The number of pairs of integers whose sums are equal to their products is

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The \(6389^{th}\) digit in this sequence is...

You have been asked to select a positive integer N which is less than 1000, such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. The number of such numbers is

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is

If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent

If \(|x| < 100\) and \(|y| < 100\), then the number of integer solutions of (x, y) satisfying the equation \(4x + 7y = 3\) is

The maximum value of the natural number n for which \(21^n\) divides 50! is

The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right-angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the t…

The remainder when \((29^{29})^{29}\) is divided by 9 is