Let f : [-1,3] R be defined as f ( x ) = * 20 c | x | + [ x ], & - 1 x < 1 x + | x |, & 1 x < 2 x + | x |, & 2 x 3 . where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at:

Let f : [-1,3] R be defined as f ( x ) = * 20 c | x

MCQ

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

$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{\left| x \right| + \left[ x \right],}&{ - 1 \leq x < 1} \\
{x + \left| x \right|,}&{1 \leq x < 2} \\
{x + \left| x \right|,}&{2 \leq x \leq 3}
\end{array}} \right.$

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

✓
only two points
B
only one point
C
four or more points
D
only three points

✓

Answer

Correct option: A.

only two points

a
$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{ - x - 1}&{x \in \left[ { - 1,0} \right)}\\
x&{x \in \left[ {0,1} \right)}\\
{2x}&{x \in \left[ {1,2} \right)}\\
{x + 2}&{x \in \left[ {2,3} \right)}
\end{array}} \right.$

$f(x)$ is discontinuous at $x=0,1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The area between the curve $y^2 (a + x) = (a - x)^3$ and its vertical asymptote is

→

The area of the region enclosed by the parabola $x^2 = y,$ the line $y = x + 2$ and the $x -$ axis, is:

→

If $f(x) = x^4+ \lambda x^3 +x^2$ $(\lambda \in R)$ has local maximum at $\frac{1}{2} ,$ then absolute minimum value of $f(x)$ is -

→

Let $PQ$ be a diameter of the circle $x ^{2}+ y ^{2}=9 .$ If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line, $x+y=2$ respectively, then the maximum value of $\alpha \beta$ is

→

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations

$x+y+z=5$ ; $x+2 y+3 z=\mu$ ; $x+3 y+\lambda z=1$

is constructed. If $\mathrm{p}$ is the probability that the system has a unique solution and $\mathrm{q}$ is the probability that the system has no solution, then :

→

Let $a, b$ and $c$ be three real numbers satisfying

$\left[\begin{array}{lll}a & b & c\end{array}\right]\left[\begin{array}{lll}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]$................$(E)$

$1.$ If the point $P(a, b, c)$, with reference to $( E )$, lies on the plane $2 x+y+z=1$, then the value of $7 a+b+c$ is

$(A)$ $0$ $(B)$ $12$ $(C)$ $7$ $(D)$ $6$

$2.$ Let $\omega$ be a solution of $x^3-1=0$ with $\operatorname{Im}(\omega)>0$. If $a=2$ with $b$ and $c$ satisfying $( E )$, then the value of $\frac{3}{\omega^a}+\frac{1}{\omega^b}+\frac{3}{\omega^c}$ is equal to

$(A)$ $-2$ $(B)$ $2$ $(C)$ $3$ $(D)$ $-3$

$3.$ Let $b=6$, with $a$ and $c$ satisfying (E). If $\alpha$ and $\beta$ are the roots of the quadratic equation $a x^2+b x+c=0$, then

$\sum_{n=0}^{\infty}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)^n$ is

$(A)$ $6$ $(B)$ $7$ $(C)$ $\frac{6}{7}$ $(D)$ $\infty$

Give the answer question $1,2$ and $3.$

→

If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then :

→

Namita walks $14$ metres towards west, then turns to her right and walks $14$ metres and then turns to her left and walks $10$ metres. Again turning to her left she walks $14$ metres.What is the shortest distance $($in metres$)$ between her starting point and the present position?

→

$\int \frac{d x}{x\left(x^{2}+1\right)}$ equals

→