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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.