To find the coefficients of the 9th, 10th, and 11th terms in the expansion of (1 + x)^n, we can use the binomial theorem.

The binomial theorem states that for any positive integer n, the expansion of (1 + x)^n can be written as:

(1 + x)^n = C(n, 0) + C(n, 1)x + C(n, 2)x^2 + ... + C(n, n)x^n

where C(n, r) represents the binomial coefficient, given by the formula:

C(n, r) = n! / (r!(n-r)!)

To find the coefficients of the 9th, 10th, and 11th terms, we need to find the values of C(n, 8), C(n, 9), and C(n, 10).

Since the coefficients are in arithmetic progression (A.P.), we can set up the following equation:

C(n, 9) - C(n, 8) = C(n, 10) - C(n, 9)

Simplifying the equation, we get:

C(n, 10) - 2C(n, 9) + C(n, 8) = 0

Using the formula for binomial coefficients, we can express this equation in terms of n:

(n! / (10!(n-10)!)) - 2(n! / (9!(n-9)!)) + (n! / (8!(n-8)!)) = 0

Simplifying further, we get:

n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9) - 2n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8) + n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7) = 0

This equation can be solved to find the value of n. However, it is a complex equation and solving it directly may be difficult.

Instead, we can consider the options given:

a) 7
b) 7 or 14
c) 14
d) 16

By substituting these values of n into the equation, we find that only option c) 14 satisfies the condition for the coefficients to be in an arithmetic progression.

Therefore, the correct answer is option c) 14.