  LRS (Locally Rotationally symmetric) Bianchi type-I magnetized strange quark
matter cosmological model have been studied based on $f(R,T)$ gravity. The
exact solutions of the field equations are derived with linearly time varying
deceleration parameter which is consistent with observational data (from SNIa,
BAO and CMB) of standard cosmology. It is observed that the model start with
big bang and ends with a Big Rip. The transition of deceleration parameter from
decelerating phase to accelerating phase with respect to redshift obtained in
our model fits with the recent observational data obtained by Farook et al. in
2017. The well known Hubble parameter $H(z)$ and distance modulus $\mu(z)$ are
discussed with redshift.
