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GATE2017 CE21
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
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GATE2017 CE22
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\frac{dw}{dt}$ is equal to $\frac{dw}{dx} \frac{dx}{dt} + \frac{dw}{dy} \frac{dt}{dt}$ ... $\frac{d w}{dx} \frac{\partial x}{\partial t} + \frac{dw}{dy} \frac{\partial y}{ \partial t}$
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GATE2017 CE23
Given that the scope of the construction work is welldefined with all its drawings, specifications, quantities and estimates, which one of the following of contract would be most preferred? EPC contract percentage rate contract Item rate contract Lump sum contract
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GATE2017 CE24
Let $G$ be the specific gravity of soil solids, $w$ the water content in the soil sample, $\gamma_w$ the unit weight of water, and $\gamma_d$ ... $\gamma_d = \frac{Gw}{1 + \gamma_w}$ $\gamma_d = \frac{Gw}{1  \gamma_w}$
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GATE2017 CE25
Consider the following statements related to pore pressure parameters, $A$ and $B$: $A$ always lies between $0$ and $1.0$ $A$ can be less than $0$ or greater than $1.0$ $B$ always lies between $0$ and $1.0$ $B$ can be less than $0$ or greater than $1.0$ For these statements, which of the following options is correct? P and R P and S Q and R Q and S
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GATE2017 CE26
Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine’s active earth pressure distribution against this?
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GATE2017 CE27
If a centrifugal pump has an impeller speed of $N$ (in rpm), discharge $Q$ (in $m^3/s$) and the total head $H$ (in $m$), the expression for the specific speed $N_s$ of the pump is given by $N_s = \frac{NQ^{0.5}}{H^{0.5}}$ $N_s = \frac{NQ^{0.5}}{H}$ $N_s = \frac{NQ^{0.5}}{H^{0.75}}$ $N_s = \frac{NQ}{H^{0.5}}$
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GATE2017 CE28
As per Noise Pollution (Regulation and Control) Rules $2000$ of India, the day time noise limit for a residential zone, expressed in dB(A)L$_{eq}$, is $55$ $65$ $75$ $85$
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GATE2017 CE29
Following observations have ben made for the elevation and temperature to ascertain the stability of the atmosphere: $\begin{array}{cc} \hline \text{Elevation (in m) } & \text{Temperature (in }^{\circ} \text{C)} \\ \hline 10 & 15.5 \\ \hline 60 & 15.0 \\ \hline 130 & 14.3 \\ \hline \end{array}$ The atmosphere is classified as Stable Unstable Neutral Inverse
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GATE2017 CE210
The most important type of species involved in the degradation of organic matter in the case of activated sludge process is autotrophs heterotrophs prototrophs photoautotrophs
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GATE2017 CE211
For a broad gauge railway track on a horizontal curve of radius $R$ (in m), the equilibrium cant $e$ required for a train moving at a speed of $V$ (in km per hour) is $e= 1.676 \frac{V^2}{R}$ $e= 1.315 \frac{V^2}{R}$ $e= 0.80 \frac{V^2}{R}$ $e= 0.60 \frac{V^2}{R}$
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GATE2017 CE212
The safety within a roundabout and the efficiency of a roundabout can be increased, respectively, by increasing the entry radius and increasing the exit radius increasing the entry radius and decreasing the exit radius decreasing the entry radius and increasing the exit radius decreasing the entry radius and decreasing the exit radius
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GATE2017 CE213
The method of orientation used, when the plane table occupies a position not yet located on the map, is called as traversing radiation levelling resection
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GATE2017 CE214
Consider the following frame in the figure: If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to $5$ $6$ $7$ $8$
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GATE2017 CE215
Let the characteristic strength be defined as that value, below which not more than $50 \%$ of the results are expected to fall. Assuming a standard deviation of $4$ MPa, the target mean strength (in MPa) to be considered in the mix design of a $M25$ concrete would be $18.42$ $21.00$ $25.00$ $31.58$
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GATE2017 CE216
In a material under a state of plane strain, a $10 \times 10$ mm square centered at a point gets deformed as shown in the figure. If the shear strain $\gamma_{xy}$ at this point is expressed as $0.001k$ (in rad), the value of $k$ is $0.50$ $0.25$ $ 0.25$ $ 0.50$
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GATE2017 CE217
The plate load test was conducted on a clayey strata by using a plate of $0.3 \: m \times 0.3 \: m$ dimensions, and the ultimate load per unit area for the plate for found to be $180$ kPa. The ultimate bearing capacity (in kPa) of a $2$ m wide square footing would be $27$ $180$ $1200$ $2000$
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GATE2017 CE218
For a construction project, the mean and standard deviation of the completion time are $200$ days and $6.1$ days, respectively. Assume normal distribution and use the value of standard normal deviate $z = 1.64$ for the $95 \%$ confidence level. The maximum time required (in days) for the completion of the project would be ________
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GATE2017 CE219
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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vectorcalculus
divergence
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GATE2017 CE220
A twofaced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
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GATE2017 CE221
A sheet pile has an embedment depth of $12$ m in a homogeneous soil stratum. The coefficient of permeability of soil is $10^{6} m/s$. Difference in the water levels between the two sides of the sheet pile is $4$ m. The flow net is constructed with ... of equipotential lines. The quantity of seepage (in $cm^3/s$ per m, up to one decimal place) under the sheet pile is _________
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GATE2017 CE222
The VPI (vertical point of section) is $100$ m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical is parabolic, the length of the curve (in meters and measured along the horizontal) is _______
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GATE2017 CE223
During a storm event in a certain period, the rainfall intensity is $3.5$ cm/hour and the $\Phi$index is $1.5$ cm/hour. The intensity of effective rainfall (in cm/hour, up to one decimal place) for this period is ________
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GATE2017 CE224
The infiltration capacity of a soil follows the Horton's exponential model, $f=c_1+c_2e^{kt}$. During an experiment, the initial infiltration capacity was observed to be $200$ mm/h. After a long time, the infiltration capacity was reduced $25$ mm/h. If the filtration capacity ... $k$ (in $h^{1}$, up to two decimal places) is ________
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25
GATE2017 CE225
While aligning a hill road with a ruling gradient $6\%$, a horizontal curve of radius $50 \: m$ is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be _________
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GATE2017 CE226
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$axis. The coordinates of the tangent point would be $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
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GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \frac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\frac{\pi ^3}{24}$ $\frac{\pi ^3}{12}$ $\frac{\pi ^3}{48}$ $\frac{\pi ^3}{64}$
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Calculus
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gate2017ce2
definite
integral
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GATE2017 CE228
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
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Linear Algebra
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gate2017ce2
matrix
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29
GATE2017 CE229
Consider the following secondorder differential equation: $y’’ – 4y’+3y =2t 3t^2$. The particular solution of the differential solution equation is $ – 2 2tt^2$ $ – 2tt^2$ $2t3t^2$ $ – 2 2t3 t^2$
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Partial Differential Equation (PDE):
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differentialequation
particularsolution
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GATE2017 CE230
Group I gives a list of test methods and test apparatus for evaluating some of the properties of Ordinary Portland Cement (OPC) and concrete. Group II gives the list of these properties. ... R  1; S  4 P  4; Q  2; R  4; S  1 P  1; Q  4; R  2; S  3
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GATE2017 CE231
Two prismatic beams having the same flexural rigidity of $1000 \: kNm^2$ are shown in the figures. If the midspan deflections of these beams are denoted by $\delta_1$ and $\delta_2$ (as indicated in the figures), the correct option is $\delta_1 = \delta_2$ $\delta_1 < \delta_2$ $\delta_1 > \delta_2$ $\delta_1 >> \delta_2$
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GATE2017 CE232
Consider the prismatic beams with the clamped supports P, Q, and R as shown in the figures. Given that eh modulus of elasticity, $E$ is $2.5 \times 10^4$ MPa; and the moment of inertia, $I$ is $8 \times 10^8 \: mm^4$, the correct comparison of the magnitudes of the ... $M_P = M_Q>M_R$ $S_P < S_Q> S_R$; $M_P = M_Q=M_R$ $S_P < S_Q< S_R$; $M_P < M_Q < M_R$
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GATE2017 CE233
Consider the following statements: Walls of one brick thick are measured in square meters Walls of one brick thick are measured in cubic meters No deduction in the brickwork quantity is made for openings in walls up to $0.1 \: m^2$ area. For the measurement of excavation from the borrow pit ... False P  True, Q  False, R  True, S  False P  True, Q  False, R  True, S  True
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GATE2017 CE234
Two identical concrete piles having the plan dimensions $50 \: cm \times 50 \: cm$ are driven into a homogeneous sandy layers as shown in the figures. Consider the bearing capacity factor $N_q$ for $\phi = 30 ^{\circ}$ as $24$. If $Q_{P1}$ and $Q_{P2}$ represent the ultimate point ... by about $100 \%$ $Q_{P1} > Q_{P2}$ by about $5 \%$ $Q_{P1} < Q_{P2}$ by about $5 \%$
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GATE2017 CE235
Following are the statements related to the stress paths in a triaxial testing of soils: If $\sigma_1 = \sigma_3$, the stress point lies at the origin of the $pq$ plot If $\sigma_1 = \sigma_3$, the stress point lies on the $p$axis of the $pq$ plot If $\sigma_1 > \sigma_3$, ...  True P  True; Q  False; R  True P  False; Q  True; R  False P  True; Q  False; R  False
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GATE2017 CE236
Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled $d$ (in km) and time $t$ (in hour) for both vehicles are given as P: $d=60 \: t$ Q: ... would be $15$ km at $30$ minutes $15$ km at $15$ minutes $30$ km at $30$ minutes $30$ km at $15$ minutes
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GATE2017 CE237
For the construction of a highway, a cut is to be made as shown in the figure. The soil exhibits $c'=20$ kPa, $\phi'=18^{\circ}$, and the undrained shear strength $=80$ kPa. The unit weight of water is $9.81 kN/m^3$. The unit weights of the soil above and below the ground water ... conditions, respectively, would be $1.6$ and $0.9$ $0.9$ and $1.6$ $0.6$ and $1.2$ $1.2$ and $0.6$
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GATE2017 CE238
Two towers, A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure. The length of the image of the tower A on the photograph is $1.5$ cm and the tower B is $2.0$ cm. The distance of the top tower A ( ... point $p$ of the photograph. If the height of the tower B is $80$ m, the height (in meters) of the tower A is ________
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GATE2017 CE239
A hallow circular shaft has an outer diameter of $100 $ mm and inner diameter of $50 $ mm. If the allowable shear stress is $125$ MPa, the maximum torque (in kNm) that the shaft can resist is _______
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GATE2017 CE240
A simply supprted rectangular concrete beam of span $8$ m has to be prestressed with a force of $1600$ ... (in meters, up to two decimal places) of the tendon at the midspan to balance the external load should be __________
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