Points of Discontinuity

Q. $y=\frac{1}{t^2+t-2}$ where $t=\frac{1}{x-1}$ then the number of points of discontinuities of $y=f\left(x\right),xϵR$ is

1. 1
2. 2
3. 3
4. Infinite

Q. The point(s) of discontinuity of the composite function y = f (f(x)) , where $f\left(x\right)=\frac{1}{x-1}$ is/are

1. x = 1
2. x = 0
3. x = 2
4. x = -2

Q. The function f(x) given by
$f\left(x\right)=\left(x-x_1\right|+\left(x-x_2\right|+\left(x-x_3\right|+....+\left(x-x_n\right|$ is continuous but not differentiable at the points $x=x_1,x_2,......,x_n$.

1. False
2. True

Q. Which of the following point(s) is/are a point of discontinuity for f(x) defined by $f\left(x\right)=\frac{4-x^2}{4x-x^3}$

1. \N
2. 2
3. -2
4. 1

Q. The number of points of discontinuity of $f\left(x\right)$ where $f\left(x\right)=|||x+\left[x\right]|-3\left[x\right]|-5\left[x\right]|\text{on}[-2,2]$ is
(where $\left[x\right]$ denotes greatest integer function)

1. 2
2. 4
3. 5
4. 6

Q. Number of point(s) where the function $f\left(x\right)=max(\sqrt{2x-x^2},2-x)$ is non-differentiable, is/are

1. 0
2. 1
3. 2
4. 3

Q. Let $f:[-1,3]\to R$ be defined as

$f\left(x\right)=\{\begin{array}{c}|x|+\left[x\right],-1\le x<1\\ x+|x|,1\le x<2\\ x+\left[x\right],2\le x\le 3\end{array}$

where $\left[t\right]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at :

1. only one point
2. only two points
3. only three points
4. four or more points

Q. Let $\left[t\right]$ denotes the greatest integer $\le t$ and $\underset{x\to 0}{lim}x\left[\frac{4}{x}\right]=A.$ Then the function, $f\left(x\right)=\left[x^2\right]\sin \pi x$ is discontinuous, when $x$ is equal to

1. $\sqrt{A+1}$
2. $\sqrt{A}$
3. $\sqrt{A+5}$
4. $\sqrt{A+21}$

Q. The number of points at which the function $f\left(x\right)=\{\begin{array}{cc}\left[\cos \pi x\right],& 0\le x\le 1\\ |x-1|[x-2],& 1<x\le 2\end{array}$
is discontinuous, is
$\left(\right[.]$ denotes the greatest integral function $)$

1. $1$
2. $2$
3. $3$
4. $4$

Q. Find the point s of discontinuity of f , where