The function

It is given that, the function $f(x)=\left\{\begin{array}{ll}\frac{\sin x}{x}+\cos x, & \text { if } x \neq 0 \\ k, & \text { if } x=0\end{array}\right.$ is continuous at $x=0$.

$\therefore f(0)=\lim _{x \rightarrow 0} f(x)$

$\Rightarrow k=\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}+\cos x\right)$

$\Rightarrow k=\lim _{x \rightarrow 0} \frac{\sin x}{x}+\lim _{x \rightarrow 0} \cos x$

$\Rightarrow k=1+1=2$

Thus, the value of k is 2.

Hence, the correct answer is option (b).