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.
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 : 

In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.