Rajasthan (Hindi: [raːdʒəsˈtʰaːn] (listen); lit. 'Land of Kings') is a state in northern India. It covers 342,239 square kilometres (132,139 sq mi) or 10.4 per cent of India's total geographical area. It is the largest Indian state by area and the seventh largest by population. It is on India's northwestern side, where it comprises most of the wide and inhospitable Thar Desert (also known as the Great Indian Desert) and shares a border with the Pakistani provinces of Punjab to the northwest and Sindh to the west, along the Sutlej-Indus River valley. It is bordered by five other Indian states: Punjab to the north; Haryana and Uttar Pradesh to the northeast; Madhya Pradesh to the southeast; and Gujarat to the southwest. Its geographical location is 23.3 to 30.12 North latitude and 69.30 to 78.17 East longitude, with the Tropic of Cancer passing through its southernmost tip. Its major features include the ruins of the Indus Valley civilisation at Kalibangan and Balathal, the Dilwara Temples, a Jain pilgrimage site at Rajasthan's only hill station, Mount Abu, in the ancient Aravalli mountain range and eastern Rajasthan, the Keoladeo National Park of Bharatpur, a World Heritage Site known for its bird life. Rajasthan is also home to three national tiger reserves, the Ranthambore National Park in Sawai Madhopur, Sariska Tiger Reserve in Alwar and the Mukundra Hills Tiger Reserve in Kota. The state was formed on 30 March 1949 when Rajputana – the name adopted by the British Raj for its dependencies in the region – was merged into the Dominion of India. Its capital and largest city is Jaipur. Other important cities are Jodhpur, Kota, Bikaner, Ajmer, Bharatpur and Udaipur. The economy of Rajasthan is the seventh-largest state economy in India with ₹10.20 lakh crore (US$130 billion) in gross domestic product and a per capita GDP of ₹118,000 (US$1,500). Rajasthan ranks 29th among Indian states in human development index.

Patna (Hindi: [ˈpəʈnaː] (listen)), historically known as Pataliputra, is the capital and largest city of the state of Bihar in India. According to the United Nations, as of 2018, Patna had a population of 2.35 million, making it the 19th largest city in India. Covering 250 square kilometres (97 sq mi) and over 2.5 million people, its urban agglomeration is the 18th largest in India. Patna serves as the seat of Patna High Court. The Buddhist, Hindu and Jain pilgrimage centres of Vaishali, Rajgir, Nalanda, Bodh Gaya and Pawapuri are nearby and Patna City is a sacred city for Sikhs as the tenth Sikh Guru, Guru Gobind Singh was born here. The modern city of Patna is mainly on the southern bank of the river Ganges. The city also straddles the rivers Sone, Gandak and Punpun. The city is approximately 35 kilometres (22 mi) in length and 16 to 18 kilometres (9.9 to 11.2 mi) wide. One of the oldest continuously inhabited places in the world, Patna was founded in 490 BCE by the king of Magadha. Ancient Patna, known as Pataliputra, was the capital of the Magadh Empire through Haryanka, Nanda, Mauryan, Shunga, Gupta and Pala dynasties. Pataliputra was a seat of learning and fine arts. It was home to many astronomers and scholars including Aryabhata, Vātsyāyana and Chanakya. During the Maurya period (around 300 BCE) its population was about 400,000. Patna served as the seat of power, and political and cultural centre of the Indian subcontinent during the Maurya and Gupta empires. With the fall of the Gupta Empire, Patna lost its glory. It was revived again in the 17th century by the British as a centre of international trade. Following the partition of Bengal presidency in 1912, Patna became the capital of Bihar and Orissa Province.Until the 19th century it was a major trading and commercial hub in India. After independence there were a few downturns but its economy was still stable. After the separation of Jharkhand from Bihar, it lost its glory. Now trials are made to develop the city. As per the Directorate of Economics and Statistics (Government of Bihar), Nominal GDP of Patna District was estimated at INR 63,176.55 crores in 2011-12. As of 2011-12, Patna already recorded per capita gross domestic product of ₹1,08,657, way ahead of many other Indian cities and state capitals. Using figures for assumed average annual growth, Patna is the 21st fastest growing city in the world and 5th fastest growing city in India according to a study by the City Mayors Foundation. Patna registered an average annual growth of 3.72% during 2006–2010. As of 2011-12, GDP per capita of Patna is ₹1,08,657 and its GDP growth rate is 7.29 per cent. In June 2009, the World Bank ranked Patna second in India (after Delhi) for ease of starting a business.