Given:
- The sequence follows the pattern of incrementing the number in the units place by 1 each time.
- The last term in the sequence is 20032.

To find:
The value of x in the expression (2003)(334)(x).

Solution:
We can observe that the sequence is obtained by incrementing the number in the units place by 1 each time. Therefore, we can write the sequence as follows:

12, 22, 32, ..., 20032

We can see that the number of terms in the sequence is 2003. Each term can be written as follows:

Term N: N * 10 + 2

So, the last term in the sequence can be written as:

2003 * 10 + 2 = 20032

Now, let's analyze the expression (1)(2003)(2)(2002)(3)(2001)....(2003)(1).

We can see that this expression represents the product of each term in the sequence. So, we can write it as:

1 * 2003 * 2 * 2002 * 3 * 2001 * ... * 2003 * 1

To simplify this expression, we can pair each term as follows:

(1 * 2003) * (2 * 2002) * (3 * 2001) * ... * (2003 * 1)

We can observe that each pair is of the form (N * (2004 - N)), where N ranges from 1 to 2003. So, we can rewrite the expression as:

(1 * (2004 - 1)) * (2 * (2004 - 2)) * (3 * (2004 - 3)) * ... * (2003 * (2004 - 2003))

Simplifying this expression, we get:

2003 * 2002 * 2001 * ... * 3 * 2 * 1

This is the product of the first 2003 natural numbers, which is equal to 2003!. Therefore, the expression can be written as:

2003!

Now, let's go back to the original expression (2003)(334)(x) and substitute the value of the expression we just found:

(2003)(334)(x) = (2003)(2003!)

We need to find the value of x. Dividing both sides of the equation by (2003)(334), we get:

x = 2003!

Using the factorial notation, we can write this as:

x = 2003!

The factorial of a number n is defined as the product of all positive integers less than or equal to n. In this case, the factorial of 2003 is:

x = 2003 * 2002 * 2001 * ... * 3 * 2 * 1

Therefore, the value of x is 2003.

Conclusion:
The value of x in the expression (2003)(334)(x) is 2003. Therefore, the correct answer is option 'A'.