If the given function $f(x)$, defined as

$f(x)=\left\{\begin{array}{cl}
5, & \text { if } x \leq 2 \\
a x+b, & \text { if } 2<x<10 \\
21, & \text { if } x ≥ 10
\end{array}\right.$

is continuous, then value of $2 a+b$ is :

5

$f(x)=\left\{\begin{array}{cc}5 & x \leq 2 \\ a x+b & 2<x<10 \\ 21 & x \geq 10\end{array}\right.$

it is continuous 

for x = 2

LHL  =  $\lim\limits_{x \rightarrow 2^{-}} f(x)=5$

RHL = $\lim\limits_{x \rightarrow 2^{+}} f(x)=2 a+b$ so $2 a+b=5$     .......(1)

for x = 10

LHL = $\lim\limits_{x \rightarrow 10^{-}} f(x)=10a+b$

RHL = $\lim\limits_{x \rightarrow 10^{+}} f(x)=21$

$10a+b=21$    ......(2)

so eq (2) - (1)

$\Rightarrow 10 a+b =21 - (2 a+b =5)$

$8a = 16$

a = 2

putting a = 2 in eq (1)

so  2 × 2 + b = 5

b = 5 - 4

b = 1

a = 2, b = 1

2a + b = 2 × 2 + 1 = 4 + 1 = 5