  A bouncing Universe avoids the big-bang singularity. Using the time-like and
null Raychaudhhuri equations, we explore whether the bounce near the big-bang,
within a broad spectrum of modified theories of gravity, allows for
cosmologically relevant power-law solutions under reasonable physical
conditions. Our study shows that certain modified theories of gravity, such as
Stelle gravity, do not demonstrate singularity resolution under any reasonable
conditions, while others including $f(R)$ gravity and Brans-Dicke theory can
demonstrate singularity resolution under suitable conditions. For these
theories, we show that the accelerating solution is slightly favoured over
ekypyrosis.
