Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If  $f(x) = \left\{ \begin{array}{l}\frac{5}{2} - x\,,\,{\rm{when\,\,}}\,x < 2\\\,\,\,1\,\,\,\,\,\,,\,{\rm{when \,\,}}x = 2\\x - \frac{3}{2},{\rm{when\,\,}}\,x > 2\end{array} \right.$, then
  • A
    $f(x)$ is continuous at $x = 2$
  • B
    $f(x)$ is discontinuous at $x = 2$
  • C
    $\mathop {\lim }\limits_{x \to 2} f(x) = 1$
  • D
    None of these
✓

Answer

$\mathop {\lim }\limits_{x \to 2 - } f(x) = \frac{1}{2}$ and
$\mathop {\lim }\limits_{x \to 2 + } f(x) = \frac{1}{2}$ and $f(2) = 1.$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A =\{2,3,6,8,9,11\}$ and $B =\{1,4,5,10,15\}$ Let $R$ be a relation on $A \times B$ define by $( a , b ) R ( c , d )$ if and only if $3 ad -7 bc$ is an even integer. Then the relation $R$ is
→
Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is
→
If $5{x^2} + \lambda {y^2} = 20$ represents a rectangular hyperbola, then $\lambda $ equals
→
If $2p$ is the length of perpendicular from the origin to the lines $\frac{x}{a} + \frac{y}{b} = 1$, then ${a^2},8{p^2},{b^2}$are in
→
Let $[x]$ be the greatest integer less than or equals to $x$. Then, at which of the following point($s$) the function $f(x)=x \cos (\pi(x+[x]))$ is discontinuous?

$[A]$ $x=-1$  $[B]$ $x=0$  $[C]$ $x=2$   $[D] x=1$

→
Let $z$ =${i^{2i}}$ , then $|z|$ is (where $i$ =$\sqrt { - 1}$ )
→
Given that ${d \over {dx}}f(x) = f\,'(x)$. The relationship $f\,'(a + b) = f\,'(a) + f\,'(b)$ is valid if $f(x)$ is equal to
→
The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies
→
The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$, the other two observations are
→
For a differentiable function $\mathrm{f}: I R \rightarrow I R$, suppose $f^{\prime}(\mathrm{x})=3 f(\mathrm{x})+\alpha$, where $\alpha \in \operatorname{IR}, f(0)=1$ and $\lim _{x \rightarrow-\infty} f(x)=7$. Then $9 \mathrm{f}\left(-\log _{\mathrm{e}} 3\right)$ is equal to ............
→