$f\left(x\right)=\left\{\begin{array}{ll}{x}^3,& x^2<1\\ x,& x^2\ge 1\end{array}\right.$, then $f\left(x\right)$ is

Important Questions on Continuity and Differentiability

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 48

If $x+4\left|y\right|=6y$, then $y$ as a function of $x$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 49

If $f\left(x\right)=\left[{\tan }^{2}x\right]$, where $\left[·\right]$ denotes the greatest integer function, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 50

The function $f\left(x\right)=\left[x^2\right]+{\left[-x\right]}^2$, where $\left[·\right]$ denotes the greatest integer function, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 51

Let $f\left(x\right)=\frac{1}{\left[\sin x\right]}$, where $\left[·\right]$ denotes the greatest integer function, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 52

The points, where the function $f\left(x\right)=\left[x\right]+\left|1-x\right|, 1\le x\le 3$, (where $\left[·\right]$ denotes the greatest integer function) is not differentiable, are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 53

Let $f\left(x\right)=\left[n+p\sin x\right]; x\in \left(0,\pi \right), n\in I, p$ is prime number and $\left[x\right]$ denotes the greatest integer less than or equal to $x$. Then, the number of points at which $f\left(x\right)$ is not differentiable, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 54

If $f\left(x\right)=-{\left(-1\right)}^{\left[x^3\right]}$, where $\left[·\right]$ denotes the greatest integer function, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 55

If $f\left(x\right)={\cos }^{-1}\left(\frac{2x}{1+x^2}\right)$, then $f\left(x\right)$ is differentiable on