Download App

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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
For the function $f(x) = \left\{ \begin{array}{l}\frac{{{{\sin }^2}ax}}{{{x^2}}},\,{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = 0\end{array} \right.$ which one is a true statement
  • A
    $f(x)$ is continuous at $x = 0$
  • ✓
    $f(x)$ is discontinuous at $x = 0$, when $a \ne \pm 1$
  • C
    $f(x)$ is continuous at $x = a$
  • D
    None of these
✓

Answer

Correct option: B.
$f(x)$ is discontinuous at $x = 0$, when $a \ne \pm 1$
b
(b) $\mathop {\lim }\limits_{x \to 0} f(x) = \frac{{{{\sin }^2}ax}}{{{{(ax)}^2}}}{a^2} = {a^2}$ and $f(0) = 1.$

Hence $f(x)$ is discontinuous at $x = 0$, when $a \ne 0$.

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 eqution of the plane contaning the two lines $\frac{\text{x}-1}{2}=\frac{\text{y}+1}{-1}=\frac{\text{z}-0}{3}$ and $\frac{\text{x}}{-2}=\frac{\text{y}-2}{-3}=\frac{\text{z}+1}{-1}$ is:
→
If the lines $\frac{{x - 1}}{{ - 3}} = \frac{{y - 2}}{{2k}} = \frac{{z - 3}}{2}$, $\frac{{x - 1}}{{3k}} = \frac{{y - 5}}{1} = \frac{{z - 6}}{{ - 5}}$ are at right angles, then $k =$
→
A contest consists of predicting the results win, draw or defeat of $7$ football matches. $A$ sent his entry by predicting at random. The probability that his entry will contain exactly $4$ correct predictions is
→
$\int\limits^{2\text{a}}_0\text{f}(\text{x})\text{dx}$ is equal to:
  1. $2\int\limits^{\text{a}}_0\text{f(x)}\text{dx}$
  2. $0$
  3. $\int\limits^{\text{a}}_0\text{f}(\text{x})\text{dx}+\int\limits^{\text{a}}_0\text{f}(2\text{a}-\text{x})\text{dx}$
  4. $\int\limits^{\text{a}}_0\text{f}(\text{x})\text{dx}+\int\limits^{2\text{a}}_0\text{f}(2\text{a}-\text{x})\text{dx}$
→
If $\cos^{-1}\text{x}+\sin^{-1}\text{x}=\pi,$ then the value of x is:
  1. $\frac{3}{2}$
  2. $\frac{1}{\sqrt{2}}$
  3. $\frac{\sqrt{3}}{2}$
  4. $\frac{2}{\sqrt{3}}$
→
The value of $\int\frac{\cos2\text{x}}{{\cos}{\text{ x}}}\text{dx}$ is equal to:
  1. $2\sin\text{x}-\ell\text{ n }\mid\sec\text{x}+\tan\text{x}\mid+\text{ c}$
  2. $2\sin\text{x}-\ell\text{ n }\mid\sec\text{x}-\tan\text{x}\mid+\text{ c}$
  3. $2\sin\text{x}+\ell\text{ n }\mid\sec\text{x}+\tan\text{x}\mid+\text{ c}$
  4. $3\sin\text{x}-\ell\text{ n }\mid\sec\text{x}+\tan\text{x}\mid+\text{ c}$
→
If f(x) defind by $\text{f(x)}=\begin{cases}\frac{|\text{x}^2-\text{x}|}{\text{x}^2-\text{x}},&\text{x}\neq0,1\\1,&\text{x}=0\\-1,&\text{x}=1\end{cases}$ then f(x) is continuse for all:
  1. x
  2. x except at x = 0
  3. x except at x = 1
  4.  x except at x = 0 and x = 1
→

A coin is tossed 10 times. The probability of getting exactly six heads is:

  1. $\frac{512}{513}$

  2. $\frac{105}{512}$

  3. $\frac{100}{153}$

  4. $\text{ }^{10}\text{C}_6$

→
If $|a\,.\,b|\, = 3$ and $|a \times b|\, = 4,$ then the angle between $a $ and $ b$  is
→
The degree of the differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{3}}}=0$   is
→