In terms of Area
Largest State of India - Rajasthan with area 342,239 sq km
Smallest State of India (without considering union territories) - Goa with area 3,702 sq km
Smallest State of India (considering union territories) - Lakshadweep with area 32 sq km
In terms of Population
Largest State of India - Uttar Pradesh with population ~200m (2011 Census)
Smallest State of India (without considering union territories) - Sikkim with population ~600K
Smallest State of India (considering union territories) - Lakshadweep with population ~65K