The conductance of a $$0.0015$$ $$M$$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $$Pt$$ electrodes. The distance between the electrodes is $$120$$ $$cm$$ with an area of cross section of $$1$$ $$c{m^2}.$$ The conductance of this solution was found to be $$5 \times {10^{ - 7}}S.$$ The $$pH$$ of the solution is $$4.$$ The value of limiting molar conductivity $$\left( {\Lambda _m^o} \right)$$ of this weak monobasic acid in aqueous solution is $$Z \times {10^2}S$$ $$c{m^2}$$ $$mo{l^{ - 1}}.$$ The value of $$Z$$ is

A crystalline solid of a pure substance has a face-centered cubic structure with a cell edge of $$400$$ $$pm.$$ If the density of the substance in the crystal is $$8$$ $$g\,c{m^{ - 3}},$$ then the number of atoms present in $$256$$ $$g$$ of the crystal is $$N \times {10^{24}}.$$ The value of $$N$$ is

The sum of the number of lone pairs of electrons on each central atom in the following species is

$${[TeB{r_6}]^{2 - }},{\left[ {Br{F_2}} \right]^ + },SNF_3,$$ and $${\left[ {Xe{F_3}} \right]^ - }$$

(Atomic numbers: $$N = 7,F = 9,$$ $$S = 16,Br = 35,$$ $$Te = 52,Xe = 54$$)

Among $${H_2},H{e_2}^ + ,L{i_2},$$ $$B{e_2},{B_2},{C_2},{N_2},O_2^ - $$ and $${F_2},$$ the number of diamagnetic species is

(Atomic numbers : $$H = 1,He = 2,$$ $$Li = 3,Be = 4,$$ $$B = 5,C = 6,$$ $$N = 7,$$ $$O = 8,F = 9$$)