"A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable."

The 5-digit number PQRST (all distinct digits) is such that $\mathbf{T} \neq \mathbf{0} . \mathbf{P}$ is thrice $\mathbf{T} . \mathbf{S}$ is greater than $\mathbf{Q}$ by 4, while $Q$ is greater than $R$ by 3 . How many such 5-digit numbers are possible?

"A network of voluntary associations stands as a 'buffer' between the relatively powerless individual and the potentially powerful State."

Consider the following statements:

I. There exists a natural number which when increased by $50 \%$ can have its number of factors unchanged.

II. There exists a natural number which when increased by $150 \%$ can have its number of factors unchanged.

Which of the statements given above is/are correct?

"A network of voluntary associations stands as a 'buffer' between the relatively powerless individual and the potentially powerful State."

What is the remainder when $9^3+9^4+9^5+9^6+\ldots+9^{100}$ is divided by 6 ?

Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of globalising behaviour; trust itself emerges as a supercommodity in the social market and defines the characteristics of goods and services in a global market. Trusting conduct also means holding others in good esteem, and an optimism that they are, or will be, competent in certain respects.

The difference between any two natural numbers is 10 . What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?