Day 102: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1 (case study, 4 parts)
Application of Derivatives. Asked once: 2025 (same type asked 4 times)
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum. On the basis of the above information, answer the following questions :
36 (i) $Taking length = breadth = x m and height = y m, express the surface area (S) of the box in terms of x and its volume (V), which is constant.$
36 (ii) $\dfrac{dS}{dx}$
36 (iii) (a) $Find a relation between x and y such that the surface area (S) is minimum.$
36 (iii) (b) $(V) = \dfrac{1}{4}(Sx - 2x^3)$
Question 2
Application of Derivatives. Asked once: 2024 (same type asked 4 times)
23 $f(x) = x^{4} - 4x^{3} + 10$
Question 3
Continuity and Differentiability. Asked once: 2026 (same type asked 4 times)
7 $f(x) = \begin{cases} x^2 \sin \dfrac{1}{x}, & x \ne 0 \\ k(x + 1), & x = 0 \end{cases}$
Tap an option to check your answer.
Question 4
Continuity and Differentiability. Asked once: 2025 (same type asked 4 times)
8 $f(x) = \begin{cases} 3ax - b, & x > 1 \\ 11, & x = 1 \\ -5ax - 2b, & x < 1 \end{cases}$
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Question 5
Continuity and Differentiability. Asked once: 2025 (same type asked 4 times)
9 $f(x) = |x|$
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Question 1 (case study, 4 parts)