  Long wavelength spectral distortions in the Cosmic Microwave Background
arising from the 21-cm transition in neutral Hydrogen are a key probe of Cosmic
Dawn and the Epoch of Reionization. These features may reveal the nature of the
first stars and ultra-faint galaxies that transformed the spin temperature and
ionization state of the primordial gas. SARAS~2 is a spectral radiometer
purposely designed for precision measurement of these monopole or all-sky
global 21-cm spectral distortions. We use 63~hr night time observing of the
radio background in the frequency band 110-200~MHz with the radiometer deployed
at the Timbaktu Collective in Southern India to derive likelihoods for
plausible redshifted 21-cm signals predicted by theoretical models. First light
with SARAS 2 disfavors the class of models that feature weak X-ray heating
(with $f_X \leq 0.1$) and rapid reionization (with peak $\frac{dT_b}{dz} \geq
120~\textrm{mK per unit redshift interval}$ ).
