Class JEE Mathematics Sets, Relations, and Functions Q #1053
KNOWLEDGE BASED
APPLY
4 Marks 2020 JEE Main 2020 (Online) 5th September Morning Slot MCQ SINGLE
A survey shows that $73$% of the persons working in an office like coffee, whereas $65$% like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be :
(A) $63$
(B) $36$
(C) $54$
(D) $38$
Prev Next
Correct Answer: B
Explanation
Let C be the set of persons who like coffee and T be the set of persons who like tea. Given: $n(C) = 73$ and $n(T) = 65$. Also, $n(C \cup T) \le 100$. Using the formula for the union of two sets: $n(C \cup T) = n(C) + n(T) - n(C \cap T)$. Let $x = n(C \cap T)$ be the percentage of people who like both coffee and tea. So, $n(C \cup T) = 73 + 65 - x \le 100$. This implies $138 - x \le 100$, which gives $x \ge 38$. Also, $x$ must be less than or equal to both $73$ and $65$ since $x$ represents the intersection. So, $x \le 73$ and $x \le 65$. Therefore, $38 \le x \le 65$. Since $x$ must be in the range $[38, 65]$, the value $x=36$ is not possible.

More from this Chapter

MCQ_SINGLE
The relation $R = {(x, y) : x, y ∈ Z$ and $x + y$ is even $}$ is:
MCQ_SINGLE
Consider the following two binary relations on the set $A = {a, b, c}$: $R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)}$ and $R_2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$. Then:
NUMERICAL
Let $A=\{1,2,3,4,5,6,7\}$. Define $B=\{T \subseteq A$ : either $1 \notin T$ or $2 \in T\}$ and $C=\{T \subseteq A: T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is ________________.
MCQ_SINGLE
Let $R$ be a relation on $Z \times Z$ defined by $(a, b)R(c, d)$ if and only if $ad - bc$ is divisible by $5$. Then $R$ is
MCQ_SINGLE
Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$. Let $R$ be a relation defined on $A \times B$ such that $R = {((a_1, b_1), (a_2, b_2)): a_1 \le b_2 \text{ and } b_1 \le a_2}$. Then the number of elements in the set R is :
View All Questions