Class JEE Mathematics Sets, Relations, and Functions Q #1054
KNOWLEDGE BASED
APPLY
4 Marks 2020 JEE Main 2020 (Online) 4th September Evening Slot MCQ SINGLE
Let $\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$ where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s, then $n$ is equal to:
(A) $30$
(B) $50$
(C) $15$
(D) $45$
Prev Next
Correct Answer: A
Explanation
$\bigcup_{i=1}^{50} X_i = X_1, X_2,....., X_{50} = 50$ sets. Given each sets having $10$ elements.
So total elements = $50 \times 10$
$\bigcup_{i=1}^{n} Y_i = Y_1, Y_2,....., Y_n = n$ sets. Given each sets having $5$ elements.
So total elements = $5 \times n$
Now each element of set $T$ contains exactly $20$ of sets $X_i$.
So number of effective elements in set $T = \frac{50 \times 10}{20}$
Also each element of set $T$ contains exactly $6$ of sets $Y_i$.
So number of effective elements in set $T = \frac{n \times 5}{6}$
$\therefore \frac{50 \times 10}{20} = \frac{n \times 5}{6}$
$\Rightarrow n = 30$

More from this Chapter

NUMERICAL
Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n 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
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:
MCQ_SINGLE
Let $A = \{-2, -1, 0, 1, 2, 3\}$. Let R be a relation on $A$ defined by $xRy$ if and only if $y = \max\{x, 1\}$. Let $l$ be the number of elements in R. Let $m$ and $n$ be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then $l + m + n$ is equal to
NUMERICAL
Let A = {n $\in$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $\in$ {1, 2, ......., 100}}. Then the sum of all the elements of A $\cap$ B is ____________.
View All Questions