The dipole moment is a measure of the separation of positive and negative charges in a molecule. Molecules with polar bonds and an asymmetrical shape often exhibit a dipole moment. The greater the electronegativity difference between atoms and the asymmetry in the molecule, the higher the dipole moment.
\( \text{NF}_3 \): Although nitrogen and fluorine have a large electronegativity difference, the structure of \( \text{NF}_3 \) (trigonal pyramidal) leads to a partial cancellation of the dipole moment due to the lone pair on nitrogen. The net dipole moment of \( \text{NF}_3 \) is lower than that of \( \text{NH}_3 \).
\( \text{CH}_4 \): Methane (\( \text{CH}_4 \)) is a nonpolar molecule with a tetrahedral structure. The dipole moments of the C-H bonds cancel each other out, resulting in a net dipole moment of zero.
\( \text{NH}_3 \): Ammonia has a trigonal pyramidal structure with a lone pair of electrons on nitrogen. This creates an asymmetrical distribution of charge and a significant net dipole moment. The lone pair on nitrogen intensifies the dipole moment, making \( \text{NH}_3 \) have a higher dipole moment compared to \( \text{NF}_3 \).
\( \text{PF}_5 \): Phosphorus pentafluoride has a trigonal bipyramidal structure, with dipole moments of the axial and equatorial bonds cancelling out. As a result, \( \text{PF}_5 \) is a nonpolar molecule with a net dipole moment of zero.
Among the given molecules, \( \text{NH}_3 \) has the maximum dipole moment due to its trigonal pyramidal structure and the presence of a lone pair on nitrogen, which increases its net dipole moment.
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: