Download App

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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}\frac{{\sin 2x}}{{5x}},{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,k,{\rm{when \,\,}}x = 0\end{array} \right.$ is continuous at $x = 0$, then the value of  $ k $ will be
  • A
    $1$
  • ✓
    $\frac{2}{5}$
  • C
    $ - \frac{2}{5}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{2}{5}$
b
(b) $\mathop {\lim }\limits_{x \to 0} \,f(x) = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{2\,\,\sin \,2x}}{{2x\,.\,5}} = \frac{2}{5} = k.$

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

$\int_{}^{} {{{\tan }^3}} 2x\sec 2x\;dx = $
→
If the co-ordinates of the points $P,\,Q,R,\,S$ be $(1, 2, 3), (4, 5, 7), (-4, 3, -6)$ and $(2, 0, 2)$ respectively, then
→
The vector equation of the plane containing the line $\vec{\text{r}}=(-2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}})+\lambda(3\hat{\text{i}}-2\hat{\text{j}}-\hat{\text{k}})$ and the point $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ is:
  1. $\vec{\text{r}}.(\hat{\text{i}}+3\hat{\text{k}})=10$
  2. $\vec{\text{r}}.(\hat{\text{i}}-3\hat{\text{k}})=10$
  3. $\vec{\text{r}}.(3\hat{\text{i}}+\hat{\text{k}})=10$
  4. $\text{None of these}$
→

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p.q > 0.

Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:

  1. P = q
  2. p = 2q
  3. p = 3q
  4. q = 3q
→
If $A = \left[ {\begin{array}{*{20}{c}}1&2&{ - 1}\\3&0&{\,\,2}\\4&5&{\,\,0}\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}1&0&0\\2&1&0\\0&1&3\end{array}} \right],$then $AB$ is
→
If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A,$ then ${A^2} + {B^2} = $
→
The differential equation  $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\frac{\text{dy}}{\text{dx}}+\text{y}+\text{x}^2=0$ of the following type:
  1. linear
  2. homogeneous
  3. order two
  4. degree one
→
$\int {\frac{{{{\sin }^{ - 1}}x - {{\cos }^{ - 1}}x}}{{{{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x}}} dx = $
→
Let $g$ is the inverse function of $f \,\&\, f ' (x) = \frac{{{x^{10}}}}{{\left( {1\,\, + \,\,{x^2}} \right)}}$. If $g(2) = a$ then $g ' (2)$ is equal to
→
If P(x, y, z) moves such that x = 0, z = 0 then the locus of P is the line whose d.cs are:
  1. y-axis
  2. 1, 0, 0
  3. 0, 1, 0
  4. 0, 0, 0
→