Statement 1 is incorrect. Both Dayabhaga and Mitakshara are the basic to the upper castes alone. Mitakshara school is followed in most of India while Dayabhaga is followed in Bengal and Assam.

Statement 2 is correct. In the Dayabhaga system, sons obtain rights to property only at the death of the father, and in the Mitakshara school, the sons and grandsons have rights over his property even while he is alive.

Statement 3 is incorrect. Both Dayabhaga and Mitakshara schools of Hindu law dealt with women’s property (stridhana). However, while the Mitakshara school imposed significant restrictions on women’s control and excluded them from coparcenary, the Dayabhaga school was relatively liberal, recognizing widows as heirs and granting greater powers over property.

Statement 1 is correct: St. Francis Xavier was a Spanish Jesuit who lived as a Roman Catholic missionary in the 1500s. He was one of the first seven members of the Jesuit order.

Statement 2 is incorrect: He did not die in Goa but at Sachian, an island off the coast of China. A church in memory of St. Xavier called the Church of Bom Jesus, is located in Goa with his mortal remains.

Statement 3 is correct: A feast in honor of St. Xavier is celebrated annually in Goa.

Statement 1 is Incorrect: The finalists for the inaugural ICC World Test Championship (2019-2021) were decided based on the Percentage of Points (PCT) earned from the total points contested, rather than the absolute number of matches won. This system was introduced by the ICC to account for the disparity in the number of matches played by different teams due to the COVID-19 pandemic.

Statement 2 is Incorrect: New Zealand was ranked ahead of England because they had a higher PCT (70.0%) compared to England (64.1%). In terms of match wins, England actually won more matches (11) than New Zealand (7) during the tournament cycle, directly contradicting the statement.

Statement 1 is Correct: The Laureus World Sports Awards were first presented in the year 2000 in Monte Carlo. American golfer Tiger Woods was the inaugural winner of the Laureus World Sportsman of the Year award.

Statement 2 is Incorrect: The award has been dominated by tennis players rather than Formula One players. By the time of the 2021 UPSC examination, tennis players had won the Sportsman of the Year award 11 times (Roger Federer-5, Rafael Nadal-2, and Novak Djokovic-4), while Formula One drivers had won it only 4 times (Michael Schumacher-2, Sebastian Vettel-1, and Lewis Hamilton-1).

Statement 3 is Correct: Roger Federer holds the record for the most wins in the Laureus World Sportsman of the Year category, having won it five times (2005, 2006, 2007, 2008, and 2018). When including his 'Comeback of the Year' award in 2018, he has a total of six Laureus statuettes, making him the most decorated individual in the history of the awards at that time.

Statement 1 is incorrect. The 32nd Summer Olympics was held in Tokyo in 2021. The Tokyo 2020 official Games motto was United by Emotion. The Rio Olympics 2016 official slogan was A New World.

Statement 2 is correct. New IOC rules for the Tokyo Olympics allowed host cities to choose popular sports for inclusion in the Games. Tokyo Olympics added six new sports, including baseball, softball, surfing, skateboarding, karate, and sports climbing. Additionally, there were new forms of basketball and cycling and mixed-team events in traditional sports.

Bhavabhuti, Hastimalla, and Kshemeshvara were renowned playwrights in ancient and early medieval India.

Bhavabhuti: An 8th-century scholar and playwright in the court of King Yashovarman of Kannauj. He is famous for his Sanskrit plays Malatimadhava, Mahaviracharita, and Uttararamacharita.

Hastimalla: A 13th-century Jain playwright who lived during the Hoysala period. He is known for his Sanskrit plays such as Vikrantakaurava, Maithilikalyana, and Anjanapavananjaya.

Kshemeshvara: A 10th-century playwright who served in the court of King Mahipala of the Pala dynasty. His notable works include the plays Chandakaushika and Naishadhananda.

Statement 1 is incorrect: The national awards such as Bharat Ratna, Padma Vibhushan, Padma Bhushan, and Padma Shri do not amount to titles within the meaning of Article 18(1) of the Constitution.

Statement 2 is incorrect: Padma awards were instituted in the year 1954 and have been suspended in years 1978, 1979, 1993, and 1997.

Statement 3 is incorrect: Although there is a general guideline to limit the Bharat Ratna to three recipients per year, this rule has been exceeded twice: In 1999, four awards were conferred (Jayaprakash Narayan, Amartya Sen, Gopinath Bordoloi, and Ravi Shankar) and in 2024, Five awards were conferred (M.S. Swaminathan, P.V. Narasimha Rao, Chaudhary Charan Singh, Karpoori Thakur, and L.K. Advani).

Statement 1 is correct: (Circular temple, Kachchhapaghata Dynasty) The Chausath Yogini Temple near Morena is a circular temple complex built during the reign of the Kachchhapaghata dynasty, estimated to be around the 11th century CE.

Statement 2 is incorrect: (Not the only circular temple) While the Chausath Yogini Temple is a well-known example, it's not the only circular temple in India. There are other circular temples across the country, such as the Shiva temple at Bhringari in Andhra Pradesh.

Statement 3 is incorrect: (Vaishnava cult) The temple is not primarily associated with the Vaishnava cult, which worships Vishnu. The specific dedication of the temple is debated, with some theories suggesting a connection to Shaktism or Tantric practices.

Statement 4 is correct: (Inspiration for Parliament building) There's a popular belief that the circular design of the Chausath Yogini Temple might have inspired the architects of the Indian Parliament building in New Delhi. However, there's no definitive historical evidence to confirm this connection.

Therefore, the correct statements are 1 and 4.

Option A is correct: The Ajanta Caves are a series of 29 rock-cut Buddhist cave monuments located in the Aurangabad district of Maharashtra. They are situated in the horseshoe-shaped gorge of the Waghora River.

Option B is incorrect: Sanchi Stupa is located on a hilltop at Sanchi in the Raisen District of Madhya Pradesh. It is situated near the Betwa River, not the Chambal River.

Option C is incorrect: The Pandu-Lena Caves (also known as Nasik Caves) are a group of 24 Buddhist caves carved into the Trirashmi hills near Nashik, Maharashtra. They are not located in the gorge of the Narmada River.

Option D is incorrect: The Amaravati Stupa is located on the banks of the Krishna River in the Guntur district of Andhra Pradesh, not the Godavari River.

Halbi, Ho, and Kui are tribal languages spoken in different regions of India:

1. Halbi (Halabi): An Indo-Aryan language spoken primarily by the Halba tribe in Chhattisgarh, Odisha, Madhya Pradesh, and Maharashtra.
2. Ho: An Austroasiatic language (Munda group) spoken by the Ho people, mainly in Jharkhand and Odisha.
3. Kui (Kondh): A South-Central Dravidian language spoken by the Kandha (Khond) tribe, primarily in Odisha. It is closely related to Gondi and Pengo languages.