300! is 1*2*3*...*300
Now there are 27 multiples of 11 from 1 to 300, so they will include 11 as a prime factor atleast once.
121 and 242 will contain an extra 11, all other will contain 11 as a factor only once.
So, total number of 11's = 27+2 = 29.
So, exponent of 11 is 29 i.e. option C.