JEE Mathematics Sets, Relations, and Functions Q #1069
KNOWLEDGE BASED
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4 Marks 2015 JEE Main 2015 (Offline) MCQ SINGLE
Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set $A \times B$, each having atleast three elements are
(A) 219
(B) 256
(C) 275
(D) 510
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Correct Answer: A
Explanation
Given, $n(A) = 4$, $n(B) = 2$

$\Rightarrow n(A \times B) = 8$

Total number of subsets of set $(A \times B) = 2^8$

Number of subsets of set $A \times B$ having no element (i.e. $\phi$) = $1$

Number of subsets of set $A \times B$ having one element = $^8C_1$

Number of subsets of set $A \times B$ having two elements = $^8C_2$

$\therefore$ Number of subsets having atleast three elements = $2^8 - (1 + ^8C_1 + ^8C_2)$ = $2^8 - 1 - 8 - 28$ = $2^8 - 37$ = $256 - 37 = 219$

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