Two vertical light poles of height $22\text{ m}$ and $16\text{ m}$ stand on the opposite sides of a $20\text{ m}$ wide road as shown below in the figure. Two ladders of length $l_1$ and $l_2$ are placed from a common point R on the road at a distance of $x\text{ m}$ from the smaller pole. Based on the above information, answer the following questions : (i) Express $p(x) = l_1 + l_2$ in terms of $x$. (ii) Find $p'(x)$. (iii) (a) Find the value of $x$ for which $l_1^2 + l_2^2$ is minimum. OR (iii) (b) If the $22\text{ m}$ long pole is replaced by another $16\text{ m}$ long pole at its place, then at what distance from each pole should the ladder be placed so that the sum of the squares of the lengths of the ladders is minimum ?

Year	Paper Code	Set	Position
CBSE 2026	Series 65-3	Set 1	Question 36
CBSE 2026	Series 65-3	Set 2	Question 38
CBSE 2026	Series 65-3	Set 3	Question 37

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)