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

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 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 9^(2x−1) − 81^(x−1) = 1944, then x is

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 value of log₀.₀₀₈√5 + log√3 81 − 7 is equal to : (log₀.₀₀₈√5 is log of √5 to base 0.008; log√3 81 is log of 81 to base √3)

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 x + 1 = x² and x > 0, then 2x⁴ is :

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