Q1: A uniform slope was measured by the method of stepping. If the difference in level between two points is 1.8 m and the slope distance between them is 15 m, the error is approximately equal to

ANS:A - cumulative, + 0.11 m

Slope correction = h^2/2L = 1.8^2/(2*15) = 0.108~0.11.
Slope error is always + ive slope correction is always -ive.
So, Cumulative Error. Now we know that given sloping distance is 15meter and difference in elevation is 1.8 meter.

That means we know the slope i.e. H:V = 15 : 1.8.
but slope gives us value of horizontal distance per unit error. We want error per unit horizontal distance here means 1.8 :15.
That gives us 0.12 which is cumulative of course due to slope. Hence it will be +0.12 cumulative or corrected for +0.11 cumulative. By Pythagoras Theorem, the ground distance is 15.10 and slope distance is 15m.

Since Error = Measured value - True Value, and here Measured value is lesser that is 15m, we get the error as -ve.

Hence correction +ve. Therefore, I agree with Option (A) In this question, they are asking for error not correction so.

Correction is always negative.

But the error is positive.
That' s why the answer is +11.

As it is a systematic error not random error so it can be called cumulative error.