PYQ Vault

Day 75: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2026 (same type asked 3 times)

    23
    Find the values of x for which f(x)=xxf(x) = x^x, x>0x > 0 is increasing.

  2. Question 2

    Application of Derivatives. Asked once: 2026 (same type asked 3 times)

    23
    Find the interval(s) for which the function f(x)=x3+3xf(x) = \dfrac{x}{3} + \dfrac{3}{x}, x≠0x \neq 0 is increasing.

  3. Question 3

    Application of Derivatives. Asked once: 2026 (same type asked 3 times)

    35 (a)
    Find the sub-interval of (0,π)(0, \pi) in which f(x)=tan⁡−1(sin⁡x−cos⁡x)f(x) = \tan^{-1}(\sin x - \cos x) is increasing and decreasing.

  4. Question 4

    Application of Derivatives. Asked once: 2026 (same type asked 3 times)

    23 (b)
    If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.

  5. Question 5

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

    23
    The area of the circle is increasing at a uniform rate of 2 cm2^2/sec. How fast is the circumference of the circle increasing when the radius r = 5 cm ?