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

Let both $p$ and $k$ be prime numbers such that $(p^2 + k)$ is also a prime number less than 30. What is the number of possible values of $k$?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of runs scored by X to runs scored by Y equals the ratio of runs scored by Y to runs scored by Z.

Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z

Which one of the following is correct?

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

How many possible values of $(p + q + r)$ are there satisfying $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} = 1$, where p, q, and r are natural numbers (not necessarily distinct)?

A 4-digit number N is such that when divided by 3, 5, 6, and 9 it leaves a remainder of 1, 3, 4, and 7 respectively. What is the smallest value of N?