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Match the pairs in the following questions by writing the corresponding letters only.

 (A). The number distinct binary trees with $n$ nodes. (P). $\frac{n!}{2}$ (B). The number of binary strings of length of $2n$ with an equal number of $0’s$ and $1’s$. (Q). $\binom{3n}{n}$ (C). The number of even permutation of $n$ objects. (R). $\binom{2n}{n}$ (D). The number of binary strings of length $6n$ which are palindromes with $2n$  $0’s$. (S). $\frac{1}{1+n}\binom{2n}{n}$
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(A) - S Catalyn no  http://gatecse.in/wiki/Number_of_Binary_trees_possible_with_n_nodes

(B) - R. Choosing n locations out of 2n to place 0. Remaining automatically become 1.

(C) -P An even permutation is a permutation obtainable from an even number of two-element swaps, For a set of elements and , there are even permutations. Ref -> http://mathworld.wolfram.com/EvenPermutation.html

(D) -> Q

Length = 6n, as it is palindrome, we need to only consider half part.

Total Length to consider 3n (Remaining 3n will be revese of this 3n)

now Choosing n 0's out of 3n. So Q is correct for D.

selected
+1 vote

A - S
B - R
C - P
D - Q