PYQ Vault

Day 6: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    6
    If f(x)={x2−4x−5x+1,x≠−1k,x=−1f(x) = \begin{cases} \dfrac{x^2 - 4x - 5}{x + 1}, & x \ne -1 \\[2mm] k, & x = -1 \end{cases} is continuous at x=−1x = -1, then the value of k is :

    Tap an option to check your answer.

  2. Question 2

    Continuity and Differentiability. Asked 2 times: 2024, 2026

    8
    The greatest integer function, f(x)=[x]f(x) = [x], 0<x<30 < x < 3 is not differentiable at how many points ?

    Tap an option to check your answer.

  3. Question 3

    Continuity and Differentiability. Asked 2 times: 2023, 2026

    28 (a)
    If xy=ex−yxy = e^{x - y}, then find dydx\dfrac{dy}{dx}.

  4. Question 4

    Continuity and Differentiability. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    22
    If x=esin⁡−1tx = e^{\sin^{-1} t} and y=ecos⁡−1ty = e^{\cos^{-1} t}, then find dydx\dfrac{dy}{dx} at t=12t = \dfrac{1}{\sqrt{2}}.

  5. Question 5

    Continuity and Differentiability. Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)

    22
    If x=asin⁡3tx = a \sin^3 t, y=bcos⁡3ty = b \cos^3 t, then find dydx\dfrac{dy}{dx} at t=π4t = \dfrac{\pi}{4}.