  In this paper, we have studied homogeneous and anisotropic, locally
rotationally symmetric (LRS) Bianchi type-I universe model with magnetized
strange quark matter (MSQM) distribution and cosmological constant $\Lambda$ in
$f(R,T)$ gravity. The exact solutions of the field equations are obtained under
bilinear and special form of time varying deceleration parameter (DP). Firstly
we have considered two specific form of bilinear DP with a single parameter of
the form: $q=\frac{\alpha(1-t)}{1+t}$ and $q=-\frac{\alpha t}{1+t}$, which
leads to a function with constant or linear nature with respect to the choice
of constant $\alpha$. Second one is the special form of the DP as
$q=-1+\frac{\beta}{1+a^{\beta}}$. From obtained results, we could say that in
the early universe the magnetic flux has more effects and it gradually reducing
its effects in later. For $t\rightarrow \infty$, we get $p\rightarrow -B_c$ and
$\rho\rightarrow B_c$. So the strange quark matter along with magnetic epoch
gives an idea of accelerated expansion of the universe as per the observations
of the type Ia Supernovae.
