  The dominant source of radio continuum emissions at low frequencies is
synchrotron radiation, which originates from star-forming regions in disk
galaxies and from powerful jets produced by active galactic nuclei (AGN). We
studied the Bootes field using the upgraded Giant Meterwave Radio Telescope
(uGMRT) at 400 MHz, achieving a central minimum off-source RMS noise of
35$\mu$Jy beam$^{-1}$ and a catalogue of 3782 sources in $\sim6$ sq. degrees of
the sky. The resulting catalogue was compared to other radio frequency
catalogues, and the corrected normalised differential source counts were
derived. We use standard multi-wavelength techniques to classify the sources in
star-forming galaxies (SFGs), radio-loud (RL) AGN, and radio-quiet (RQ) AGN
that confirm a boost in the SFGs and RQ\,AGN AGN populations at lower flux
levels. For the first time, we investigated the properties of the radio--IR
relations at 400\,MHz in this field. The $L_{\rm 400 MHz}$--$L_{\rm TIR}$
relations for SFGs were found to show a strong correlation with non-linear
slope values of $1.10\pm0.01$, and variation of $q_{\rm TIR}$ with $z$ is given
as, $q_{\rm TIR} = (2.19 \pm 0.07)\ (1+z)^{-0.15 \pm 0.08}$. This indicates
that the non-linearity of the radio--IR relations can be attributed to the mild
variation of $q_{\rm TIR}$ values with $z$. The derived relationships exhibit
similar behaviour when applied to LOFAR at 150 MHz and also at 1.4 GHz. This
emphasises the fact that other parameters like magnetic field evolution with
$z$ or the number densities of cosmic ray electrons can play a vital role in
the mild evolution of $q$ values.
