Let  $\overrightarrow a = \widehat i - 2\widehat j + 3\widehat k$,   $\overrightarrow b = \widehat i + \widehat j + \widehat k$   and   $\overrightarrow c$   be a vector such that   $\overrightarrow a + \left( {\overrightarrow b \times \overrightarrow c } \right) = \overrightarrow 0$  and   $\overrightarrow b \,.\,\overrightarrow c = 5$. Then the value of   $3\left( {\overrightarrow c \,.\,\overrightarrow a } \right)$ is equal to _________.

Number of ambidentate ligands in a representative metal complex $\left[\mathrm{M}(\mathrm{en})(\mathrm{SCN})_{4}\right]$ is ___________.

$\mathrm{NO}_2$ required for a reaction is produced by decomposition of $\mathrm{N}_2 \mathrm{O}_5$ in as by equation

The disproportionation of $\mathrm{MnO}_{4}^{2-}$ in acidic medium resulted in the formation of two manganese compounds $\mathrm{A}$ and . If the oxidation state of in is smaller than that of A, then the spin-only magnetic moment value of B in BM is __________. (Nearest integer)

The conductivity of a solution of complex with formula $\mathrm{CoCl}_{3}\left(\mathrm{NH}_{3}\right)_{4}$ corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is __________.

Number of complexes which will exhibit synergic bonding amongst, $[Cr{(CO)_6}]$, $[Mn{(CO)_5}]$ and is ___________.

$9.3 \mathrm{~g}$ of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100% yield/conversion) is ________ g. (nearest integer)

Number of ambidentate ligands among the following is _________.

$\mathrm{NO}_2^{-}, \mathrm{SCN}^{-}, \mathrm{C}_2 \mathrm{O}_4^{2-}, \mathrm{NH}_3, \mathrm{CN}^{-}, \mathrm{SO}_4^{2-}, \mathrm{H}_2 \mathrm{O} \text {. }$

The limiting molar conductivities of NaI, NaNO₃ and AgNO₃ are 12.7, 12.0 and 13.3 mS m² mol^$-$1, respectively (all at 25$^\circ$C). The limiting molar conductivity of AgI at this temperature is ____________ mS m² mol.

Reaction of [Co(H₂O)₆]²⁺ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t_2g-orbitals of the product is ___________.

The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is ________ $\times 10^{-2}$.

(Given antilog $0.2006=1.587$)

$\mathrm{X} \mathrm{~g}$ of ethanamine was subjected to reaction with $\mathrm{NaNO}_2 / \mathrm{HCl}$ followed by hydrolysis to liberate and . The generated was completely neutralised by 0.2 moles of is _________ g.

Number of colourless lanthanoid ions among the following is __________.

$\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd}^{3+}, \mathrm{La}^{3+}, \mathrm{Sm}^{3+}$

Number of metal ions characterized by flame test among the following is ________.

$\mathrm{Sr}^{2+}, \mathrm{Ba}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Cu}^{2+}, \mathrm{Zn}^{2+}, \mathrm{Co}^{2+}, \mathrm{Fe}^{2+}$