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
26 The sum of all the elements of the set $$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$ is __________.
NUMERICAL
The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is __________.
MCQ_SINGLE
Let $A = { (\alpha, \beta ) \in R \times R : |\alpha - 1| \leq 4$ and $|\beta - 5| \leq 6 }$ and $B = { (\alpha, \beta ) \in R \times R : 16(\alpha - 2)^{2}+ 9(\beta - 6)^{2} \leq 144 }$. Then
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 _____________.
NUMERICAL
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is _________.
View All Questions