Trigonometric levelling was carried out from two stations P and Q to find the reduced level (R. L.) of the top of hillock, as shown in the table. The distance between Stations P and Q is 55 m. Assume Stations P and Q, and the hillock are in the same vertical plane. The R. L. of the top of the hillock (in m) is ____________ (round off to three decimal places).

$$ \begin{array}{|c|c|c|c|} \hline \text { Station } & \begin{array}{c} \text { Vertical } \\ \text { angle of } \\ \text { the top of } \\ \text { hillock } \end{array} & \begin{array}{c} \text { Staff } \\ \text { reading on } \\ \text { benchmark } \end{array} & \begin{array}{c} \text { R.L. of } \\ \text { bench } \\ \text { mark } \end{array} \\ \hline \mathrm{P} & 18^{\circ} 45^{\prime} & 2.340 \mathrm{~m} & \begin{array}{c} 100.000 \\ \mathrm{~m} \end{array} \\ \hline \mathrm{Q} & 12^{\circ} 45^{\prime} & 1.660 \mathrm{~m} & \\ \hline \end{array} $$

The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is _______.

A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle 𝜙′ = 32°. What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each of the sample to identify the failure mechanism? Identify the correct combination from the following options:

P : Triaxial compression test

Q : Triaxial extension test

R : Direct shear or shear box test

S : Vane shear test