2018 · Q71
A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r₁, r₂, r₃, …, rₙ₋₁ such that r₁ < r₂ < r₃ < … < rₙ₋₁ concentric with the circle C. If pₘ = rₘ₊₁/rₘ where m = 1, 2, 3, …, (n - 2), then which one of the following is correct?
Elementary MathematicsMensuration
- Ap increases as m increases
- Bp decreases as m increases
- Cp remains constant as m increases
- Dp increases for some values of m as m increases and then decreases thereafter
Explanation
The m-th circle encloses area m·(A/n), so r_m = R√(m/n) and p_m = r_{m+1}/r_m = √((m+1)/m) = √(1 + 1/m). As m increases, 1/m decreases, so p_m decreases, option (B).