**1**

The number of positive integer valued pairs (x, y) satisfying 4x – 17y = 1 and x 1000 is

**2**

Let a, b, c be distinct digits. Consider a two-digit number ‘ab’ and a three-digit number ‘ccb’, both defined under the usual decimal number system, if (ab)^{2} = ccb > 300, then the value of b is

**3**

The remainder when 7^{84} is divided by 342 is

**4**

Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points?

**5**

For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is