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

MCQ_SINGLE
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor transitive
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
Consider the sets $A = \{(x, y) \in R \times R : x^2 + y^2 = 25\}$, $B = \{(x, y) \in R \times R: x^2 + 9y^2 = 144\}$, $C = \{(x, y) \in Z \times Z: x^2 + y^2 \leq 4\}$ and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:
NUMERICAL
Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on $A \times B$ by $(a_1, b_1) R(a_2, b_2)$ if and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $R$ is __________.
NUMERICAL
Let $A=\{0,3,4,6,7,8,9,10\}$ and $R$ be the relation defined on $A$ such that $R=\{(x, y) \in A \times A: x-y$ is odd positive integer or $x-y=2\}$. The minimum number of elements that must be added to the relation $R$, so that it is a symmetric relation, is equal to ____________.
View All Questions