Introduction
In this problem, we have to find the number of 9 lettered words that can be formed using all the letters of the word "MEENANSHU", in such a way that alike letters are never adjacent.

Solution
To solve the problem, we can use the concept of permutations and combinations. We can follow the following steps to find the solution:

1. Count the number of letters in "MEENANSHU". We have 9 letters in total.

2. Count the number of alike letters in "MEENANSHU". We have 2 E's and 2 N's.

3. Find the number of ways to arrange the 9 letters without any restrictions. This can be done using the formula for permutation, which is n!/(n-r)!, where n is the total number of objects and r is the number of objects taken at a time. In this case, n=9 and r=9. Therefore, the number of ways to arrange the 9 letters without any restrictions is 9!/(9-9)! = 362880.

4. Find the number of ways to arrange the 9 letters with the restriction that alike letters are adjacent. This can be done by treating each set of alike letters as a single object. Therefore, we have 7 objects to arrange - M, EE, N, A, N, S, H, U. The number of ways to arrange these objects is 7!/(2!2!) = 1260. The division by 2!2! is done because there are 2 E's and 2 N's.

5. Subtract the number of ways to arrange the 9 letters with the restriction from the number of ways to arrange the 9 letters without any restrictions to get the final answer. Therefore, the number of 9 lettered words that can be formed using all the letters of the word "MEENANSHU" if alike are never adjacent is 362880 - 1260 = 361620.

Conclusion
Therefore, the number of 9 lettered words that can be formed using all the letters of the word "MEENANSHU" if alike are never adjacent is 361620.

11.7!