$A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ of $A$ is again chosen. The number of ways of choosing $P$ and $Q$, so that $P \cap Q=\phi$, is

JEE MATHEMATICS MCQ: PERMUTATIONS

1 Easy

1 of 1

Application +4 | -1

A

is a set containing

n

elements. A subset

P

A

is chosen. The set

A

is reconstructed by replacing the elements of

P

. A subset

Q

A

is again chosen. The number of ways of choosing

P

and

Q

, so that

P \cap Q=\phi

, is

View answer and explanation

Correct option: D

3^n

Option D (

3^n

) is correct because each element in set A has three possibilities: belonging to P only, Q only, or neither, ensuring P and Q have no intersection.

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r

n

1,2,3,4

\left( {m + n} \right)

n