A student studying the weather for d days observed that $\left(\mathrm{i}\right)$ it rained on $7$days, morning or afternoon, $\left(\mathrm{ii}\right)$ when it rained in the afternoon, it was clear in the morning,$\left(\mathrm{iii}\right)$ there were five clear afternoons, and$\left(\mathrm{iv}\right)$ there were six clear mornings. Then, d equals:

Tanveer constructs a wall working in a special way and takes $12$days to complete it. If ${\mathrm{S}}_{\mathrm{n}}$ is the length of the wall (in $\mathrm{m}$) that he constructs on the nth day, then

${\mathrm{S}}_{\mathrm{n}}=2\mathrm{n},0\le \mathrm{n}\le 4$

$S_{\mathrm{n}}=8$ for $\mathrm{n}=5$

${\mathrm{S}}_{\mathrm{n}}=3\mathrm{n}-7,6\le \mathrm{n}\le 12$

 Find the total length of the wall he constructs in the first $10$days.

Two poles, one $78 \mathrm{m}$ in height above the ground and the other $91 \mathrm{m}$ in height above the ground, are at some distance from each other. Two strings are tied, one from the top of one pole to the bottom of the other and the other from the top of the second pole to the bottom of the first. What is the height above the ground at which the string meets?

(Note: You may wonder why this question, which is apparently using the concepts of geometry, is placed in this chapter. Look at the solution to find the traces of the similarity in the formation of this problem and the time and work concept.)