For \( \text{NO}_3^- \):
The structure of \( \text{NO}_3^- \) (nitrate ion) shows that nitrogen is involved in three sigma bonds and has no lone pairs on it.
The hybridization of nitrogen in \( \text{NO}_3^- \) is \( sp^2 \).
For \( \text{BCl}_3 \):
Boron in \( \text{BCl}_3 \) forms three sigma bonds with no lone pairs, resulting in a planar triangular structure.
The hybridization of boron in \( \text{BCl}_3 \) is \( sp^2 \).
For \( \text{ClO}_2^- \):
In \( \text{ClO}_2^- \) (chlorite ion), chlorine has two sigma bonds with oxygen atoms and two lone pairs of electrons.
The hybridization of chlorine in \( \text{ClO}_2^- \) is \( sp^3 \), resulting in a bent or V-shaped geometry.
For \( \text{ClO}_3^- \):
In \( \text{ClO}_3^- \) (chlorate ion), chlorine forms three sigma bonds with oxygen atoms and has one lone pair of electrons.
The hybridization of chlorine in \( \text{ClO}_3^- \) is \( sp^3 \), resulting in a pyramidal structure.
From the analysis above, \( \text{ClO}_2^- \) and \( \text{ClO}_3^- \) have \( sp^3 \) hybridization for the central atom.
The number of molecules/ions in which the central atom is involved in \( sp^3 \) hybridization is 2, corresponding to Option (1).
From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are : 
Compound 'P' undergoes the following sequence of reactions : (i) NH₃ (ii) $\Delta$ $\rightarrow$ Q (i) KOH, Br₂ (ii) CHCl₃, KOH (alc), $\Delta$ $\rightarrow$ NC-CH₃. 'P' is : 

Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.