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).
Resonance in X$_2$Y can be represented as 
The enthalpy of formation of X$_2$Y is 80 kJ mol$^{-1}$, and the magnitude of resonance energy of X$_2$Y is:
Given below are two statements :
Statement I : Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes.
Statement II : Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes.
In the light of the above statements, choose the Correct answer from the options given below
Match the LIST-I with LIST-II
| LIST-I | LIST-II |
| A. PF5 | I. dsp2 |
| B. SF6 | II. sp3d |
| C. Ni(CO)4 | III. sp3d2 |
| D. [PtCl4]2- | IV. sp3 |
Choose the correct answer from the options given below:
Given below are two statements:
Statement I : The N-N single bond is weaker and longer than that of P-P single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of above statements, choose the correct answer from the options given below

Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.
If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is: