We report the results of photometric observations of the blazars Mrk 421 and 3C 454.3 designed to search for intraday variability (IDV) and short-term variability (STV). Optical photometric observations were spread over eighteen nights for Mrk 421 and seven nights for 3C 454.3 during our observing run in 2009-2010 at the 1.04 m telescope at ARIES, India. Genuine IDV is found for the source 3C 454.3 but not for Mrk 421. Genuine STV is found for both sources. Mrk 421 was revealed by the MAXI X-ray detector on the International Space Station to be in an exceptionally high flux state in 2010 January - February. We performed a correlation between the X-ray and optical bands to search for time delays and found a weak correlation with higher frequencies leading the lower frequencies by about ten days. The blazar 3C 454.3 was found to be in high flux state in November-December 2009. We performed correlations in optical observations made at three telescopes, along with X-ray data from the MAXI satellite and public release gamma-ray data from the Fermi space telescope. We found strong correlations between the gamma-ray and optical bands at a time lag of about four days but the X-ray flux is not correlated with either. We briefly discuss the possible reasons for the time delays between these bands within the framework of existing models for X-ray and gamma-ray emission mechanisms.
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