We study the random field p-spin model with Ising spins on a fully connected graph using the theory of large deviations in this paper. This is a good model to study the effect of quenched random field on systems which have a sharp first order transition in the pure state. For p=2, the phase-diagram of the model, for bimodal distribution of the random field, has been well studied and is known to undergo a continuous transition for lower values of the random field (h) and a first order transition beyond a threshold, htp(≈0.439). We find the phase diagram of the model, for all p≥2, with bimodal random field distribution, using large deviation techniques. We also look at the fluctuations in the system by calculating the magnetic susceptibility. For p=2, beyond the tricritical point in the regime of first order transition, we find that for htp<h<0.447, magnetic susceptibility increases rapidly (even though it never diverges) as one approaches the transition from the high temperature side. On the other hand, for 0.447<h≤0.5, the high temperature behaviour is well described by the Curie–Weiss law. For all p≥2, we find that for larger magnitudes of the random field (h>ho=1/p!), the system does not show ferromagnetic order even at zero temperature. We find that the magnetic susceptibility for p≥3 is discontinuous at the transition point for h<ho.