The question asks which of the following options is not a part of the challenges faced by India for sustainable growth, as deliberated in the Fourth BRICS Summit in New Delhi in March 2012.

Option 1 is "Improvements required in public sector management." This option suggests that improving public sector management is not one of the challenges discussed during the summit.

Option 2 is "Inclusive growth." Inclusive growth refers to economic growth that benefits all segments of society, especially the marginalized and disadvantaged. This was mentioned as one of the challenges faced by India for sustainable growth.

Option 3 is "Improvements required in physical infrastructure." This option refers to the need for better infrastructure, such as roads, bridges, and transportation systems. It was identified as a challenge during the summit.

Option 4 is "Development in the agricultural sector." This option relates to the need for growth and improvement in the agricultural industry. It was discussed as one of the challenges faced by India for sustainable growth.

Therefore, after analyzing all the options, we can conclude that option 1, "Improvements required in public sector management," is not a part of the formulated challenges discussed during the Fourth BRICS Summit.