  In this work, we study the inflationary cosmology in modified gravity theory
$f(R, T) = R + 2 \lambda T$ ($\lambda$ is the modified gravity parameter) with
three distinct class of inflation potentials (i) $\phi^p e^{-\alpha\phi}$, (ii)
$(1-\phi^p)e^{-\alpha\phi}$ and (iii) $\frac{\alpha\phi^2}{1+\alpha\phi^2}$
where $\alpha$, $p$ are the potential parameters. We have derived the Einstein
equation, potential slow-roll parameters, the scalar spectral index $n_s$,
tensor to scalar ratio $r$, and tensor spectral index $n_T$ in modified gravity
theory. We obtain the range of $\lambda$ using the spectral index constraints
in the parameter space of the potentials. Comparing our results with PLANCK
2018 data and WMAP data, we found out the modified gravity parameter $\lambda$
lies between $-0.37<\lambda<1.483$.
