The molecule in question is N,N-dimethyl pivalamide, represented by the formula $Me_3CC(O)NMe_2$. Its structure is $(CH_3)_3C-C(O)-N(CH_3)_2$. We need to identify the distinct types of protons in this molecule to predict the number of signals in its $^1H$ NMR spectrum.
There are two main types of proton environments in N,N-dimethyl pivalamide:
The tert-butyl group consists of three methyl groups attached to a central carbon atom. The nine protons within these methyl groups are chemically equivalent due to the molecule's symmetry and free rotation around the $C-C$ bonds. These equivalent protons will give rise to a single resonance signal. Since there are no neighboring protons for spin-spin coupling, this signal appears as a singlet.
The two methyl groups attached to the nitrogen atom, $-N(CH_3)_2$, require careful consideration. The amide group ($C(O)-N$) has partial double bond character, which restricts rotation around the $C(O)-N$ bond. At room temperature, this restricted rotation often leads to the two N-methyl groups being in distinct chemical environments.
As a result, the two methyl groups are chemically non-equivalent. Each methyl group will produce its own distinct resonance signal. Each of these signals will consist of 3 protons and will appear as a singlet because there are no adjacent protons to couple with.
The total number of singlet resonances observed in the $^1H$ NMR spectrum is the sum of the singlets from the tert-butyl group and the N,N-dimethyl groups.
Total Singlets = (Singlets from tert-butyl) + (Singlets from N,N-dimethyl)
Total Singlets = $1 + 2 = 3$
Therefore, 3 singlet resonances are observed.
In the $^1H$-NMR spectrum of the following molecule, the signal of proton $H_a$ appears as

The $^1H$ NMR spectrum of the given iridium complex at room temperature gave a single signal at 2.6 ppm, and its $^{31}P$ NMR spectrum gave a single signal at 23.0 ppm. When the spectra were recorded at lower temperatures, both these signals split into a complex pattern. The intra-molecular dynamic processes shown by this molecule are
Compound K displayed a strong band at $1680 \text{ cm}^{-1}$ in its IR spectrum. Its $^1H$-NMR spectral data are as follows: $\delta$ (ppm) 7.30 (d, J = 7.2 Hz, 2H), 6.8 (d, J = 7.2 Hz, 2H), 3.8 (septet, J = 7.0 Hz, 1H), 2.2 (s, 3H), 1.9 (d, J = 7.0 Hz, 6H). The correct structure of compound K is
$^1H$ NMR spectrum of a mixture containing $CH_3Br$ ($x$ mol) and $(CH_3)_3CBr$ ($y$ mol) shows two singlets at 2.7 ppm and 1.8 ppm, with the relative ratio of 3:1 (integration value), respectively. The value of $x/y$ is ____________
(rounded off to the nearest integer)
Consider the following $^1H$-NMR ($400$ MHz, DMSO-$d_6$) data of a compound:
$\delta$ in ppm: $3.85$ (s, $6H$), $6.73$ (t, $J = 2.2$ Hz, $1H$), $7.1$ (d, $J = 2.2$ Hz, $2H$), and $13.05$ (brs, $1H$).
The compound is