Class JEE Mathematics Sets, Relations, and Functions Q #1069
KNOWLEDGE BASED
APPLY
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
Prev Next
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 = $2^8 - (1 + ^8C_1 + ^8C_2)$ = $2^8 - 1 - 8 - 28$ = $2^8 - 37$ = $256 - 37 = 219$

More from this Chapter

NUMERICAL
Let A = {n $\in$ N | n2 $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.
NUMERICAL
For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________
MCQ_SINGLE
If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :
MCQ_SINGLE
Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$. Then the number of elements in the relation $R = {((a_1, b_1), (a_2, b_2)) \in (A \times B, A \times B) : a_1$ divides $b_2$ and $a_2$ divides $b_1}$ is :
NUMERICAL
Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.
View All Questions