  We have studied neutral and charged current (anti)neutrino induced $\eta$
production off the free nucleon target at MicroBooNE energies, in the light of
recent results reported by the MicroBooNE collaboration for the total $\eta$
production cross section. This study has been made using a theoretical model in
which the weak hadronic current receives contribution from the nonresonant Born
terms as well as from the resonance excitations. The Born terms are obtained
using the SU(3) symmetric chiral model, used earlier in the study of $K-$meson
production. The contribution from the resonance terms is considered from the
excitation of five nucleon resonances viz. $S_{11}(1535)$, $S_{11}(1650)$,
$P_{11}(1710)$, $P_{11}(1880)$, and $S_{11}(1895)$. To fix the parameters of
the vector current interaction, this model is first used to study the
electromagnetic production of $\eta$ mesons induced by real and virtual
photons, and the theoretical results have been compared with the data from the
MAINZ and JLab experiments. The partially conserved axial-vector current
hypothesis and generalized Goldberger-Treiman relation are used to fix the
parameters of the axial-vector current interaction. The results are presented
for the total cross section for the neutral and charged current induced $\eta$
production, ratio of the cross sections for the charged current to neutral
current, MicroBooNE flux averaged cross section $\langle \sigma \rangle$,
$\left \langle \frac{d\sigma}{dQ^2} \right\rangle$ and $\left\langle
\frac{d\sigma}{dp_\eta} \right\rangle$, which may be useful in the future
analysis of MicroBooNE as well as other accelerator and atmospheric neutrino
experiments being performed in the ${\cal O}$(1)~GeV energy region.
