List of top Mathematics Questions on Continuity and differentiability asked in MHT CET

If \( y = \sin^{-1}(3x - 4x^3) \), find \( \dfrac{dy}{dx}. \)

Find the value of \( k \) if the function \( f(x) = \dfrac{k\cos x}{\pi - 2x} \) is continuous at \( x = \dfrac{\pi}{2} \).

If \( y = \sin^{-1}(3x - 4x^3) \), find the derivative \( \dfrac{dy}{dx} \) in its standard form.

If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

Derivative of \[ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}} \] is:

If $f(x) = \begin{cases} \frac{9^x - 2 \cdot 3^x + 1}{\log(1+3x) \cdot \tan 2x} & , \text{if } x \neq 0 \\ a(\log b)^c & , \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $a+b+c =$

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is

Derivative of $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\dots\infty}$ is

If $f(x) = \begin{cases} \frac{9^x - 2 \cdot 3^x + 1}{\log(1+3x) \cdot \tan 2x} & , \text{if } x \neq 0 \\ a(\log b)^c & , \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $a+b+c =$

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is

If $f(x) = \begin{cases} \frac{9^x - 2 \cdot 3^x + 1}{\log(1+3x) \cdot \tan 2x} & , \text{if } x \neq 0 \\ a(\log b)^c & , \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $a+b+c =$

Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).

If $x^{2}+y^{2}=t+\frac{1}{t}$ and $x^{4}+y^{4}=t^{2}+\frac{1}{t^{2}}$, then $\frac{dy}{dx}$ is equal to

If $f(1)=1$, $f^{\prime}(1)=3$, then the derivative of $f(f(f(x)))+(f(x))^{2}$ at $x=1$ is

The function $f$ defined on $\left(-\frac{1}{3}, \frac{1}{3}\right)$ by $f(x) = \left\{ \begin{array}{ll} \frac{1}{x} \log\left(\frac{1+3x}{1-2x}\right) & , x \neq 0 \\> k & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then $k$ is

The function $f(x)=[x]\cdot \cos\left(\frac{2x-1}{2}\pi\right)$ where $[\cdot]$ denotes the greatest integer function, is discontinuous at

If $y = \left[(x+1)(2x+1)(3x+1)\cdots(nx+1)\right]^n$, then $\frac{dy}{dx}$ at $x=0$ is

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then the value of $x^{2025} + x^{2026} + x^{2027}$ is

Let \( f:\mathbb{R}\rightarrow \mathbb{R} \) be a function such that \( f(x)=x^{3} + x^{2}f^{\prime}(1) + x f^{\prime\prime}(2) + 6 \) for \( x \in \mathbb{R} \), then \( f(2) \) equals

If $y = (\sin^{-1}x)^2 + (\cos^{-1}x)^2$, then $(1 - x^2)\,y'' - x\,y' = $