If X = 4 n - 3 n - 1   :   n ∈ N and Y = 9 n - 1   :   n ∈ N , where N is…

If X=4n-3n-1 : n∈N  and Y=9n-1 : n∈N, where N is the set of natural numbers, then X∪Y is equal to
  1. X
  2. Y
  3. N
  4. Y-X

Solution

X=4n-3n-1:n∈N

4n-3n-1=3+1n-3n-1

=nC03o1n+nC1311n-1+.....+nCn3n-3n-1

=1+n3+nC232+.....+3n-3n-1

=nC232+nC333+.....+3n

=32nC2+nC331+nC432+.....+3n-2

=9k, where k is a natural number.

Y=9n-1 : n∈N

∴  X⊆Y

∴  X∪Y=Y

Asked in: JEE Main 2014 (06 Apr)

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