Answer :
Final answer:
Without additional constraints or an explicit formula for the function f, it is impossible to determine the exact number of one-one functions that satisfy the given equation 2f(a) - f(b) + 3f(c) + f(d) = 0.
Explanation:
The question asks for the number of one-one functions from the set {a, b, c, d} to the set {0, 1, 2, …, 10} such that 2f(a) – f(b) + 3f(c) + f(d) = 0. To find the number of such functions, we must consider that each element in the domain must map to a unique element in the codomain to satisfy the one-one (injective) property. However, without additional constraints or explicit formulas for the function, we cannot determine the exact number of functions just based on this information. The options provided (A: 30, B: 42, C: 60, D: 84) cannot be verified without a specific rule for the function f.
