The displacement x of a particle varies with time according to the relation x=ab1−e−bt. Then  take e−1≃13

Velocity of the particle is given by v=dxdt=ddtab1−e−bt=ae−btAcceleration of the particle is given by α=dvdt=ddtae−bt=−abe−btAt t =1/b, the displacement of the particle is x=ab1−e−1≃ab1−13≃23ab ∵e−1≃13Hence choice (a) is wrong. At t= 0, the values v and α respectively are v=ae−0=a and α=−abe-0=-ab.Hence choice (b) is also wrong. The displacement x is maximum when t→∞,i.e., xmax=ab1-e-∞=ab.Hence choice (c ) is correct.