JEE MAINS PRACTICE · Mathematics
Continuity and Differentiability
393 practice questions for JEE Mains Practice — 196 easy · 186 medium · 11 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
Let $\(f(x)=|\sin x|\). Then
MCQ
If $f(x)=\left\{\begin{array}{cc}x, & 0 \leq x \leq 1 \\ 2 x-1, & 1 \lt x\end{array}\right.$, then
MCQ
Q348 (image question)
MCQ
If $f(x)=\min \left\{1, x^2, x^3\right\}$, then
MCQ
The set of points where the function $f(x)=x|x|$ is differentiable, is
MCQ
If $f(x)=\left\{\begin{array}{cc}a x^2+b, & 0 \leq x \lt 1 \\ x+3, & 1 \lt x \leq 2 \\ 4, & x=1\end{array}\right.$, then the value of $(a, b)$ for which $f(x)$ cannot be continuous at $x=1$ is
MCQ
If $f(x)=\left\{\begin{array}{cc}x+1, & x \leq 1 \\ 3-a x^2, & x\gt1\end{array}\right.$ is continuous at $x=1$, then the value of $a$ is
MCQ
If [] denotes the greatest integer function, then $f(x)=[x]+\left[x+\frac{1}{2}\right]$
MCQ
If $|f(x)|$ is continuous at $x=a$, then $f(x)$ is
MCQ
If $f(x)= \begin{cases}\frac{\sin (\cos x)-\cos x}{(\pi-2 x)^3}, & x \neq \frac{\pi}{2} \\ k, & x=\frac{\pi}{2}\end{cases}$ is a continuous at $x=\frac{\pi}{2}$, then $k$ is equal to
MCQ
The value of $f(0)$, so that the function $f(x)=\frac{2-(256-7 x)^{1 / 8}}{(5 x+3 x)^{1 / 5}-2}, x \neq 0$ is continuous everywhere is given by
MCQ
The function $f(x)=[x] \cos \left[\frac{2 x-1}{2}\right] \pi$ where [] denotes the greatest integer function, is discontinuous at