  We have carried out molecular dynamics simulations to understand the dynamics
of a tagged pair of atoms in a strongly non-ideal glass-forming binary
Lennard-Jones mixture (commonly known as Kob-Andersen model). The generalized
time-dependent pair distribution function is calculated separately for the
three pairs (AA, BB and AB). The three pairs are found to behave differently.
The relative diffusion constants are found to vary in the order $D_R^{BB} >
D_R^{AB} > D_R^{AA}$, with $D_R^{BB} \simeq 2D_R^{AA}$, showing the importance
of the hopping process (B hops much more than A). We introduce a non-Gaussian
parameter ($\alpha_2^P (t)$) to monitor the relative motion of a pair of atoms,
and evaluate it for all the three pairs, with initial separations chosen to be
at the first peak of the corresponding partial radial distribution functions.
At intermediate times, significant deviation from the Gaussian behavior of the
pair distribution functions is observed, with different degree for the three
pairs. A simple mean-field (MF) model, proposed originally by Haan [Phys. Rev.
A ${\bf 20}$, 2516 (1979)] for one component liquid, is applied to the case of
binary mixture, and compared with the simulation results. While the MF model
successfully describe the dynamics of the AA and AB pair, the agreement for the
BB pair is less satisfactory. This is attributed to the large scale anharmonic
motions of the B particles in a weak effective potential. Dynamics of next
nearest neighbor pairs are also investigated.
