The study aims to investigate the observability of pseudoscalar Higgs boson A and neutral heavy CP even Higgs boson H, at different benchmark points, in the framework of type-I 2HDM. The study is done for e-e+\documentclass[12pt]{minimal}
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\begin{document}$$e^{-}e^{+}$$\end{document} collisions at s\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}$$\end{document} = 1000 GeV center of mass energy (c.m.s.), a possible scenario in future lepton collider. The associated production of A and H in e+e-\documentclass[12pt]{minimal}
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\begin{document}$$e+ e-$$\end{document} collisions are investigated in a fully hadronic final state in two different channels. The first one is AH→ZHH→jj¯bb¯bb¯\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{AH} \rightarrow \mathrm{ZHH} \rightarrow j\bar{j} b \bar{b}b\bar{b}$$\end{document}, while the other one is AH→bb¯bb¯\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm{AH} \rightarrow b \bar{b}b\bar{b}$$\end{document}. The observability of neutral heavy Higgs and pseudoscalar Higgs signal is possible within the parameter space (tanβ,mA)\documentclass[12pt]{minimal}
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\begin{document}$$ (\tan \beta , m_{A}) $$\end{document} which satisfies all experimental and theoretical constraints. The CP odd and CP even Higgs bosons in all scenarios are observable when the signal exceeds 5σ\documentclass[12pt]{minimal}
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\begin{document}$$ 5\sigma $$\end{document}, which is the final extracted value of signal significance. The signal significance is calculated at different integrated luminosities. It is concluded from the current analysis that a fully hadronic channel is promising for search and measurement of the neutral Higgs bosons in 2HDM.