Advanced Quiz – 14 September 2026 | Polity

Answer: (c) Only three

Explanation:
Statements 1, 2 and 4 are correct.

The World Development Report 2024 describes a sequential framework:

• 1i: Investment
• 2i: Investment + Infusion
• 3i: Investment + Infusion + Innovation

Lower-middle-income economies are expected to add infusion, meaning the adoption and domestic diffusion of foreign technologies, to investment. Upper-middle-income economies then add innovation.

Statement 3 is incorrect because innovation does not replace infusion. Under the 3i framework, innovation is added to investment and infusion.

Answer: (b) 1, 3 and 4 only

Explanation:
Statements 1, 3 and 4 are correct.

PM SHRI, or Pradhan Mantri Schools for Rising India, is a Centrally Sponsored Scheme. Its objective is to strengthen more than 14,500 existing schools, rather than create an entirely separate network of newly established schools.

Eligible institutions include schools under the Central Government as well as State/UT Governments and local bodies. They are intended to showcase the implementation of NEP 2020 and function as exemplar institutions for neighbouring schools.

Statement 2 is therefore incorrect. As of July 2026, 13,092 schools had been selected under the scheme.

Answer: (c) Only three

Explanation:
Statements 1, 2 and 3 are correct.

The project envisages lifting water from the Tunga River to the Bhadra reservoir and subsequently lifting water from the Bhadra reservoir for utilisation under the project.

The river relationship is:

Tunga + Bhadra → Tungabhadra → Krishna

Therefore, both Tunga and Bhadra belong to the wider Krishna basin.

Statement 4 is incorrect. The Central Water Commission has assessed the project’s proposed utilisation against Karnataka’s allocation under the Krishna Water Disputes Tribunal-I. It is not a Cauvery-to-Krishna transfer.

Answer: (c) Only three

Explanation:
Pairs 1, 2 and 3 are correctly matched.

Yudh Abhyas is an India-US Army exercise. U.S. Army personnel, including elements of the 11th Airborne Division, participated in Yudh Abhyas 2026 in India.

Vajra Prahar involves the Special Forces of India and the United States, while Cope India is an air exercise involving the two countries.

Pair 4 is incorrect. Malabar is not exclusively bilateral. It currently involves the naval forces of the four Quad countries: India, United States, Japan and Australia.

Answer: (b) 1, 2 and 4 only

Explanation:
Statements 1, 2 and 4 are correct.

Navier-Stokes equations describe fluid motion, including the behaviour of liquids and gases.

The Millennium Prize Problem concerns the mathematical behaviour of solutions to the three-dimensional Navier-Stokes equations, particularly questions of existence, smoothness and possible breakdown.

Statement 3 is incorrect. The official problem is not restricted to proving global smoothness. An appropriate breakdown result satisfying the stipulated mathematical conditions can also resolve the problem.

OpenAI announced in September 2026 that an internal system had produced a proposed finite-time singularity proof and a Lean formalisation. Formal verification, however, does not by itself constitute official recognition of a Millennium Prize solution.