  The remarkable progress in cosmic microwave background (CMB) studies over
past decade has led to the era of precision cosmology in striking agreement
with the $\Lambda$CDM model. However, the lack of power in the CMB temperature
anisotropies at large angular scales (low-$\ell$), as has been confirmed by the
recent Planck data also (up to $\ell=40$), although statistically not very
strong (less than $3\sigma$), is still an open problem. One can avoid to seek
an explanation for this problem by attributing the lack of power to cosmic
variance orcan look for explanations i.e., different inflationary potentials or
initial conditions for infl ation to begin with, non-trivial topology, ISW
effect etc. Features in the primordial power spectrum (PPS) motivated by the
early universe physics has been the most common solution to address this
problem. In the present work we also follow this approach and consider a set of
PPS which have features and constrain the parameters of those using WMAP 9 year
and Planck data employing Markov-Chain Monte Carlo (MCMC) analysis. The
prominent feature of all the models of PPS that we consider is an infra-red cut
off which leads to suppression of power at large angular scales. We consider
models of PPS with maximum three extra parameters and use Akaike information
criterion ($AIC$) and Bayesian information criterion ($BIC$) of model and
Bayesian information criterion ($BIC$) of model selection to compare the
models. For most models, we find good constraints for the cut off scale $k_c$,
however, for other parameters our constraints are not that good. We find that
sharp cut off model gives best likelihood value for the WMAP 9 year data, but
is as good as power law model according to $AIC$. For the joint WMAP 9+Planck
data set, Starobinsky model is slightly preferred by $AIC$ which is also able
to produce CMB power suppression up to $\ell\leq30$ to some extent.
