Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a − b)² + (a − c)² + (a − d)² is

The shortest distance of the point (1/2, 1) from the curve y = |x − 1| + |x + 1| is

If f1(x) = x² + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is :

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is :

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

If f(x) = (5x + 2)/(3x − 5) and g(x) = x² − 2x − 1, then the value of g(f(f(3))) is :