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← CBSE Class 12 PYQ

Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

  1. Q1 2026
    Check whether function $f(x)$ defined as…
  2. Q2 2026
    If $e^{-x}+e^{-y}=2$, then $\frac{dy}{dx}$ is
  3. Q3 2026
    For f(x) = x + $\frac{1}{x}$ (x ≠ 0)
  4. Q4 2026
    If $x = a\sin^3 t,\ y = b\cos^3 t$, then find $\dfrac{dy}{dx}$ at $t = \dfrac{\pi}{4}$.
  5. Q5 2026
    Find the absolute maximum value of $f(x) = \cos x + \sin^2 x,\ x \in [0, \pi]$
  6. Q6 2026
    The value of k for which the function…
  7. Q7 2026
    If $\sin^{-1} x = y$, then $\frac{dy}{dx}$ is…
  8. Q8 2026
    The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is…
  9. Q9 2026
    If $x = t + \frac{1}{t}$ and $y = t - \frac{1}{t}$, find $\frac{dy}{dx}$ at $t = 2$.
  10. Q10 2026
    If $(\sin x)^y=y^{\cos x}$, then find $\frac{dy}{dx}$.
  11. Q11 2025
    If $f(x) = |x| + |x - 1|$, then which of the following is correct ?
  12. Q12 2025
    The absolute maximum value of function $f(x) = x^3 - 3x + 2$ in $[0, 2]$ is…
  13. Q13 2025
    Assertion (A) : $f(x)=\begin{cases}3x-8, & x\le 5\\ 2k, & x>5\end{cases}$ is continuous at $x = 5$ for…
  14. Q14 2025
    Differentiate $2^{\cos^2 x}$ w.r.t. $\cos^2 x$.
  15. Q15 2025
    The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate its area increasing…
  16. Q16 2025
    Find the absolute maximum and absolute minimum of function $f(x)=2x^3-15x^2+36x+1$ on $[1,5]$.
  17. Q17 2025
    If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the… (with a figure)
  18. Q18 2025
    If $x = e^{x/y}$, then prove that $\frac{dy}{dx} = \frac{x - y}{x \log x}$.
  19. Q19 2025
    If $y = \sin^{-1} x$, then $(1 - x^2)\dfrac{d^2y}{dx^2}$ is equal to…
  20. Q20 2025
    If $f(x) = \begin{cases} 3x - 2, & 0 < x \le 1 \\ 2x^2 + ax, & 1 < x < 2 \end{cases}$ is continuous for…
  21. Q21 2025
    The function f defined by…
  22. Q22 2025
    If $f(x) = 2x + \cos x$, then $f(x)$…
  23. Q23 2025
    Find k so that…
  24. Q24 2024
    Which of the following statements is true for the function…
  25. Q25 2024
    Let $f(x)$ be a continuous function on $[a, b]$ and differentiable on $(a, b)$. Then, this function $f(x)$ is…
  26. Q26 2024
    The derivative of $\sin(x^2)$ w.r.t. $x$, at $x = \sqrt{\pi}$ is…
  27. Q27 2024
    A function $f(x) = |1 - x + |x||$ is…
  28. Q28 2024
    If the sides of a square are decreasing at the rate of $1.5$ cm/s, the rate of decrease of its perimeter is…
  29. Q29 2024
    The derivative of $2^x$ w.r.t. $3^x$ is…
  30. Q30 2024
    If $x\cos(p+y)+\cos p\sin(p+y)=0$, prove that $\cos p\,\frac{dy}{dx} = -\cos^2(p+y)$, where p is a constant.
  31. Q31 2024
    The number of points of discontinuity of…
  32. Q32 2024
    The derivative of $\tan^{-1}(x^2)$ w.r.t. $x$ is…
  33. Q33 2024
    If $f(x) = |\tan 2x|$, then find the value of $f'(x)$ at $x = \dfrac{\pi}{3}$.
  34. Q34 2024
    If $x = e^{\cos 3t}$ and $y = e^{\sin 3t}$, prove that $\frac{dy}{dx} = -\frac{y\log x}{x\log y}$.
  35. Q35 2023
    The value of k for which function $f(x) = \begin{cases} x^2, & x \geq 0 \\ kx, & x < 0 \end{cases}$ is…
  36. Q36 2023
    If $y = \frac{\cos x - \sin x}{\cos x + \sin x}$, then $\frac{dy}{dx}$ is…
  37. Q37 2023
    If $y = x^{\frac{1}{x}}$, then find $\frac{dy}{dx}$ at $x = 1$.
  38. Q38 2023
    The value of k for which $f(x) = \begin{cases} 3x+5, & x \ge 2 \\ kx^2, & x < 2 \end{cases}$ is a continuous…
  39. Q39 2023
    If $y = (x + \sqrt{x^2 - 1})^2$, then show that $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = 4y^2$.
  40. Q40 2023
    The function $f(x) = x|x|$ is
  41. Q41 2023
    If $\tan\left(\frac{x+y}{x-y}\right) = k$, then $\frac{dy}{dx}$ is equal to