Which of the following numbers in the Venn Diagram represents youth who are unemployed but not illiterate?
To find the region that represents youth who are unemployed but not illiterate, we need to look at the intersection of the circles based on the given conditions:
Youth: Must be inside the "Youth" circle (numbers: 3, 6, 2, 5).
Unemployed: Must also be inside the "Unemployed" circle (numbers sharing both circles: 2, 5).
Not Illiterate: Must be outside the "Illiterate" circle. This eliminates the number 5 (since 5 represents youth who are both unemployed and illiterate).
The only number that is inside both the Youth and Unemployed circles but completely outside the Illiterate circle is 2.
The number 2 represents youth who are unemployed but not illiterate.
Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______

Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is: