Download App

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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
The function defined by $f(x) = \left\{ \begin{array}{l}|x - 3|\,;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \ge 1\\\frac{1}{4}{x^2} - \frac{3}{2}x + \frac{{13}}{4};\,x < 1\end{array} \right.$ is
  • A
    Continuous at $x = 1$
  • B
    Continuous at $x = 3$
  • C
    Differentiable at $x = 1$
  • ✓
    All the above
✓

Answer

Correct option: D.
All the above
d
(d) Since $|x - 3|\, = x - 3,$ if $x \ge 3$$ = - x + 3,$ if $x < 3$

$\therefore $ The given function can be defined as

$f(x) = \left\{ {\begin{array}{*{20}{r}}{\frac{1}{4}{x^2} - \frac{3}{2}x + \frac{{13}}{4},}&{x < 1\,\,\,\,\,\,\,\,}\\{3 - x,}&{1 \le x < 3}\\{x - 3,}&{x \ge 3\,\,\,\,\,\,\,}\end{array}} \right.$

Now proceed to check the continuity and differentiability 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

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

If $a = i + 2j + 3k,\,\,\,b = - i + 2j + k$ and $c = 3i + j,$ then the unit vector along its resultant is
→
$\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x$ is equal to
→
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to
→
Two squares are chosen at random on a chess-board. The probability that they have a side in common, is
→
Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be defined as

$f(x+y)+f(x-y)=2 f(x) f(y), f\left(\frac{1}{2}\right)=-1 .$ Then, the value of $\sum_{\mathrm{k}=1}^{20} \frac{1}{\sin (\mathrm{k}) \sin (\mathrm{k}+\mathrm{f}(\mathrm{k}))}$ is equal to:

→
The line $y = mx$ bisects the area enclosed by the curve $y = 1 + 4x - x^2\,\, \&$ the lines $x = 0, x = \frac{3}{2} \& \,\,y = 0.$ Then the value of $m$ is:
→
The inverse of $\left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&2\end{array}} \right]$is
→
Read the following mathematical statements carefully :

$I.$ Adifferentiable function $' f '$ with maximum at $x = c$ ==> $ f "(c) < 0$.

$II.$ Antiderivative of a periodic function is also a periodic function.

$III.$ If $f$ has a period $T$ then for any $a \in R$. $\int\limits_0^T {f(x)\,dx} = \int\limits_0^T {f(x + a)\,dx} $

$IV.$ If $f (x)$ has a maxima at $x = c$ , then $'f '$ is increasing in $(c - h, c)$ and decreasing in $(c, c + h)$ as $h \rightarrow 0$ for $h > 0.$ Now indicate the correct alternative.

→
$\int\frac{\text{dx}}{1+\text{cos x}}=$
  1. $\tan\frac{\text{x}}{2}+\text{k}$
  2. $\frac{1}{2}\tan\frac{\text{x}}{2}+\text{k}$
  3. $2\tan\frac{\text{x}}{2}+\text{k}$
  4. $\tan^2\frac{\text{x}}{2}+\text{k}$
→
If $f(x) = 3x + 10$, $g(x) = {x^2} - 1$, then ${(fog)^{ - 1}}$ is equal to
→