Which of the following function$(s)$ not defined at $x = 0$ has/have an irremovable discontinuity at $x = 0$?

If the function $f(x) = \begin{cases} (1+|\cos x|)^{\frac{\lambda}{|\cos x|}} & , 0 < x < \frac{\pi}{2} \\ \mu & , x = \frac{\pi}{2} \\ e^{\frac{\cot 6x}{\cot 4x}} & , \frac{\pi}{2} < x < \pi \end{cases}$ is continuous at $x = \frac{\pi}{2}$,then $9\lambda + 6 \log_{e} \mu + \mu^6 - e^{6\lambda}$ is equal to

Let $[t]$ denote the greatest integer $\leq t$ and $\lim_{x \to 0} x[\frac{4}{x}] = A$. Then the function $f(x) = [x^2] \sin(\pi x)$ is discontinuous when $x$ is equal to

If $f(x) = \frac{1+\cos \pi x}{\pi(1-x)^2}$ for $x \neq 1$ is continuous at $x=1$,then $f(1)$ is equal to

If $f(x) = \log(\sec^2 x)^{\cot^2 x}$ for $x \neq 0$ and $f(x) = K+1$ for $x=0$ is continuous at $x=0$,then the value of $K$ is

If $[x]$ denotes the greatest integer not exceeding the number $x$,then $f(x)$ defined by $f(x) = \begin{cases} [x], & \text{if } x < 2 \\ [x]-1, & \text{if } x \geq 2 \end{cases}$ is continuous in the interval.