The Deterrent
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Our Agni IV has the CEP of less than 25m. Our BM are very accurate and don't have such large CEP. If you know, any RV requires path correction device which takes it position from the satellite or any navigational device even if it is for few seconds.
In case of unitary warheads, terminal maneuvering can be done (for example as in DF-21). But that isn't really of much use in case of nuclear warheads.
Most of the correction systems correct the trajectory in space, and since the RVs are spinning during re-entry (for stability), maneuvering cannot be easily achieved. That is why use of decoys and multiple warheads is preferred (as in case of Minuteman-III).
I highly doubt that CEP figure as consistently achievable.