GATE Civil Engineering 2022 SET-2

According to given condition given function f(x,y) is nothing but constant function i.e. f(x,y)=3 because this is the only function whose value is 3 at any point on the boundary of unit circle and it is also satisfying Laplace equation, so
f(0,0)=3

MTA- Marks to All
I=\int \left ( x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...\infty \right )dx
I=\frac{x^2}{2}-\frac{x^3}{6}+\frac{x^4}{12}-\frac{x^5}{20}+...
Option (A)
\frac{1}{1+x}=(1+x)^{-1}=1-x+x^2-x^3...\infty
So, its incorrect.
Option (B)
\frac{1}{1+x^2}=(1+x^2)^{-1}=1-x^2+x^4-x^6...\infty
So, its incorrect.
Similarly option (C) and (D) both are incorrect.
No-correct choice given.

E=2G(1+\mu )
G= Shear modulas
\mu =Poission's ratio
E= Young's modulus

The question is based on LSM design principle as it is describing different conditions related to strain
Depending on amount of reinforcement in a cross- section, here ca be three types of sections viz. balanced, under reinforced and over reinforced.
Balanced section is a section that is expected to result in a balanced failure. It means at the ultimate limit state in flexure, the concrete will attain a limiting compressive strain of 0.0035 and steel will attain minimum specified tensile strain of 0.002+\frac{0.87f_y}{E_s}
Under reinforced section is a section in which steel yield before collapse. Over reinforced section is a section in which crushing of concrete in compression i.e. attainment of compressive strain of 0.0035 occurs prior to yielding of steel.
In case of over reinforced section the deflection, crack width remain relatively low and failure occurs without any sign of warning and hence over reinforced flexural members are not recommended by IS code.
Based on the above information:
Statement I is true.
Statement II is true.
Statement III is false.
Statement IV is false.

C_3S- Responsible for early age strength
C_2S - Responsible for later age strength and lowest heat of hydration
C_3A- Flash setting and highest heat of hydration

Static indeterminacy, SI=r-3=(3+2)-3=2
Kinematic indeterminacy=0+1=1

In monsoon season sand will be fully saturated hence this will be critical condition in designing of shallow foundation.
In case of sudden drawdown flow direction reverses hence for slope stability, it will be critical condition.
In sandy sea beach, quicksand condition can arise only if existing hydraulic gradient exceeds the critical hydraulic gradient.

\begin{aligned} \Sigma F_x &=0 \\ \sigma _x(BC)-\tau _Z \times (AB)\sigma _1 \sin \theta &= 0\\ \sigma _x\left ( \frac{AC \sin \theta }{\cos \theta } \right )+\tau _{zx}\left ( \frac{AC \cos \alpha }{\cos \theta } \right ) &=\sigma _1 \frac{AC \sin \theta }{\cos \theta }\\ \sigma _x \tan \theta +\tau _{zx} &=\sigma _1 \tan \theta \\ \tan \theta(\sigma _1-\sigma _2) &= \tau _{zx}\\ \tan \theta &= \left ( \frac{\tau _{zx}}{\sigma _1-\sigma _x} \right ) \end{aligned}

Actual evapotranspiration (ET_C)
=K_S \times K_C \times Reference evapotranspiration (ET_0)
=0.8 \times 1.2 \times 6=5.76mm