Question

The total number of functions, 

f : {1, 2, 3, 4} • {1, 2, 3, 4, 5, 6} 

such that f(1) + f(2) = f(3), is equal to : 

(A) 60

(B) 90

(C) 108

(D) 126

Answer 1

Correct option is (B) 90

A = {1, 2, 3, 4} 

B = {1, 2, 3, 4, 5, 6} 

Here f(3) can be 2, 3, 4, 5, 6 

f(3) = 2, (f(1), f(2)) → (1,1) → 6 cases 

f(3) = 3, (f(1), f(2)) → (1,2), (2,1) 

→ 2 × 6 = 12 cases 

f(3) = 4, (f(1), f(2)) → (1,3), (3,1), (2,2) 

→ 3 × 6 = 18 cases 

f(3) = 5, (f(1), f(2)) → (1,4), (4,1), (2,3), (3,2) 

→ 4 × 6 = 24 cases 

f(3) = 6, (f(1), f(2)) → (1,5),(5,1),(2,4),(4,2),(3,3) 

→ 5 × 6 = 30 cases