In the present paper, we have reported the result of simultaneous multi-wavelength observations of the TeV blazar Mrk 421 during February $-$ March 2003. In this period, we have observed Mrk 421 using Pachmarhi Array of v{C}erenkov Telescopes (PACT) of Tata Institute of Fundamental Research at Pachmarhi, India. Other simultaneous data were taken from the published literature and public data archives. We have analyzed the high quality X-ray (2-20 keV) observations from the NASA Rossi X-Ray Timing Explorer (RXTE). We have seen a possible correlated variability between X-ray and J band (1.25 $mu$) near infrared (NIR) wavelength. This is the first case of X-ray and NIR correlated variability in Mrk 421 or any high energy peaked (HBL) blazar. The correlated variability reported here is indicating a similar origin for NIR and X-ray emission. The emission is not affected much by the environment of the surrounding medium around the central engine of the Mrk 421. The observations are consistent with the shock-in-jet model for the emission of radiations.
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