Equations Algebra CAT 2025 Slot 1 Actual Questions

If a −6b + 6c = 4 and 6a + 3b − 3c = 50, where a, b, and c are real numbers, the value of 2a + 3b − 3c is

The number of non-negative integer values of k for which the quadratic equation x² – 5x + k = 0 has only integer roots, is

Let 3 ≤ x ≤ 6 and [x²] = ([x])², where [x] is the greatest integer not exceeding x. If S represents all feasible values of x, then a possible subset of S is

A value of c for which the minimum value of f(x) = x² – 4cx + 8c is greater than the maximum value of g(x) = –x² + 3cx – 2c, is