PYQ Vault

Day 198: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    33
    Find the absolute maximum and absolute minimum of function f(x)=2x3−15x2+36x+1f(x) = 2x^3 - 15x^2 + 36x + 1 on [1,5][1, 5].

  2. Question 2

    Application of Derivatives. Asked once: 2024 (same type asked 3 times)

    25
    Show that f(x)=ex−e−x+x−tan⁡−1xf(x) = e^x - e^{-x} + x - \tan^{-1} x is strictly increasing in its domain.

  3. Question 3

    Application of Derivatives. Asked once: 2023 (same type asked 3 times)

    21
    Consider the statement "There exists at least one value of b∈Rb \in \mathbb{R} for which f(x)=bxf(x) = \frac{b}{x}, b≠0b \neq 0 is strictly increasing in R−{0}\mathbb{R} - \{0\}." State True or False. Justify.

  4. Question 4

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    10
    A spherical ball has a variable diameter 52(3x+1)\dfrac{5}{2}(3x + 1). The rate of change of its volume w.r.t. x, when x=1x = 1, is :

    Tap an option to check your answer.

  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    14
    The derivative of 2x2^x w.r.t. 3x3^x is :

    Tap an option to check your answer.