If the function f(x)= cc 3 x-8, & if x 5 2 k, & if x>5 . is conti… - Vidyadip

MCQ

If the function $f(x)=\left\{\begin{array}{cc}3 x-8, & \text { if } x \leq 5 \\ 2 k, & \text { if } x>5\end{array}\right.$ is continuous, then the value of $k$ is

A
$2 / 7$
✓
$7 / 2$
C
$3 / 7$
D
$4 / 7$

✓

Answer

Correct option: B.

$7 / 2$

$\text { : Since } f(x) \text { is continuous at } x=5 \text {, }$
$\Rightarrow \lim _{x \rightarrow 5} f(x)=\lim _{x \rightarrow 5^{+}} f(x)=f(5)$
$\Rightarrow 3(5)-8=2 k$
$\Rightarrow 7=2 k$
$\Rightarrow k=\frac{7}{2}$

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 Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\Omega$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either $0$ or $1$ . Five of these entries are $1$ and four of them are $0$ .

$1.$ The number of matrices in $\Omega$ is

$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$

$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations

$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is

$(A)$ less than $4$

$(B)$ at least $4$ but less than $7$

$(C)$ at least $7$ but less than $10$

$(D)$ at least $10$

$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations

$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is

$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$

What is the value of $\int\limits_{-1}^{1} \sin^3\text{x}\cos^2\text{x dx} :$

The antiderivative of every odd function is :

Let $f:[0,4 \pi] \rightarrow[0, \pi]$ be defined by $f(x)=\cos ^{-1}(\cos x)$. The number of points $x \in[0,4 \pi]$ satisfying the equation $f(x)=\frac{10-x}{10}$ is

If $\text{x }\in\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big),$ then the value of $\tan^{-1}\Big(\frac{\tan\text{x}}{4}\Big)+\tan^{-1}\Big(\frac{3\sin2\text{x}}{5+3\cos2\text{x}}\Big)$ is:

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?

The set of equations $x - y + 3z = 2 , 2x - y + z = 4 , x - 2y + \alpha z = 3$ has

$f(x) = \left| {\begin{array}{*{20}{c}}
{{x^3}}&{{x^2}}&{3{x^2}}\\
1&{ - 6}&4\\
p&{{p^2}}&{{p^3}}
\end{array}} \right|$ , here $ p $ is a constant, then ${{{d^3}f(x)} \over {d{x^3}}}$ is

if $x$ lies in the interval $[0,1]$, then the least value of $x^2+x+1$ is :

The value of the integral $\int\limits^\infty_0\frac{\text{x}}{(1+\text{x})(1+\text{x}^2)}\text{dx}$ is: