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

3x_{1}+2x_{2}=c_{1}

4x_{1}+x_{2}=c_{2}

The characteristic equation for these simultaneous equations 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 |

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

\frac{dw}{dx}\frac{dx}{dt}+\frac{dw}{dy}\frac{dt}{dt} | |

\frac{\partial w}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial t} | |

\frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt} | |

\frac{dw}{dx}\frac{\partial x}{\partial t}+\frac{dw}{dy}\frac{\partial y}{\partial t} |

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}

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?

EPC contract | |

Percentage rate contract | |

Item rate contract | |

Lump sum contract |

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

\gamma _{d}=\frac{G\gamma _{w}}{1+Gw} | |

\gamma _{d}=\frac{G\gamma _{w}}{Gw} | |

\gamma _{d}=\frac{Gw}{1+\gamma _{w}} | |

\gamma _{d}=\frac{Gw}{1-\gamma _{w}} |

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}

\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?

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?

P and R | |

P and S | |

Q and R | |

Q and S |

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.