NIMCET 2015 — Mathematics PYQ

The given numbers are in an Arithmetic Progression: $a=1$, common difference $=d$, and number of terms $n=101$ (since the sequence goes from $0d$ to $100d$).

For an AP, the mean is the average of the first and last terms:

2. Calculate the Mean Deviation (M.D.)

The formula for Mean Deviation from the mean is:

Substitute $x_i=1+id$ and $\bar{x}=1+50d$:

Assuming d > 0, the sum becomes:

This consists of two identical series of $1$ to $50$:

3. Solve for $d$

Given $M.D.=255$ and $n=101$:

Multiply by $101$:

Divide by $255$:

Correct Option: (b)