RL circuit and pure inductor
But when we add resistance in series with inductor and apply dc
  voltage we get exponential increase in current


It's not an exponential rise but a reverse exponential rise: -



Picture from here.

As current rises, the volt drop across the resistor increases and this reduces the effective terminal voltage appearing across the inductor hence, the rate of change of current in the inductor (as defined by \$\dfrac{di}{dt} = \dfrac{V}{L}\$) has to fall.