a$)$ Table $1\mathrm{.}0$ show booking for a looping levelling survey was made at TBM$1$ with an initial reduced level of $12\mathrm{.}500m.$ Given that the constant $m$ value is $10.$ Check and complete the calculation and adjustment using Rise and Fall Method. Indicate the missing values denoted as $a,b,c,d,e,f,g,h$ and $i.$

b$)$ As described in Table $2\mathrm{.}0,$ a line of surveying levelling work is to be carried out from TBM$201$ of $15\mathrm{.}550m$ and close back to TBM$201.$ Conduct checking out on the leveling problem using Height of Collimation Method.

c$)$ Calculate and check the staff readings for the following leveling survey as shown in Figure $1\mathrm{.}0.$ Use the Rise and Fall Method to complete the calculations.

Figure $1\mathrm{.}0$ Leveling work

d$)$ A point $Y$ is to be set out from a point $x$ using $50m$ steel tape. The horizontal length of $xY$ is designed as $27\mathrm{.}000m.$ During the setting out the steel tape is laid on the ground and a tension of $70N$ is applied, the mean temperature at the time was $4C.$ The reduced levels of $x$ and $Y$ are $22\mathrm{.}75m$ and $24\mathrm{.}86m$ respectively. The tape was standardized on site as $40\mathrm{.}983m$ at $50N$ tension and $12C$ on a baseline of length $41\mathrm{.}005m$ and it has a cross$-$sectional area of $2\mathrm{.}4m{m}^2.$ Calculate the length that should be set out on the tape along the direction XY to establish the exact position of point $Y.$