← CBSE Class 12 PYQ

Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

23 of 41 · show all

Q2 2026

If $e^{-x}+e^{-y}=2$, then $\frac{dy}{dx}$ is
Q4 2026

If $x = a\sin^3 t,\ y = b\cos^3 t$, then find $\dfrac{dy}{dx}$ at $t = \dfrac{\pi}{4}$.
Q6 2026

The value of k for which the function…
Q7 2026

If $\sin^{-1} x = y$, then $\frac{dy}{dx}$ is…
Q9 2026

If $x = t + \frac{1}{t}$ and $y = t - \frac{1}{t}$, find $\frac{dy}{dx}$ at $t = 2$.
Q12 2025

The absolute maximum value of function $f(x) = x^3 - 3x + 2$ in $[0, 2]$ is…
Q13 2025

Assertion (A) : $f(x)=\begin{cases}3x-8, & x\le 5\\ 2k, & x>5\end{cases}$ is continuous at $x = 5$ for…
Q14 2025

Differentiate $2^{\cos^2 x}$ w.r.t. $\cos^2 x$.
Q15 2025

The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate its area increasing…
Q17 2025

If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the… (with a figure)
Q20 2025

If $f(x) = \begin{cases} 3x - 2, & 0 < x \le 1 \\ 2x^2 + ax, & 1 < x < 2 \end{cases}$ is continuous for…
Q21 2025

The function f defined by…
Q22 2025

If $f(x) = 2x + \cos x$, then $f(x)$…
Q23 2025

Find k so that…
Q24 2024

Which of the following statements is true for the function…
Q25 2024

Let $f(x)$ be a continuous function on $[a, b]$ and differentiable on $(a, b)$. Then, this function $f(x)$ is…
Q26 2024

The derivative of $\sin(x^2)$ w.r.t. $x$, at $x = \sqrt{\pi}$ is…
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…
Q32 2024

The derivative of $\tan^{-1}(x^2)$ w.r.t. $x$ is…
Q35 2023

The value of k for which function $f(x) = \begin{cases} x^2, & x \geq 0 \\ kx, & x < 0 \end{cases}$ is…
Q36 2023

If $y = \frac{\cos x - \sin x}{\cos x + \sin x}$, then $\frac{dy}{dx}$ is…
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…
Q40 2023

The function $f(x) = x|x|$ is