Q1: Two hill tops A and B 20 km apart are intervened by a third top C. If the top most contour of the three hill tops are of the same value, state whether the line of sight AB

ANS:B - passes below the hill top C

According to me, here reciprocal levelling is considered as two hilltops is intervened by the third hilltop. so for large obstruction like this reciprocal levelling is done and this levelling completely eliminates the curvature effect and line of collimation error but refraction is partly left. Due to partly left refraction, it makes the object look higher than what it is actually sine we apply + correction for this. So by this 3rd hill top appear to be raised so LOS passes below hill c. For long sights and accurate levelling work, the effects of the curvature of the earth and refraction of the line of sight shall have to be taken into consideration. The effect of curvature is greater than that of refraction, the combined effect causes the points to appear to be lower than they actually are.
Consider it practically, with total correction=Cc+Rc =(-) 26.94m.

This is a correction for point B, means B will be around 27 meters below what we can see without considering hilltop C.

Now if hilltop C is considered, then we can not sight B as C will be in between A&B actual level line.

In this case distance between point A and B is more than that of Point A & C, the effect of the curvature of the earth and refraction of the line of sight is more in case of A & B compares to A and C, so point B will be lower than C and the line of sight from A to B passes below C.

The Correct answer is option B. The combined correction due to refraction and curvature is always negative indicating the value we got is more than the actual due to curvature of earth.

So even if we consider both refraction and curvature; the line of sight should be above C only. The logic we are missing is that if B is sighted from A, the line of sight will be obviously below the hill top. This is because in the given question it is mentioned, the top levels of all 3 hills are same. Now hill C is in between A and B.

In brief, the distance between A and C is less than the distance between A and B. So accordingly, when you sight B it simply indicates that you are sighting relatively lower point than top level of C (the same reason you people told.. due to curvature of earth) so the line of sight will be obviously below C.  I think it is because of both due curvature & refraction effect. If we go only go with earth curvature effect the correction is negative (Cc=-.0785d2) it means the line of sight go above the hill top "c".

and if we go with refraction effect than the correction is +tive (Cr=+(1/7)Cc) it means the line of sight gets deflected downward. For the above problem we consider both curvature & refraction effect which is (Cc+Cf)= -0.0673d2 it means the line sight gets deflected downward so the answer B is right. It is given that hill tops of A&B are intervened y third top, but height of third top is not given.

Therefore, m not able to understand how option B is correct.

Question is not clear to me.