Match the pairs in the following questions by writing the corresponding letters only.
B. The number of binary strings of length of $2n$ with
an equal number of $0’s$ and $1’s$.
Length $= 6n$, as it is palindrome, we need to select only the first half part of the string.
Total length to consider is $3n$ (Remaining $3n$ will be revese of this $3n$)
Now, choose $n \ 0's$ out of $3n$. So Q is correct for D.
The option for the number of binary trees is incorrect.
Number of BSTs (Binary Search Trees) = nth Catalan Number, whereas number of Binary Tress = (n!) * nth Catalan number.
Source : https://www.geeksforgeeks.org/total-number-of-possible-binary-search-trees-with-n-keys/