The Pradhan Mantri Awas Yojana primarily aims to provide housing for the lower income group.

The Pradhan Mantri Fasal Bima Yojana provides insurance coverage and financial support to farmers in the agriculture sector.

The Pradhan Mantri Gram Sadak Yojana aims to construct all-weather roads to improve connectivity in rural areas.

The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched to improve road connectivity in rural areas.

The Pradhan Mantri Jan Dhan Yojana (PMJDY) aims to promote financial inclusion by providing banking facilities to the unbanked population.

The Pradhan Mantri Jan Dhan Yojana aims to ensure universal access to banking facilities for all citizens.

The Pradhan Mantri Kisan Samman Nidhi (PM-KISAN) scheme, launched in 2019, provides direct income support to small and marginal farmers.

The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from below the poverty line.

The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from Below Poverty Line (BPL) households.

The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from Below Poverty Line households.

The Preamble of the Indian Constitution declares India to be a Sovereign State.

The President of India is elected by an electoral college comprising the elected members of both Houses of Parliament and the elected members of the Legislative Assemblies of States and Union territories.

The President of India is elected by an Indirect Election method.

Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.

According to Gay-Lussac's law, the pressure of an ideal gas is directly proportional to its temperature when the volume is held constant.

This relationship is known as Boyle's Law, which states that the pressure of an ideal gas is inversely proportional to its volume at constant temperature.

The UNDP focuses on supporting sustainable development and reducing poverty globally.

The WTO, established in 1995, aims to facilitate international trade and ensure that trade flows as smoothly and predictably as possible.

Bernoulli's Principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure.

Sublimation is the process where a solid changes directly into a gas without passing through the liquid state.

The product of the roots is given by c/a. Here, c = 1 and a = 2, so the product is 1/2.

The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 2 and a = 2, so the product is 2/2 = 1.

The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 6 and a = 2, so the product is 6/2 = 3.

The product of the roots is given by c/a = 10/1 = 10.

Using Vieta's formulas, the product of the roots is k = 10. Thus, k = 17.

The product of the roots is given by c/a, which is 9/3 = 3.

The product of the roots is given by c/a = 6/1 = 6.

z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - i^2 = 2 + 1 + i = 3 + i.

Let the integers be n and n+1. Then n(n+1) = 240. Solving the quadratic equation n^2 + n - 240 = 0 gives n = 14, so the integers are 14 and 15.

A comprehensive understanding suggests that the lecture was thorough and insightful, making option 2 the correct choice.