Self-employment is a key avenue for employment generation in India, and here's why:
- High Employment Potential: India, with its large rural population and limited job opportunities in the formal sector, has seen self-employment emerge as a crucial way for individuals to earn their livelihoods. Agriculture, handicrafts, and small businesses are common forms of self-employment.
- Entrepreneurship and Innovation: Self-employment fosters entrepreneurship and innovation, as individuals take the initiative to create businesses and services that cater to local and regional needs.
- Lower Barriers to Entry: Unlike formal employment that requires certain qualifications or skills, self-employment offers flexibility and lower barriers to entry, allowing many individuals, particularly in rural areas, to enter the workforce.
- Government Initiatives: Various government schemes like PMEGP (Prime Minister's Employment Generation Programme) and MUDRA Yojana support the self-employment sector by providing loans, training, and other resources. Therefore, self-employment is crucial in India's economic context, providing a valuable route to employment for a large section of the population.
Two players \( A \) and \( B \) are playing a game. Player \( A \) has two available actions \( a_1 \) and \( a_2 \). Player \( B \) has two available actions \( b_1 \) and \( b_2 \). The payoff matrix arising from their actions is presented below:

Let \( p \) be the probability that player \( A \) plays action \( a_1 \) in the mixed strategy Nash equilibrium of the game.
Then the value of p is (round off to one decimal place).
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is: