Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. 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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The function $f(x)=x^3+3 x$ is increasing in interval
→
Objective of linear programming for an objective function is to:
  1. Maximize or minimize.
  2. Subset or proper set modeling.
  3. Row or column modeling.
  4. Adjacent modeling.
→
If $A = \left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,B = \left| {\,\begin{array}{*{20}{c}}1&1&1\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,C = \left| {\,\begin{array}{*{20}{c}}a&b&c\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,$ then which relation is correct
→
Derivative of $e^{\sin ^2 x}$ with respect to $\cos x$ is
→
Angle between vectors $\bar{a}=6 \hat{i}+2 \hat{j}-8 \hat{k}$ and $\bar{b}=4 \hat{i}-4 \hat{j}+2 \hat{k}$ is ___________ .
→
find the coordinate of the tip of the position vector which is equivalent to $\overrightarrow{\text{AB}}$ where the coordinates of A and B are (-1, 3) and (-2, 1) respectively:
  1. (+1, +2)
  2. (+1, -2)
  3. (-1, +2)
  4. (-1, -2)
→
If $A = \int\limits_1^{\sin \theta } {\frac{t}{{1 + {t^2}}}} dt$ and $B = \int\limits_1^{\cos ec\theta } {\frac{dt}{{t\left( {1 + {t^2}} \right)}}} $ , (where $\theta  \in \left( {0,\frac{\pi }{2}} \right))$, then the-value of $\left| {\begin{array}{*{20}{c}}
A&{{A^2}}&{ - B}\\
{{e^{A + B}}}&{{B^2}}&{ - 1}\\
1&{{A^2} + {B^2}}&{ - 1}
\end{array}} \right|$ is
→
If $\text{y}=\text{a}\sin\text{mx}+\text{b}\cos\text{mx},$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is equal to:
  1. -m2y
  2. m2y
  3. -my
  4. my
→
If $f(x)=\left\{\begin{array}{l}\frac{k x}{|x|} \text {, if } x<0 \\ 3, \text { if } x \geq 0\end{array}\right.$ is continuous at $x=0$, then the value of $k$ is
→
If a matrix  $A$  is such that $3{A^3} + 2{A^2} + 5A + I = 0,$ then its inverse is
→