Which of the following is a latex-based alkaloid?

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centered cubic,and face-centered cubic,then the ratio of radii of the spheres in these systems will be respectively:

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is:

If $l_1 = \lim_{x \rightarrow 2^{+}} (x + [x])$,$l_2 = \lim_{x \rightarrow 2^{-}} (2x - [x])$ and $l_3 = \lim_{x \rightarrow \pi / 2} \frac{\cos x}{x - \pi / 2}$,then:

Consider the following statements regarding Werner's theory of coordination compounds:
$(1)$ Ligands are connected to the metal ions by coordinate bonds (dative bonds).
$(2)$ Secondary valencies have directional properties.
$(3)$ Secondary valencies are non-ionisable.
Which of these statements are correct?

Assign $A, B, C, D$ from the given type of reaction.
$HgI_2 \downarrow + 2KI \rightleftharpoons K_2[HgI_4]$