  We study the connection between the variations in the far ultra-violet (FUV),
near ultra-violet (NUV) and X-ray band emission from NGC 4051 using 4-days long
AstroSat observations performed during 5-9 June 2016. NGC 4051 showed rapid
variability in all three bands with the strongest variability amplitude in the
X-ray band ($F_{var} \sim 37\%$) and much weaker variability in the UV bands
($F_{var} \sim 3 - 5\%$). Cross-correlation analysis performed using
Interpolated cross-correlation Functions (ICCF) and Discrete cross-correlation
Functions (DCF) revealed a robust correlation ($\sim 0.75$) between the UV and
X-ray light curves. The variations in the X-ray band are found to lead those in
the FUV and NUV bands by $\sim 7.4{\rm~ks}$ and $\sim 24.2{\rm~ks}$,
respectively. The UV lags favour the thermal disc reprocessing model. The FUV
and NUV bands are strongly correlated ($\sim 0.9$) and the variations in the
FUV band lead those in the NUV band by $\sim 13{\rm~ks}$. Comparison of the UV
lags found using the AstroSat observations with those reported earlier and the
theoretical model for thermal reverberation time-lag suggests a possible change
in either the geometry of the accretion disc/corona or the height of the
corona.
