(a) It is given that function $f(x) = x^4 - 62x^2 + ax + 9$ attains local maximum value at $x = 1$. Find the value of 'a', hence obtain all other points where the given function $f(x)$ attains local maximum or local minimum values. OR (b) The perimeter of a rectangular metallic sheet is $300 \text{ cm}$. It is rolled along one of its sides to form a cylinder. Find the dimensions of the rectangular sheet so that volume of cylinder so formed is maximum.

Year	Paper Code	Set	Position
CBSE 2024	Series Other	Set 1	Question 33
CBSE 2024	Series Other	Set 1	Question 32
CBSE 2024	Series Other	Set 1	Question 34

• 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)