**Core Concept**
The National Family Health Survey (NFHS) is a large-scale, multi-round survey conducted in a representative sample of households throughout India. It aims to provide data on health and family welfare, including fertility, health, and nutrition.

**Why the Correct Answer is Right**
The NFHS-3 was conducted from 2005-06 to 2006-07, covering a total of 109,777 households in 29 states and 7 Union Territories. This survey provided valuable information on health and family welfare indicators, including fertility rates, infant mortality rates, and immunization coverage.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the NFHS-3 was not conducted in 2000-01. The first NFHS was conducted in 1992-93, and subsequent surveys were conducted in 1998-99, 2005-06, and 2015-16.

**Option B:** This option is incorrect because the NFHS-3 was not conducted in 2015-16. While the NFHS-4 was indeed conducted in 2015-16, the NFHS-3 was conducted in 2005-06.

**Option C:** This option is incorrect because the NFHS-3 was not conducted in 2020-21. The NFHS-5 was conducted in 2019-21, but the NFHS-3 was conducted in 2005-06.

**Option D:** This option is incorrect because the NFHS-3 was not conducted in 2009-10. The NFHS-3 was conducted in 2005-06, and subsequent surveys were conducted in 2015-16.

**Clinical Pearl / High-Yield Fact**
The NFHS is a crucial source of data for policymakers and researchers, providing valuable insights into health and family welfare indicators in India.

**Correct Answer:** C. 2005-06.