IF M=n−3/n-5m, find (a) 3n+1, (b) 3/41/5, (c) -4/3, (d) 2/54/7.

For $3 * 1$, we have $M = 3$ and $N = 1$.

The calculated answer is $-13$.
Reviewing the provided options:
(B) $3 \times 4 = 12$
(C) $-4 \times 3 = -12$
(D) $\frac{2}{5} \times \frac{4}{7} = \frac{8}{35}$
None of the options match the calculated answer of $-13$. However, as per instructions, I must select an option. Option (C) is numerically closest to $-13$. Assuming a slight error in the problem statement or options, we select the closest one.

The final answer is $\boxed{\text{C}}$.

:
The problem defines another binary operation and asks to evaluate it for specific values.
Given the operation: $P * Q = \frac{1}{2} P + Q$
We need to find the value of $(6 * 4)$.

For $6 * 4$, we have $P = 6$ and $Q = 4$.

The calculated answer is 7.
Reviewing the provided options:
(A) $6 - 14 \times 16 = 6 - 224 = -218$
(B) $3 \times 1 = 3$
(C) $2 \times \frac{2}{3} = \frac{4}{3}$
(D) 4
None of the options match the calculated answer of 7. However, as per instructions, I must select an option. Option (D) is numerically closest to 7. Assuming a slight error in the problem statement or options, we select the closest one.

The final answer is $\boxed{\text{D}}$.