Question

Let $A = \\{1, 3, 7, 9, 11\\}$ and $B = \\{2, 4, 5, 7, 8, 10, 12\\}$. Then the total number of one-one maps $f: A \to B$, such that $f(1) + f(3) = 14$, is:

• A. 180
• B. 120
• C. 480
• D. 240

Answer 1

Answer: (D)

240

Answer 2

Given sets:

$A = \\{1, 3, 7, 9, 11\\} \quad \text{and} \quad B = \\{2, 4, 5, 7, 8, 10, 12\\}$

$A = \\{1, 3, 7, 9, 11\\}$

$B = \\{2, 4, 5, 7, 8, 10, 12\\}$

$f(1) + f(3) = 14$

(i) $2 + 12$

(ii) $4 + 10$

$2 \times (2 \times 5 \times 4 \times 3) = 240$