Which kingdoms include decomposers?

Cerium $(Z = 58)$ is an important member of the lanthanoids. Which of the following statements is $NOT$ correct for Cerium?

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$

The extreme values of $4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)$ over $\mathbb{R}$ are