# GATE CE 2017 SET-2

 Question 1
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 equations is
 A $\lambda ^{2}-4\lambda -5=0$ B $\lambda ^{2}-4\lambda+5=0$ C $\lambda ^{2}+4\lambda-5=0$ D $\lambda ^{2}+4\lambda+5=0$
Engineering Mathematics   Linear Algebra
Question 1 Explanation:
\begin{aligned} \left [ A \right ]&=\begin{bmatrix} 3 & 2\\ 4 & 1 \end{bmatrix} \\ \left [ A-\lambda I \right ]&=\begin{bmatrix} 3-\lambda & 2\\ 4 & 1-\lambda \end{bmatrix} \\ \left | A-\lambda I \right |&=0 \\ \left ( 3-\lambda \right )\left ( 1-\lambda \right )-8&=0 \\ 3-4\lambda +\lambda ^{2}-8&=0 \\ \lambda ^{2}-4\lambda -5&=0 \end{aligned}
 Question 2
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
 A $\frac{dw}{dx}\frac{dx}{dt}+\frac{dw}{dy}\frac{dt}{dt}$ B $\frac{\partial w}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial t}$ C $\frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt}$ D $\frac{dw}{dx}\frac{\partial x}{\partial t}+\frac{dw}{dy}\frac{\partial y}{\partial t}$
Engineering Mathematics   Calculus
Question 2 Explanation:
$w=f\left ( x, y \right )$
By Chain rule,
$\frac{dw}{dt}=\frac{\partial w}{\partial x}\times \frac{dx}{dt}+\frac{\partial w}{\partial y}\times \frac{dy}{dt}$

 Question 3
Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be most preferred?
 A EPC contract B Percentage rate contract C Item rate contract D Lump sum contract
Construction Materials and Management
Question 3 Explanation:
Scope of construction work is well-defined with all its drawings, specification quantities and estimates, then lump sum contract is used.
 Question 4
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 $\gamma _{d}$ the dry unit weight of the soil. The equation for the zero air voids line in a compaction test plot is
 A $\gamma _{d}=\frac{G\gamma _{w}}{1+Gw}$ B $\gamma _{d}=\frac{G\gamma _{w}}{Gw}$ C $\gamma _{d}=\frac{Gw}{1+\gamma _{w}}$ D $\gamma _{d}=\frac{Gw}{1-\gamma _{w}}$
Geotechnical Engineering   Properties of Soils
Question 4 Explanation:
Percentage air void line is relation between dry unit weight and water content at constant air void. Hence equation of zero air void line is
\begin{aligned} \gamma_{\mathrm{d}}&=\left(1-n_{\mathrm{a}}\right) \frac{G \gamma_{\mathrm{w}}}{1+w G} &\left(n_{\mathrm{a}}=0\right) \\ \gamma_{\mathrm{d}}&=\frac{G \gamma_{\mathrm{w}}}{1+w G} \end{aligned}
 Question 5
Consider the following statements related to the pore pressure parameters, A and B:
P. A always lies between 0 and 1.0
Q. A can be less than 0 or greater than 1.0
R. B always lies between 0 and 1.0
S. B can be less than 0 or greater than 1.0

For these statements, which one of the following options is correct?
 A P and R B P and S C Q and R D Q and S
Geotechnical Engineering   Consolidation of Soils
Question 5 Explanation:
Pore pressure parameter B lies in between 0 to 1 and pore pressure parameter A may be as low as -0.5 and may be as high as 3.

There are 5 questions to complete.