Which of the following States registered the highest population growth rate during 2001–2011?

The correct option is Rajasthan.

To understand why Rajasthan registered the highest population growth rate among the given options during the 2001–2011 decade, we can examine the decadal growth rates of population for each of the listed states according to the Census of India 2011 data:

1. Rajasthan: The decadal population growth rate was approximately 21.3%.
2. Karnataka: The decadal population growth rate was approximately 15.6%.
3. Maharashtra: The decadal population growth rate was approximately 16.0%.
4. Tamil Nadu: The decadal population growth rate was approximately 15.6%.

Comparing these values:
$$21.3\%>16.0\%>15.6\%$$
Thus, among the choices provided (Karnataka, Tamil Nadu, Rajasthan, and Maharashtra), Rajasthan clearly registered the highest population growth rate during the 2001–2011 period.