  Using a theoretical framework based on the next-to-leading order QCD improved
effective Hamiltonian, we have estimated the branching ratios and asymmetry
parameters for the two body charmless nonleptonic decay modes of $\Lambda_b$
baryon i.e. $\Lambda_b \to p (\pi/\rho),~p(K/K^*)$ and $\Lambda (\pi/\rho)$,
within the framework of generalized factorization. The nonfactorizable
contributions are parametrized in terms of the effective number of colors,
$N_c^{eff}$. So in addition to the naive factorization approach ($N_c^{eff}=3
$), here we have taken two more values for $N_c^{eff}$ i.e., $N_c^{eff}=2 $ and
$\infty $. The baryonic form factors at maximum momentum transfer ($ q_m^2 $)
are evaluated using the nonrelativistic quark model and the extrapolation of
the form factors from $q_m^2$ to the required $q^2$ value is done by assuming
the pole dominance. The obtained branching ratios for $\Lambda_b \to p\pi, ~pK$
processes lie within the present experimental upper limit .
