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Q.

 Number of Nine-letter words that can be formed using all the letters of the word “KAMALJEET” if alike letters are never adjacent is K(6!) then K is 

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answer is 77.

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Detailed Solution

P = both A comes together 
Q = both E comes together
nP'∩Q'=n(P∪Q)'=n(U)−n(P∪Q)=9!2!2!−8!2!+8!2!−7!=9!2!2!−[8!−7!]=9.87!4−[7.7!]=77.6!   

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