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$f(x) = \left\{ \begin{array}{l}\frac{{|x - a|}}{{x - a}},{\rm{when\,\,}}\,x \ne a\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = a\end{array} \right.,$ then
  • A
    $f(x)$ is continuous at $x = a$
  • B
    $f(x)$ is discontinuous at $x = a$
  • C
    $\mathop {\lim }\limits_{x \to a} f(x) = 1$
  • D
    None of these
✓

Answer

$\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

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

Similar questions

The equation of the chord of contact, if the tangents are drawn from the point $(5, -3)$ to the circle ${x^2} + {y^2} = 10$, is
→
If the shortest distance of the parabola $y^2=4 x$ from document security settings le $x^2+y^2-4 x-16 y+64=0$ is $\mathrm{d}$, then $\mathrm{d}^2$ is equal to :
→
If $x + \frac{1}{x} = 2$, the principal value of ${\sin ^{ - 1}}$ $x$ is
→
The number of direct common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 -8x -8y + 7 = 0$ , is
→
If $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB,$ then $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ =
→
If the circles ${x^2} + {y^2} = {a^2}$and ${x^2} + {y^2} - 2gx + {g^2} - {b^2} = 0$ touch each other externally, then
→
The number of continuous functions $f:[0,1] \rightarrow(-\infty, \infty)$ satisfying the condition $\int \limits_0^1(f(x))^2 dx =2 \int_0^1 f( x ) dx$ is
→
If the sides of a right angled triangle are $\{cos2\alpha + cos2\beta + 2cos(\alpha + \beta )\}$ and $\{sin2\alpha + sin2\beta + 2sin(\alpha + \beta )\}$, then the length of the hypotenuse is :
→
Let $f(x)=x \sin \pi x, x>0$. Then for all natural numbers $n, f^{\prime}(x)$ vanishes at

$(A)$ a unique point in the interval $\left(n, n+\frac{1}{2}\right)$

$(B)$ a unique point in the interval $\left(n+\frac{1}{2}, n+1\right)$

$(C)$ a unique point in the interval $( n , n +1$ )

$(D)$ two points in the interval $( n , n +1)$

→
If $A = \left[ {\begin{array}{*{20}{c}}2&4&5\\4&8&{10}\\{ - 6}&{ - 12}&{ - 15}\end{array}} \right]$. Then rank of $A$ is equal to
→