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1
GATE2017 CE1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct? $PQ=I$ but $QP \neq I$ $QP=I$ but $PQ \neq I$ $PQ=I$ and $QP= I$ $PQQP= I$
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Mar 26, 2018
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gate2017ce1
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2
GATE2017 CE1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are $2$ and $2$ $1$ and $2$ $2$ and $1$ $1$ and $1$
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Mar 26, 2018
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gate2017ce1
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3
GATE2017 CE1: 3
Let $x$ be a continuous variable defined over the interval $( \infty, \infty)$, and $f(x) = e^{xe^{x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to $e^{e^{x}}$ $e^{e^{x}}$ $e^{e^{x}}$ $e^{x}$
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Mar 26, 2018
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gate2017ce1
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4
GATE2017 CE1: 4
An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$, and Young's modulus $E$ is fixed at the two ends. The temperature of the bar is increased by $T$, resulting in an axial stress $\sigma$. Keeping all other parameters unchanged ... , the axial stress would be $\sigma$ $2 \: \sigma$ $0.5 \: \sigma$ $0.25 \: \alpha \: \sigma$
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Mar 26, 2018
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gate2017ce1
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5
GATE2017 CE1: 5
A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true? Maximum or minimum shear force occurs where the curvature is zero Maximum or minimum bending moment occurs where the shear force is ... minimum bending moment occurs where the curvature is zero Maximum bending moment and maximum shear force occur at the same section
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gate2017ce1
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6
GATE2017 CE1: 6
According to $IS \: 456  2000$, which one of the following statements about the depth of neutral axis $x_{\text{u, bal}}$ for a balanced reinforced concrete section is correct? $x_{\text{u, bal}}$ ... both the grade of concrete and grade of steel $x_{\text{u, bal}}$ does not depend on the grade of concrete and grade of steel
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gate2017ce1
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7
GATE2017 CE1: 7
The figure shows a twohinged parabolic arch of span $L$ subjected to a uniformly distributed load of intensity $q$ per unit length. The maximum bending moment in the arch is equal to $\frac{qL^2}{8}$ $\frac{qL^2}{12}$ zero $\frac{qL^2}{10}$
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Mar 26, 2018
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gate2017ce1
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8
GATE2017 CE1: 8
Group I lists the type of gain or loss of strength in soils. Group II lists the property or process responsible for the loss or gain of strength in soils. ... $P3, \: Q2; \: R1, \: S4$ $P4, \: Q2; \: R1, \: S3$
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gate2017ce1
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9
GATE2017 CE1: 9
A soil sample is subjected to a hydrostatic pressure, $\sigma$. The Mohr circle for any point in the soil sample would be a circle of radius $\sigma$ and center at the origin a circle of radius $\sigma$ and center at a distance $\sigma$ from the origin a point at a distance $\sigma$ from the origin a circle of diameter $\sigma$ and center at the origin
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gate2017ce1
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10
GATE2017 CE1: 10
A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion $c_u$. The ultimate bearing capacity of the footing is equal to $2 \pi \: c_u$ $\pi \: c_u$ $( \pi +1) \: c_u$ $(\pi + 2) \: c_u$
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Mar 26, 2018
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gate2017ce1
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11
GATE2017 CE1: 11
A uniformly distributed line road of $500 \: kN/m$ is acting on the ground surface. Based on Boussinesq’s theory, the ratio of vertical stress at a depth $2$ m to that at $4$ m, right below the line of loading, is $0.25$ $0.5$ $2.0$ $4.0$
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Mar 26, 2018
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gate2017ce1
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12
GATE2017 CE1: 12
For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is linear with zero value at the plates linear with zero value at the center quadratic with zero value at the plates quadratic with zero value at the center
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Mar 26, 2018
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gate2017ce1
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13
GATE2017 CE1: 13
The reaction rate involving reactants $A$ and $B$ is given by $k[A]^{\alpha} [B]^{\beta}$. Which one of the following statements is valid for the reaction to be firstorder reaction? $\alpha=0$ and $\beta=0$ $\alpha=1$ and $\beta=0$ $\alpha=1$ and $\beta=1$ $\alpha=1$ and $\beta=2$
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Mar 26, 2018
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gate2017ce1
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14
GATE2017 CE1: 14
The wastewater from a city, containing a high concentration of biodegradable organics, is being steadily discharged into a flowing river at a location S. If the rate of aeration of the river water is lower than the rate of degradation of the organics, then the ... the location S. remains constant all along the length of the river. is lowest at a point downstream of the location S.
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Mar 26, 2018
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gate2017ce1
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15
GATE2017 CE1: 15
Which one of the following is NOT present in the acid rain? $HNO_3$ $H_2SO_4$ $H_2CO_3$ $CH_3COOH$
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Mar 26, 2018
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11.8k
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gate2017ce1
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16
GATE2017 CE1: 16
A superelevation $e$ is provided on a circular horizontal curve such that a vehicle can be stopped on the curve without sliding. Assuming a design speed $v$ and maximum coefficient of side friction $f_{max}$, which one of the following criteria should be satisfied? $e \leq f_{max}$ $e > f_{max}$ no limit on $e$ can be set $e = \frac{1(f_{max})^2}{f_{max}}$
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Mar 26, 2018
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Milicevic3306
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11.8k
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gate2017ce1
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17
GATE2017 CE1: 17
A runway is being constructed in a new airport as per the International Civil Aviation Organization (ICAO) recommendations. The elevation and the airport reference temperature of this airport are $535 \: m$ above the mean sea level and $22.65^{\circ}C$, respectively. Consider the ... length of runway corrected for the temperature is $2223 \: m$ $2250 \: m$ $2500 \: m$ $2750 \: m$
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Mar 26, 2018
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11.8k
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gate2017ce1
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18
GATE2017 CE1: 18
The accuracy of an Electronic Distance Measuring Instrument (EDMI) is specified as $\pm (a \: mm + b \: ppm)$. Which one of the following statements is correct? Both $a$ and $b$ remain constant, irrespective of the distance being measured $a$ ... proportion to the distance being measured and $b$ remains constant Both $a$ and $b$ vary in proportion to the distance being measured
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Mar 26, 2018
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gate2017ce1
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19
GATE2017 CE1: 19
The number of spectral bands in the Enhanced Thematic Mapper sensor on the remote sensing satellite Landsat$7$ is: $64$ $10$ $8$ $15$
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Mar 26, 2018
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11.8k
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gate2017ce1
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20
GATE2017 CE1: 20
Consider the following partial differential equation: $3 \frac{\partial ^2 \phi}{ \partial x^2} + B \frac{ \partial ^2 \phi}{\partial x \partial y} + 3 \frac{\partial ^2 \phi}{\partial y^2} + 4 \phi =0$ For this equation to be classified as parabolic, the value of $B^2$ must be ________
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gate2017ce1
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21
GATE2017 CE1: 21
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2x} \bigg)$ is equal to _________
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Mar 26, 2018
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gate2017ce1
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22
GATE2017 CE1: 22
A $3 \: m$ thick clay layer is subjected to an initial uniform pore pressure of $145 \: kPa$ as shown in the figure. For the given ground conditions, the time (in days, rounded to the nearest integer) required for $90 \%$ consolidation would be ________
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Mar 26, 2018
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11.8k
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gate2017ce1
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23
GATE2017 CE1: 23
A triangular pipe network is shown in the figure. The head loss in each pipe is given by $h_f = rQ^{1.8}$, with the variables expressed in a consistent set of units. The value of $r$ for the pipe $AB$ is $1$ and for the pipe $BC$ is $2$. If the ... is equally divided between the pipes $AB$ and $AC$, the value of $r$ (up to two decimal places) for the pipe $AC$ should be _______
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Mar 26, 2018
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11.8k
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gate2017ce1
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24
GATE2017 CE1: 24
The ordinates of a $2$hour unit hydrograph for a catchment are given as $\begin{array}{llllll} \text{Time (h)} & 0 & 1 & 2 & 3 & 4 \\ \text{Ordinate } (m^3/s) & 0 & 5 & 12 & 25 & 41 \end{array}$ The ordinate (in $m^3/s$) of a $4$hour unit hydrograph for this catchment at the time of $3$ h would be _________
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Mar 26, 2018
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gate2017ce1
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25
GATE2017 CE1: 25
Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is $900$ vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than $8$ seconds is ___________
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Mar 26, 2018
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Milicevic3306
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11.8k
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gate2017ce1
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26
GATE2017 CE1: 26
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct? $a=1,b=4$ $b=0.5,b=1$ $a=0,b=1$ $a=1,b=1$
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Mar 26, 2018
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Milicevic3306
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11.8k
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gate2017ce1
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27
GATE2017 CE1: 27
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is $Q(t)=e^{t}1$ $Q(t)=1+ e^{t}$ $Q(t)=1 e^t$ $Q(t)=1 e^{t}$
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Mar 26, 2018
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Milicevic3306
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11.8k
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gate2017ce1
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28
GATE2017 CE1: 28
Consider the matrix $\begin{bmatrix} 5 & 1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix? Eigenvalue $3$ has a multiplicity of $2$, and only one independent ... has a multiplicity of $2$, and no independent eigenvector exists. Eigenvalues are $3$ and $3$, and two independent eigenvectors exist.
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Mar 26, 2018
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gate2017ce1
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29
GATE2017 CE1: 29
A planar truss tower structure is shown in the figure. Consider the following statements about the external and internal determinacies of the truss. Externally Determinate External Static Indeterminacy $=1$ External Static Indeterminacy $=2$ Internally Determinate Internal Static Indeterminacy $=1$ ... SFalse; TFalse; U True PTrue; Q True; RFalse; STrue; TFalse; U True
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Mar 26, 2018
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Milicevic3306
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gate2017ce1
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30
GATE2017 CE1: 30
Group I contains three broad classes of irrigation supply canal outlets, Group II presents hydraulic performance attributes. ... $P  2; \: Q  3; \: R  1$ $P  1; \: Q  3; \: R  2$
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Mar 26, 2018
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gate2017ce1
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31
GATE2017 CE1: 31
A $1$ m wide rectangular channel has a bed slope of $0.0016$ and the Manning’s roughness coefficient is $0.04$ Uniform flow takes the place in the channel at a flow depth of $0.5$m. At a particular section, gradually varied flow (GVF) is observed and the flow depth is measured as $0.6$ m. The GVF profile at section is classified as $S_1$ $S_2$ $M_1$ $M_2$
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Mar 26, 2018
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gate2017ce1
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32
GATE2017 CE1: 32
The following observations are made while testing aggregate for its suitability in pavement construction: Mass of ovendry aggregate in air $=1000 $ g Mass of saturated surfacedry aggregate in air $=1025 $ g Mass of saturated surfacedry aggregate under water $=625 $ g ... and water absorption $=2.5 \%$ apparent specific gravity of aggregate $=2.5$ and water absorption $=2.4 \%$
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Mar 26, 2018
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gate2017ce1
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33
GATE2017 CE1: 33
The queue length (in number of vehicles) versus time (in seconds) plot for an approach to a signalized intersection with the cycle length of $96$ seconds is shown in the figure (not drawn to scale) At time $t=0$, the light has just turned red. The ... delay per vehicle $=45$ seconds $s=1200$ vph, and for this cycle, the average stopped delay per vehicle $=28.125$ seconds
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Mar 26, 2018
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11.8k
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gate2017ce1
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34
GATE2017 CE1: 34
The radius of a horizontal circular curve on a highway is $120$ m. The design speed is $60$ km/hour, and the design coefficient of lateral friction between the tyre and road surface is $0.15$. The estimated value of superrelevation required (if full lateral friction is assumed to develop), and the ... $0.37$ $\frac{1}{11.6}$ and $0.24$ $\frac{1}{12.9}$ and $0.24$
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gate2017ce1
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35
GATE2017 CE1: 35
The observed bearings of a traverse are given below: ... $R$ Only $S$ $R$ and $S$ $P$ and $Q$
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gate2017ce1
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36
GATE2017 CE1: 36
The laboratory tests on a soil sample yields the following results: natural moisture content $=18 \%$, liquid limit $=60 \%$, plastic limit $=25 \%$, percentage of clay sized fraction $=25\%$. The liquidity index and activity (as per the expression proposed by Skempton) of the soil, respectively, are $0.2$ and $1.4$ $0.2$ and $1.4$ $1.2$ and $0.714$ $1.2$ and $0.714$
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gate2017ce1
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37
GATE2017 CE1: 37
Consider the equation $\dfrac{du}{dt}=3t^2+1$ with $u=0$ at $t=0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t=2$. The absolute error in the solution at the end of the first time step is _______.
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38
GATE2017 CE1: 38
A pretensioned rectangular concrete beam $150$ mm wide and $300$ mm depth is prestressed with three straight tendons, each having a crosssectional are of $50 \: mm^2$, to an initial stress of $1200 \: N/mm^2$. The tendons are located at $100$ ... is $6$, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is _________.
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gate2017ce1
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39
GATE2017 CE1: 39
Consider the stepped bar made with a linear elastic material and subjected to an axial load of $1$ kN, as shown in the figure. Segments $1$ and $2$ have crosssectional area of $100 \: mm^2$ and $60 \: mm^2$, Young's modulus of $2 \times 10^5$ MPa ... mm and $900$ mm, respectively. The strain energy (in Nmm, up to one decimal place) in the bar due to the axial load is __________
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gate2017ce1
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40
GATE2017 CE1: 40
The value of $M$ in the beam ABC shown in the figure is such that the joint B does not rotate. The value of support reaction (in kN) at B should be equal to _________.
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