$AB_{3(g)}$ dissociates as $AB_{3(g)} \rightleftharpoons AB_{2(g)} + \frac{1}{2}B_{2(g)}$. When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated (in $\%$)?

Fungi are filamentous with the exception of $X$ which is unicellular. Identify $X$.

Many ionic crystals dissolve in water because

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k=$

Let $\overline{a}=\hat{i}+\hat{j}+\hat{k}$,$\overline{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\overline{v}$ in the plane of $\overline{a}$ and $\overline{b}$,whose projection on $\overline{c}$ is $\frac{1}{\sqrt{3}}$,is given by

Assertion : $Pb^{4+}$ compounds are stronger oxidizing agents than $Sn^{4+}$ compounds.
Reason : The higher oxidation states for the group $14$ elements are more stable for the heavier members of the group due to 'inert pair effect'.