Concept:
The Census of India 2011 provides important demographic statistics regarding population, density, literacy, growth rate, and sex ratio.
Step 1: Examine Statement A.
Uttar Pradesh had the highest population among all Indian states according to Census 2011.
Therefore, Statement A is correct.
Step 2: Examine Statement B.
The population density of India in Census 2011 was:
\[
382 \text{ persons per km}^2
\]
and not \(284\).
Hence, Statement B is incorrect.
Step 3: Examine Statement C.
India's share in world population was approximately:
\[
17.5%
\]
and not \(27.76%\).
Thus, Statement C is incorrect.
Step 4: Examine Statement D.
Nagaland recorded the lowest decadal population growth rate in Census 2011.
Therefore, Statement D is correct.
Step 5: Examine Statement E.
Kerala had the highest sex ratio in India, not Meghalaya.
Thus, Statement E is incorrect.
Step 6: Identify the correct statements.
Only statements:
\[
A \text{ and } D
\]
are correct.
Step 7: Conclusion.
Therefore, the correct answer is:
\[
\boxed{\text{A \& D Only}}
\]