Vitamin $B_{12}$ contains which of the following metals?

If $f(x) = \left| \begin{array}{ccc} 2 \cos x & 1 & 0 \\ x - \frac{\pi}{2} & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{array} \right|$,then $f^{\prime}(\pi)$ is equal to

$A$ molecule $(X)$ has $(i)$ four sigma bonds formed by the overlap of $sp^2$ and $s$ orbitals,$(ii)$ one sigma bond formed by $sp^2$ and $sp^2$ orbitals,and $(iii)$ one $\pi$ bond formed by $p_z$ and $p_z$ orbitals. Which of the following is $X$?

Which of the following is the closest relative of humans?

Which of the following metal carbonates decomposes upon heating?

The perimeter of a sector is a constant. If its area is to be maximum,the sectorial angle is: