(a) Number theory and the discovery of “Kaprekar’s constants”
Dattaraya Ramchandra Kaprekar was born at Dahanu near Bombay. He discovered the shortest possible routes to solve mathematical problems. In 1927, he won the wrangler R. P. Paranjpe Mathematical Prize for an Original Piece of work in mathematics. He discovered ‘Kaprekar Constant’ in 1946. It is the number “6174”. The constant 6174 is arrived at and this number then generates itself into one set of numbers called “self-numbers” that is also known by his name. Kaprekar passed away in 1988.

(a) Only One
ODF, ODF+, and ODF++ are part of the Swachh Bharat Mission (SBM). ODF stands for Open Defecation Free. ODF+ and ODF++ were launched in 2018 to help cities maintain their ODF status.
ODF+ focuses on the maintenance and hygiene of toilets with water. ODF++ focuses on toilets with sludge and septage management.
An ODF Plus village is one which has sustained its Open Defecation Free (ODF) status along with implementing either solid or liquid waste management systems. As on date, more than 2.96 lakh villages have declared themselves ODF Plus, which is a significant step towards achieving the SBM-G phase II goals by 2024-25.
The Wayanad district in Kerala became India’s first open defecation-free (ODF) Plus district in 2023.
(Statement 3 is incorrect).

(d) Nashik inscription
Nasik inscription highlights the achievements of Gautamiputra Satakarni. It is also known as Nashik prashasti in which his mother Gautami Balasri’s has given a eulogy, which credits him with extensive military conquests. It gives a detailed account of the Satavahana dynasty. There is another Nasik inscription made in the Nasik Caves in the year 120 CE by Ushavadata, a viceroy of the Western Satraps ruler Nahapana. It is the earliest known instance of Sanskrit usage in western India, though in a rather hybrid form.

(d) All four
The Kakatiya Dynasty was a South Indian Telugu dynasty that ruled most of eastern Deccan region in present-day India between 12th and 14th centuries. Early Kakatiya rulers served as feudatories to Rashtrakutas and Western Chalukyas for more than two centuries. They assumed sovereignty under Prataparudra I in 1163 CE by suppressing other Chalukya subordinates in the Telangana region.
Marco Polo, who visited India around 1289–1293, made note of Rudrama Devi’s rule and nature in flattering terms.
The Kakatiya polity was based on the monarchical system. The Kakatiya ruler was the pivot of the entire administrative structure, yet he was not an absolute autocrat.
Generally, in the process of succession, they followed the law of primogeniture (is a law of inheritance that gives the firstborn child the right to inherit the deceased’s property, wealth, and/or title) and as already referred; a woman coming to the throne was a remarkable exception.

(d) None
All the statements are correct.
The International Financial Services Centres Authority (IFSCA) is a statutory body that regulates financial services, products, and institutions in India’s International Financial Services Centre (IFSC). The IFSCA was established in 2020 under the International Financial Services Centres Authority Act, 2019. The IFSCA’s headquarters are located at GIFT City, Gandhinagar in Gujarat.
The GIFT City is a multi-service Special Economic Zone (SEZ) that houses India’s first IFSC and a Domestic Tariff Area (DTA).
The IFSCA’s primary role is to ensure inter-regulatory coordination within the financial sector. Some of the operations that take place at IFSCs include:
• Global and regional corporate treasury management
• Risk management operations such as insurance and reinsurance
• Merger and acquisition activities among trans-national corporations
India International Bullion Exchange (IIBX) is India’s first bullion exchange, launched on 29 July 2022 in Gujarat. Bullion refers to physical gold and silver of high purity often kept in the form of bars, ingots, or coins.