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JEE Main 20137 April

Exam: JEE Main
Year: 2013
Date: 7 April
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2013 · 7 April · Mathematics · Sets and Relations

Let A and B be two sets containing 2 elements and 4 elements...

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

Options

A $219$
B $211$
C $256$
D $220$

Correct answer

A. $219$

Step-by-step solution

As

n\left(A\right) = 2

and

n\left(B\right) = 4

Hence

n\left(A \times B\right) = 8

Now subsets of

A \times B

containing

3

or more elements will be
=Total

-

(no element

-

one element

- 2

elements)

=

{2}^{8}{-}^{8}{C}_{0}{-}^{8}{C}_{1}{-}^{8}{C}_{2} = 219

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