Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
If$f(x) = \left\{ \begin{array}{l}\frac{{|x - a|}}{{x - a}},{\rm{when\,\,}}\,x \ne a\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = a\end{array} \right.$,then
  • A
    $f(x)$ is continuous at $x = a$
  • ✓
    $f(x)$ is discontinuous at $x = a$
  • C
    $\mathop {\lim }\limits_{x \to a} f(x) = 1$
  • D
    None of these
✓

Answer

Correct option: B.
$f(x)$ is discontinuous at $x = a$
b
(b) $\mathop {\lim }\limits_{x \to a - } f(x) = - 1,\,\mathop {\lim }\limits_{x \to a + } f(x) = 1,\,\,f(a) = 1.$

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

Let $A = \left( {\begin{array}{*{20}{c}}0&0&{ - 1}\\0&{ - 1}&0\\{ - 1}&0&0\end{array}} \right)$, the only correct statement about the matrix $A$ is
→
The true solution set of the inequality,

$\sqrt {5\,x\,\, - \,\,6\,\, - \,\,{x^2}} \,\, + \,\,\frac{\pi }{2}\,\,\int\limits_0^x {} $$dz > x \int\limits_0^\pi  {} sin^2 x \,dx$ is :

→
$\smallint \left( {1 + x - \frac{1}{x}} \right){e^{x + \frac{1}{x}}}\;dx = $
→
If $x$ is real$,$ the minimum value of $x^2 - 8x + 17$ is:
→
If $f(y) = {e^y},\,g(y) = y;\,y > 0$ and $F(t) = \int_{\,0}^{\,t} {\,f(t - y)\,g(y)\,dy,} $ then
→
The value of the integral $\int_{-1}^{1} \log \left(x+\sqrt{x^{2}+1}\right)\, d x$ is:
→
A random variable $X$ has the following probability distribution :
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X)$ $a$ $6 a$ $6 a$ $4 a$ $8 a$ $8 a$ $6 a$ $9 a$
Find the value of $a$.
→
$\frac{d}{{dx}}\left( {{e^{\sqrt {1 - {x^2}} }}.\tan x} \right)$
→
Choose the correct answer from given four options in each of the Exercise: The area of a triangle with vertices $(-3, 0), (3, 0) $ and $(0, k)$ is $\text{9 sq. units}.$ The value of $k$ will be:
→
Choose the correct answer from the given four options.If $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\cot^{-1}(\pi\text{x})\end{bmatrix}$ and $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\tan^{-1}(\pi\text{x})\end{bmatrix}$ then A - B is:
→