$A$ 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 so that $(P \cup Q)$ is a proper subset of $A$, is

JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Analyzing +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 so that

(P \cup Q)

is a proper subset of

A

, is

View answer and explanation

Correct option: D

4^n-3^n

The correct answer is D (

4^n - 3^n

) because by considering all possible combinations of elements in subsets P and Q and subtracting the cases where their union is not a proper subset of A, we find the number of ways is

4^n - 3^n

More Questions from COMBINATIONS

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A rectangle of dimension

m \times n

(

m

and

n

being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is: Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to The number of ways choosing a committee of 4 woman and 5 men from 10 women and 9 men, if Mr.

A

refuses to serve on the committee when Ms.

B

is a member of the committee, is A man has 7 friends. In how many ways he can invite one or more of them for a tea party? If

{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

, then

n

is equal to