subjected to a shear force of $100$ kN. Find the magnitude of the shear stress (in $N/mm^2$) in the web at its junction with the top flange _______

A symmetric I-section (with width of each flange $=50$ mm, thickness of each flange $=10$ mm, depth of web $=100$ mm, and thickness of web $=10$ mm) of steel is subjected...

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459

GATE Civil 2013 | Question: 10
The pin-jointed $2-D$ truss is loaded with a horizontal force of $15 \: kN$ at joint S and another $15 \: kN$ vertical force at joint U, as shown. Find the force in member RS (in $kN$) and report your answer taking tension as positive and compression as negative _________

The pin-jointed $2-D$ truss is loaded with a horizontal force of $15 \: kN$ at joint S and another $15 \: kN$ vertical force at joint U, as shown. Find the force in membe...

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460

GATE Civil 2013 | Question: 2
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ columns, and matrix R has $4$ rows and $1$ column. __________

What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ column...

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461

GATE Civil 2013 | Question: 7
As per $IS \: 456:2000$ for $M20$ grade concrete and plain barsin tension the design bond stress $\tau_{bd}=1.2$ MPa. Further, $IS \: 456:2000$ permits this design bond stress value to be increased by $60 \%$ for HSD bars. The stress ... tension, $\sigma_s=360$ MPa. Find the required development length, $L_d$, for HSD barsin terms of the bar diameter, $\phi$ ________

As per $IS \: 456:2000$ for $M20$ grade concrete and plain barsin tension the design bond stress $\tau_{bd}=1.2$ MPa. Further, $IS \: 456:2000$ permits this design bond s...

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462

GATE Civil 2013 | Question: 1
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of $x$ that minimizes the sum of squares of the errors in the two equations. _____ $2x=3$ $4x=1$

There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find...

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463

GATE2018 CE-2: 55
An aerial photographer of a terrain having an average elevation of $1400$ m is taken at a scale of $1:7500$. The focal length of the camera is $15$ cm. The altitude of the flight above mean sea level (in m, up to one decimal place) is ______

An aerial photographer of a terrain having an average elevation of $1400$ m is taken at a scale of $1:7500$. The focal length of the camera is $15$ cm. The altitude of th...

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464

GATE2018 CE-2: 54
A $7.5$ m wide two-lane road on a plain terrain is to be laid along a horizontal curve of radius $510$ m. For a design speed of $100$ kmph, super elevation is provided as per $\text{IRC:}73-1980$. Consider acceleration due to gravity as $9.81 m/s^2$. The level difference between the inner and outer edges of the road (in m, upto three decimal places is ________

A $7.5$ m wide two-lane road on a plain terrain is to be laid along a horizontal curve of radius $510$ m. For a design speed of $100$ kmph, super elevation is provided as...

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465

GATE2018 CE-2: 50
A coal containing $2 \%$ sulfur is burned completely to ash in a brick kiln at a rate of $30$ kg/min. The sulfur content in the ash was found to be $6 \%$ of the initial amount of sulfur present in the coal fed to the brick kiln. The ... /mole, respectively. The annual rate of sulfur dioxide $(SO_2)$ emission from the kiln (in tonnes/year, up to two decimal places) is ________

A coal containing $2 \%$ sulfur is burned completely to ash in a brick kiln at a rate of $30$ kg/min. The sulfur content in the ash was found to be $6 \%$ of the initial ...

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466

GATE2018 CE-2: 52
A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids shown in the figure. $S_0$, $S$ = readily biodegradable soluble BOD, mg/L $Q, \: Q_r, \: Q_w$ = flow rates $m^3/d$ ... (mixed liquor soils volatile suspended solids or MLVSS ), mg/l The mean cell residence time (in days, up to one decimal place) is _____

A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids shown in the figure. $S_0$, $S$ = readily biodegradable soluble B...

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467

GATE2018 CE-2: 53
The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are $80$ kmph and $100$ vehicles/km respectively. The traffic flow (in vehicles/h, up to one decimal place) corresponding to a speed of $40$ kmph is ____

The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are $80$ kmph and $100$ vehicles/km re...

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468

GATE2018 CE-2: 49
A flocculation tank contain $1800 \: m^3$ of water, which is mixed using paddles at an average velocity gradient $G$ of $100/s$. The water temperature and the corresponding dynamic viscosity are $30^{\circ}C$ and $0.798 \times 10^{-3} \: Ns/m^2$, respectively. The theoretical power required to achieve the stated value of $G$ (in kW, up to two decimal places) is _____

A flocculation tank contain $1800 \: m^3$ of water, which is mixed using paddles at an average velocity gradient $G$ of $100/s$. The water temperature and the correspondi...

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469

GATE2018 CE-2: 51
At a small water treatment plant which has $4$ filters, the rates of filteration and backwashing are $200 \: m^3/d/m^2$ and $1000 m^3/d/m^2$, respectively. Backwashing is done for $15$ min per day. The maturation, which ... the water being wasted during backwashing and maturation. The percentage increase in the filtered water produced (up to two decimal places) would be ______

At a small water treatment plant which has $4$ filters, the rates of filteration and backwashing are $200 \: m^3/d/m^2$ and $1000 m^3/d/m^2$, respectively. Backwashing is...

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470

GATE2018 CE-2: 46
A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids ($S_1, \: S_2$) are given in the figure. The gauge pressure value (in $kN/m^2$, up to two decimal places), of $p_1$ is _______

A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids ($S_1, \: S_2$) are given in the figure.The gauge pressure valu...

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471

GATE2018 CE-2: 47
The total rainfall in a catchment of area $1000 \: km^2$, during a $6$ h storm, is $19$ cm. The surface runoff due to this storm computed from triangular direct runoff hydrograph is $ 1 \times 10^8 \: m^3$. The $\phi_{\text{index}}$ for this storm (in cm/h, up to one decimal place) is ____

The total rainfall in a catchment of area $1000 \: km^2$, during a $6$ h storm, is $19$ cm. The surface runoff due to this storm computed from triangular direct runoff hy...

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472

GATE2018 CE-2: 48
A rough pipe of $0.5$ m diameter, $300$ m length and roughness height of $0.25$ mm, carries water (kinematic viscosity $= 0.9 \times 10^{-6} \: m^2/s$) with velocity of $3$ m/s. Friction factor $(f)$ for laminar flow is given by $f=64/R_e$, and for ... k=roughness height and $g=9.81 \: m/s^2$. The head loss (in m, up to three decimal places) in the pipe due to friction is _______

A rough pipe of $0.5$ m diameter, $300$ m length and roughness height of $0.25$ mm, carries water (kinematic viscosity $= 0.9 \times 10^{-6} \: m^2/s$) with velocity of $...

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473

GATE2018 CE-2: 42
A cable PQ of length $25$ m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is $20$ m. A point load of $150$ kN is applied at point R which divides into two equal parts. Neglecting the self-weight of the cable, the tension (in kN, in integer value) in the cable due to the applied load will be _______

A cable PQ of length $25$ m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is $20$ m. A point load of $15...

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474

GATE2018 CE-2: 40
A prismatic propped cantilever beam of span $L$ and plastic moment capacity $M_p$ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is $\alpha \dfrac{M_p}{L}$, the value of $\alpha$ is ______

A prismatic propped cantilever beam of span $L$ and plastic moment capacity $M_p$ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is...

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475

GATE2018 CE-2: 38
An $8$ m long simply-supported elastic beam of rectangular cross-section ($100$ mm $\times 200 $mm) is subjected to a uniformly distributed load of $10$ kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at $2$ m from the support is _______

An $8$ m long simply-supported elastic beam of rectangular cross-section ($100$ mm $\times 200 $mm) is subjected to a uniformly distributed load of $10$ kN/m over its ent...

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476

GATE2018 CE-2: 39
A prismatic beam P-Q-R of flexural rigidity $EI = 1 \times 10^4 kNm^2$ is subjected to a momemnt of $180 kNm$ at Q as shown in the figure The rotation at Q (in rad. up to two decimal places is_____

A prismatic beam P-Q-R of flexural rigidity $EI = 1 \times 10^4 kNm^2$ is subjected to a momemnt of $180 kNm$ at Q as shown in the figureThe rotation at Q (in rad. up to ...

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477

GATE2018 CE-2: 37
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r}) = x^2 \hat{i} + y^2 \hat{j} $ along $C$ which is a straight line joining $(0, 0)$ to $(1, 1)$ is _________

The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r...

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478

GATE2018 CE-2: 41
A $6$ m long simply-supported beam is prestressed as shown in the figure. The beam carries a uniformly distributed load of $6$ kN/m over its entire span. If the effective flexural rigidity $EI=2 \times 10^4 \: kNm^2$ and the effective prestressing force is $200$ kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is _____

A $6$ m long simply-supported beam is prestressed as shown in the figure.The beam carries a uniformly distributed load of $6$ kN/m over its entire span. If the effective ...

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479

GATE2018 CE-2: 43
The compression curve (void ratio $e$ vs. effective stress, $\sigma_v^{\text{'}}$ for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes through the points ($e = 1.2; \: \sigma_v=50 \: kPa$) and ($e = 0.6; \sigma_v = 800 \: kPa$). The compression index (up to two decimal places) of the soil is ______

The compression curve (void ratio $e$ vs. effective stress, $\sigma_v^{\text{'}}$ for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes th...

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480

GATE2018 CE-2: 44
The total horizontal and vertical stresses at a point X in a saturated sandy medium are $170$ kPa and $300$ kPa, respectively. The static pore-water pressure is $30$ kPa. At failure, the excess pore-water pressure is measured to be $94.50$ kPa, and the shear ... angle of internal friction is $36^{\circ}$. The shear strength (in kPa, up to two decimal places) at point X is _____

The total horizontal and vertical stresses at a point X in a saturated sandy medium are $170$ kPa and $300$ kPa, respectively. The static pore-water pressure is $30$ kPa....

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