  We present the results of timing and spectral analysis of the HMXB pulsar,
Cen X-3, with the help of observations carried out using the Large Area X-ray
Proportional Counter (LAXPC) on board $\textit{AstroSat}$. As part of our
analysis, we sampled the source properties during 4 different observation
epochs covering two widely different intensity states. We obtain a timing
solution and report precise measurements of the spin and orbital parameters
corresponding to these observational epochs. The pulse profiles during the two
intensity states reveal dramatically varying shapes within a time span of one
month. We report the detection of one of the lowest measured frequencies of
quasi-periodic oscillations (QPO) at 0.026$\pm$0.001 Hz for Cen X-3 during its
low-intensity state. We also find correlated periodic and aperiodic noise
components in the power density spectra. We further carried out a phase
averaged and a pulse phase resolved spectral study, where we find that the best
fit continuum spectrum is well described by an absorbed comptonization model
along with a blackbody. Cen X-3 exhibited the presence of the $\sim$28 keV CRSF
absorption line and a $\sim$6.6 keV Fe emission line in both the intensity
states. Significant variations in the line forming regions and mode of
accretion for Cen X-3 within time spans of a month make Cen X-3 a highly
dynamic persistent binary.
