If n is an odd natural number greater than 1, then the product of its successor and predecessor

(a) is an odd natural number (b) is an even natural number

(c) can be even or odd (d) None of these

The successor and predecessor of an odd natural number are both even.
Here, n = odd. So
Successor of n = n + 1 (Even natural number)
Predecessor of n = n − 1 (Even natural number)
Product = (n + 1) $\text{×}$ (n − 1) = even $\text{×}$ even = even
Thus, the product of the successor and predecessor of n is an even number.
Hence, the correct option is (b).