# GATE Civil Engineering 2020 SET-1

 Question 1
In the following partial differential equation, $\theta$ is a function of t and z, and D and K are functions of $\theta$

$D(\theta )\frac{\partial^2 \theta }{\partial z^2}+\frac{\partial K(\theta )}{\partial z}-\frac{\partial \theta }{\partial t}=0$

The above equation is
 A a second order linear equation B a second degree linear equation C a second order non-linear equation D a second degree non-linear equation
Engineering Mathematics   Ordinary Differential Equation
Question 1 Explanation:
$\because \;\;1^{st}$ term of given D. Equation contains product of dependent variable with it's derivative, so it is non-linear and also we have 2nd order derivative so it's order is two
i.e., 2nd order non linear equation.
 Question 2
The value of $\lim_{x \to \infty }\frac{x^2-5x+4}{4x^2+2x}$
 A 0 B $\frac{1}{4}$ C $\frac{1}{2}$ D 1
Engineering Mathematics   Calculus
Question 2 Explanation:
It is in $\left (\frac{\infty }{\infty } \right )$ from so by L-Hospital Rule
\begin{aligned} =&\lim_{x \to \infty }\left ( \frac{2x-5}{8x+2} \right )=\frac{\infty }{\infty }\\ =&\lim_{x \to \infty }\left ( \frac{2}{8} \right )=\frac{1}{4} \end{aligned}
 Question 3
The true value of ln(2) is 0.69. If the value of ln(2) is obtained by linear interpolation between ln(1) and ln(6), the percentage of absolute error (round off to the nearest integer), is
 A 35 B 48 C 69 D 84
Engineering Mathematics   Calculus
Question 3 Explanation:
True value of $\ln 2=0.69=T$
\begin{aligned} &x &&y=\ln x \\ &x_0=1 & &0 \\ &x_1=6& &1.79 \end{aligned}
Divided differentiation
\begin{aligned} \frac{1.79-0}{6-1}&=0.358=f[x_0,x_1] \\ \text{Approx:}\;\;\ln 2 &=f[x_0]+(x-x_0)f[x_0,x_1] \\ &= 0+(2-1)0.358\\ &= 0.358=A\\ \% \; error &= \frac{T-A}{T}\times 100=48.11\% \end{aligned}
 Question 4
The area of an ellipse represented by an equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
 A $\frac{\pi a b}{4}$ B $\frac{\pi a b}{2}$ C $\pi a b$ D $\frac{4 \pi a b}{3}$
Engineering Mathematics   Ordinary Differential Equation
Question 4 Explanation:

\begin{aligned} \text{Area} &=\int \int (1)dydx \\ &=\int_{x=-a}^{a}\int_{y=-\frac{b}{a}}^{+\frac{b}{a}}(1)dydx \\ &=4\int_{x=0}^{a} \int_{y=0}^{\frac{b}{a}\sqrt{a^2-x^2}}(1)dydx\\ &= 4 \int_{x=0}^{a}\int_{y=0}^{\frac{b}{a}\sqrt{a^2-x^2}} dx\\ &= \pi ab \end{aligned}
 Question 5
Consider the planar truss shown in the figure (not drawn to the scale)

Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the load P, is
 A 6 B 7 C 8 D 9
Structural Analysis   Trusses
Question 5 Explanation:

As $\Delta _{AB}=0$, hence $F _{AB}=0$
Total number of zero force member = 8
 Question 6
A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force P. The figure that appropriately represents the distribution of the magnitude of bond stress (represented as hatched region), along the embedded length of the bar, is
 A A B B C C D D
RCC Structures   Shear, Torsion, Bond, Anchorage and Development Length
 Question 7
In a two-dimensional stress analysis, the state of stress at a point P is
$[\sigma ]=\begin{bmatrix} \sigma _{xx} &\tau _{xy} \\ \tau _{xy}& \sigma _{yy} \end{bmatrix}$
The necessary and sufficient condition for existence of the state of pure shear at the point P, is
 A $\sigma _{xx}\sigma _{yy} -\tau^2 _{xy}=0$ B $\tau _{xy}=0$ C $\sigma _{xx}+\sigma _{yy}=0$ D $(\sigma _{xx}-\sigma _{yy})^2 +4\tau^2 _{xy}=0$
Solid Mechanics   Principal Stress and Principal Strain
Question 7 Explanation:

In pure shear condition $\sigma _x=0, \sigma _y=0, \tau _{xy}=\tau$

For this condition $\sigma _{xx}+ \sigma _{yy}=0$ is true.
 Question 8
During the process of hydration of cement, due to increase in Dicalcium Silicate ($C_2S$) content in cement clinker, the heat of hydration
 A increases B decreases C initially decreases and then increases D does not change
RCC Structures   Working Stress and Limit State Method
Question 8 Explanation:
Due to increase in $C_2S$ heat of hydration decreases.
 Question 9
The Los Angeles test for stone aggregates is used to examine
 A abrasion resistance B crushing strength C soundness D specific gravity
Transportation Engineering   Highway Materials
Question 9 Explanation:
Los Angles abrasion test is carried out to examine the hardness i.e., abrasion resistance property of aggregate
 Question 10
Which one of the following statements is NOT correct?
 A A clay deposit with a liquidity index greater than unity is in a state of plastic consistency. B The cohesion of normally consolidated clay is zero when tri-axial test is conducted under consolidated undrained condition. C The ultimate bearing capacity of a strip foundation supported on the surface of sandy soil increase in direct proportion to the width of footing. D In case of a point load, Boussinesq's equation predicts higher value of vertical stress at a point directly beneath the load as compared to Westergaard's equation.
Geotechnical Engineering   Stress Distribution in the Soil
Question 10 Explanation:
A clay deposit with liquidty index greater then 1, will be in liquid stage of consistency.
$\because \;\;I_L=\frac{w_n-w_p}{w_l-w_p} \gt 1$
$\therefore \;\; w_n \gt w_L$
There are 10 questions to complete.