Download App

Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f(x)=\left\{\begin{array}{l}\frac{5}{2}-x, \text { when } x<2 \\ 1, \text { when } x=2 \\ x-\frac{3}{2}, \text { when } x>2\end{array}\right.$, then
  • A
    $f (x)$ is continuous at $x=2$
  • ✓
    $f (x)$ is discontinuous at $x=2$
  • C
    $\lim _{x \rightarrow 2} f (x)=1$
  • D
    none of these
✓

Answer

Correct option: B.
$f (x)$ is discontinuous at $x=2$
(B)
$\lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2}\left(\frac{5}{2}-x\right)=\frac{1}{2}$
$\lim _{x \rightarrow 2^{+}} f (x)=\lim _{x \rightarrow 2}\left(x-\frac{3}{2}\right)=\frac{1}{2}$ and $f (2)=1$
$\therefore \quad \lim _{x \rightarrow 2^{-}} f (x)=\lim _{x \rightarrow 2^{+}} f (x) \neq f (2)$
$\therefore f (x)$ is discontinuous at $x=2$.

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 "MCQ" from Continuity→Continuity — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$f: R \rightarrow R, f(x)=x^2+3 x+4$ is __________
→
Let $z_1$ be a complex number with $\left|z_1\right|=1$ and $z_2$ be any complex number, then $\left|\frac{z_1-z_2}{1-z_1 \bar{z}_2}\right|=$
→
The value of $\lim _{x \rightarrow 0}\left\{\frac{a^x+b^x+c^x}{3}\right\}^{1 / x}$ is
→
B is an extremity of the minor axis of an ellipse whose foci are S and $S ^{\prime}$. If $\angle SBS ^{\prime}$ is a right angle, then the eccentricity of the ellipse is
→
If $f (x)=\frac{1-\sin x}{(\pi-2 x)^2}$, when $x \neq \frac{\pi}{2}$ and $f \left(\frac{\pi}{2}\right)=\lambda$, then $f (x)$ will be continuous function at $x=\frac{\pi}{2}$, when $\lambda=$
→
The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$ are :
→
The equation of the ellipse whose centre is (2, -3), one of the foci is (3, -3) and the corresponding vertex is (4, -3), is
→
$\lim _{x \rightarrow 0}\left(\frac{3+5 x}{3-4 x}\right)^{\frac{1}{x}}=$
→
The vertices of a triangle are $(6, 0), (0, 6)$ and $(6, 6)$. The distance between its circumcentre and centroid is :
→
If $z=\frac{\sqrt{3}+i}{2}$, then $z^{69}$ is equal to
→