PYQ Vault

Day 14: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked 2 times: 2023, 2025

    27 (b)
    Check the differentiability of function f(x)=x∣x∣f(x) = x|x| at x=0x = 0.

  2. Question 2

    Continuity and Differentiability. Asked 2 times: 2024, 2025

    25 (a)
    If x=exyx = e^{\frac{x}{y}}, then prove that dydx=x−yxlog⁡x\dfrac{dy}{dx} = \dfrac{x - y}{x \log x}.

  3. Question 3

    Continuity and Differentiability. Asked 2 times: 2024, 2025

    32 (a)
    If 1−x2+1−y2=a(x−y)\sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y), then prove that dydx=1−y21−x2\frac{dy}{dx} = \sqrt{\frac{1 - y^2}{1 - x^2}}.

  4. Question 4

    Continuity and Differentiability. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    34 (b)
    Find dydx\dfrac{dy}{dx} if yx+xy+xx=aby^x + x^y + x^x = a^b, where a and b are constants.

  5. Question 5

    Continuity and Differentiability. Asked 2 times: 2024, 2025

    4
    If y=sin⁡−1xy = \sin^{-1} x, then (1−x2)d2ydx2(1 - x^2)\frac{d^2y}{dx^2} is equal to :

    Tap an option to check your answer.