**Solution:**

To find the value of n, we need to solve the equation nP1 = 10.

**Permutation Formula:**

\(nP1 = n!\)

The factorial of a number n is the product of all positive integers from 1 to n.

**Simplifying the equation:**

Using the permutation formula, we can simplify the equation as follows:

\(nP1 = n!\)

Since there is only 1 element in the permutation, the factorial of 1 is equal to 1.

Therefore, the equation becomes:

\(n! = 10\)

**Solving the equation:**

To find the value of n, we can try different values of n and calculate their factorial until we find the value that satisfies the equation.

Let's try the given options one by one:

- For option a) n = 2

\(2! = 2 \times 1 = 2\)

Since 2 is not equal to 10, option a) is incorrect.

- For option b) n = 5

\(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)

Since 120 is not equal to 10, option b) is also incorrect.

- For option c) n = 10

\(10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3628800\)

Since 3628800 is not equal to 10, option c) is incorrect.

- For option d) n = 1

\(1! = 1\)

Since 1 is equal to 10, option d) is correct.

Therefore, the value of n that satisfies the equation nP1 = 10 is n = 1, which corresponds to option d).

Hence, the correct answer is option 'd'.