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In the present investigation, LRS Bianchi type-I universe with variable deceleration parameter in the frame work of f (R,T) theory of gravity is considered where f (R,T) is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T . The gravitational field equations are obtained in the metric formalism, which follows from the covariant divergence of the stress-energy tensor. The field equations correspond for a specific choice of ( , ) ( ) ( ) 1 2 f R T f R f T , with the individual superior functions f R R 1 1 ( ) and f R T 2 2 ( ) . It is observe that in f(R, T) gravity, an extra acceleration is always present due to coupling between matter and geometry. Allowing for time dependent deceleration parameter the solutions of the field equations and some physical and geometric properties of the model along with physical acceptability of the solutions have also been discussed in details.
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