"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 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."

$\mathbf{X}$ can complete one-third of a certain work in $\mathbf{6}$ days, $\mathbf{Y}$ can complete one-third of the same work in $\mathbf{8}$ days and $\mathbf{Z}$ can complete three-fourth of the same work in 12 days. All of them work together for $n$ days and then $X$ and $Z$ quit and $Y$ alone finishes the remaining work in $8 \frac{2}{3}$ days. What is $n$ equal to?

"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 ?