Q. Let $f\left(x\right)=\left\{\begin{matrix} max \left\{\left|x\right| , x^{2}\right\} & \left|x\right|\leq 3 \\ 12-\left|x\right| & \, \, 3 < \left|x\right|\leq 12 . \end{matrix}\right$ If $S$ is the set of points in the interval $\left(- 12 , 12\right)$ at which $f$ is not differentiable, then $S$ is

NTA AbhyasNTA Abhyas 2020Continuity and Differentiability Report Error

A

equal to $\left\{- 3 , 3\right\}$

B

equal to $\left\{- 3 , - 1 , 1 , 3\right\}$

C

an empty set

D

equal to $\left\{- 3 , - 1 , 0 , 1 , 3\right\}$

Solution:

Here, $f(x)=\left\{\begin{array}{cc}12+x & -12 \leq x < -3 \\ x^{2} & -3 \leq x \leq-1 \\ |x| & -1 < x < 1 \\ x^{2} & 1 \leq x \leq 3 \\ 12-x & 3 < x \leq 12\end{array}\right.$

Hence, $f\left(x\right)$ is not differentiable at $x=-3,-1,0,1,3$
$\Rightarrow S=\left\{- 3 , - 1 , 0 , 1 , 3\right\}$

Questions from NTA Abhyas 2020

1. The value of $\displaystyle \int _{- 1}^{1} \left(x - \left[x\right]\right) d x$ (where [.] denotes greatest integer function) is

Integrals

2. A flag - staff of $5$ meters high stands on a building of $25$ meters height. For an observer at a height of $30$ meters, the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag - staff is

3. If $R=\left\{\left(x , \, y\right) \left|\right. x , \, y \in Z , \, x^{2} + y^{2} \leq 4\right\}$ is a relation in $Z$ , then domain of $R$ is

4. If $5^{97}$ is divided by $52$ $,$ then the remainder obtained is

Binomial Theorem

5. If $y=4x-5$ is tangent to the curve $y^{2}=px^{3}+q$ at $\left(\right.2, \, 3\left.\right)$ then $\left(\right.p,q\left.\right)$ is

Application of Derivatives

Questions from Continuity and Differentiability

1. If $x= \frac{1-t}{1+t} ; y= \frac{2t}{1+t}, $ then $\frac{d^{2}y}{dx^{2}} = $

COMEDK 2012

2. If $x = \sec \theta - \cos \; \theta, y = \sec^n \theta - \cos^n \theta $, then $(x^2 + 4) \left( \frac{dy}{dx} \right)^2$ is equal to

VITEEE 2010

3. If $ y=\frac{3a{{t}^{2}}}{1+{{t}^{3}}},\,x=\frac{3at}{1+{{t}^{3}}}, $ then $ \frac{dy}{dx} $ is equal to

J & K CET 2008

4. If $f ''\left(0\right)=k, k\ne0,$ then the value of $\displaystyle \lim_{x \to 0}$
$\frac{2f \left(x\right)-3f \left(2x\right)+f \left(4x\right)}{x^{2}}$ is

WBJEE 2017

5. If f(x)=$ \left(\frac{x}{2}\right)^{10}, then\, f \left(1\right)+\frac{f '\left(1\right)}{\lfloor1}+\frac{f \left(1\right)}{\lfloor2}+\frac{f '\left(1\right)}{\lfloor3}+\ldots+\frac{f ^{\left(10\right)}\left(1\right)}{\lfloor10}$ is equal to

KEAM 2016

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals