

CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Feb. 13, 2025 by Teachoo
Question 27 According to a psychologist, the ability of a person to understand spatial concepts is given by ๐ด=1/3 โ๐ก, where ๐ก is the age in years, ๐กโ[5, 18]. Show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18 .Given ๐ด=1/3 โ๐ก We need to show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18 Thus, we need to show Rate of increase in ability is decreasing in [5, 18] i.e. R is decreasing in [5, 18] i.e. Rโ < 0 in [๐, ๐๐] Now, Rate of increase in ability = ๐๐จ/๐ ๐ = ๐(1/3 โ๐ก)/๐๐ก = ๐/๐ ร ๐ (โ๐)/๐ ๐ = 1/3 ร1/(2โ๐ก) = ๐/(๐โ๐) And, Rโ = ๐ /๐ ๐(๐ ๐จ/๐ ๐) Rโ = ๐(1/(6โ๐ก))/๐๐ก Rโ = ๐/๐ ๐ (๐/โ๐)/๐ ๐ Rโ = 1/6 ๐(๐ก^(โ1/2) )/๐๐ก Rโ = 1/6 ร โ1/2 ๐ก^(โ1/2โ1) Rโ = (โ๐)/๐๐ ๐^(โ๐/๐) Now, for t in [5, 18] Rโ < 0 Thus, Rate of increase in ability is decreasing in [5, 18]