In this paper, we have studied homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I model with magnetized strange quark matter (MSQM) distribution and cosmological constant A in f(R, T) gravity where R is the Ricci scalar and T the trace of matter source. 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 forms of bilinear DP with a single parameter of the form: q = alpha(1-t/1+t) and q = -alpha t/1+t, which leads to the constant or linear nature of the function based on the constant a. Second one is the special form of the DP as q = -1 + beta/1+a(beta) From the results obtained here, one can observe that in the early universe magnetic flux has more effects and it reduces gradually in the later stage. For t -> infinity, we get p -> -Bc, and p -> B-c. The behaviour of 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.