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 $f(x) = \left\{ \begin{array}{l}a{x^2} - b,{\rm{ }}0 \le x < 1\\2,\;{\rm{ }}x = 1\\x + 1,{\rm{ 1}} < x \le 2\end{array} \right.$ is continuous at $x = 1$, then the most suitable value of $a, b$ are
  • A
    $a = 2,\;b = 0$
  • B
    $a = 1,\;b = - 1$
  • C
    $a = 4,\;b = 2$
  • D
    All the above
✓

Answer

$\mathop {\lim }\limits_{x \to 1 - } f(x) = a - b,\mathop {\lim }\limits_{x \to 1 + } f(x) = 2 $
$\Rightarrow a - b = 2$
All the given sets of $a, b$ make $f(x)$ continuous at $x=1$.

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

Consider the matrices $A =$ $\left[ {\begin{array}{*{20}{c}}4&6&{ - 1}\\3&0&2\\1&{ - 2}&5\end{array}} \right]$ , $B =$ $\left[ {\begin{array}{*{20}{c}}2&4\\0&1\\{ - 1}&2\end{array}} \right]$ , $C =$ $\left[{\begin{array}{*{20}{c}}3\\1\\2\end{array}} \right]$ . Out of the given matrix products
$(i)$ $(AB)^TC$           $(ii)$ $C^TC(AB)^T$          $(iii)$ $C^TAB$        and       $(iv)$ $A^TABB^TC$
→
Let $A (-1,1), B (3,4)$ and $C (2,0)$ be given three points. $A$ line $y = mx , m > 0$, intersects lines $AC$ and $BC$ at point $P$ and $Q$ respectively. Let $A _{1}$ and $A _{2}$ be the areas of $\Delta ABC$ and $\Delta PQC$ respectively, such that $A _{1}=3 A _{2}$, then the value of $m$ is equal to:
→
If $P = \left[ {\begin{array}{*{20}{c}}1&\alpha &3\\1&3&3\\2&4&4\end{array}} \right]$ is the adjoint of  $3×3 $ matrix $A$  and $ |A|=4$  then $\alpha $ is equal to 
→
$\log ab - \log |b| = $
→
The angle between the straight lines $\frac{{x + 1}}{2} = \frac{{y - 2}}{5} = \frac{{z + 3}}{4}$ and $\frac{{x - 1}}{1} = \frac{{y + 2}}{2} = \frac{{z - 3}}{{ - 3}}$ is ......... $^o$
→
The equation of a circle which touches both axes and the line $3x - 4y + 8 = 0$ and whose centre lies in the third quadrant is
→
Match the integrals in Column $I$ with the values in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$ Column $II$
$(A)$ $\int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}$ $(p)$ $\frac{1}{2} \log \left(\frac{2}{3}\right)$
$(B)$ $\int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}$ $(q)$ $2 \log \left(\frac{2}{3}\right)$
$(C)$ $\int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}$ $(r)$ $\frac{\pi}{3}$
$(D)$ $\int_1^2 \frac{d x}{x \sqrt{x^2-1}}$ $(s)$ $\frac{\pi}{2}$
→
If $\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,$ then $\theta = $
→
A circle with centre $(2,3)$ and radius $4$ intersects the line $x + y =3$ at the points $P$ and $Q$. If the tangents at $P$ and $Q$ intersect at the point $S(\alpha, \beta)$, then $4 \alpha-7 \beta$ is equal to $........$.
→
If $z_1 = 1+2i$ and $z_2 = 3+5i$ , then ${\mathop{\rm Re}\nolimits} \,\left( {\frac{{{{\overline Z }_2}{Z_1}}}{{{Z_2}}}} \right) = $
→