JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Application +4 | -1

Let

\bigcup\limits_{i=1}^{50} X_i=\bigcup\limits_{j=1}^n Y_j=Z

, where each

X_i

contains 10 elements and each

Y_j

contains 5 elements. If each element of

Z

is an element of exactly 20 of sets

X_i^{\text {'s }}

and exactly 6 of sets

Y_j^{\text {'s }}

, then

n

is equal to

View answer and explanation

Correct option: C

Option C (30) is correct because by equating the total number of elements counted in two ways, we can solve for n.

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S

2 a_1 a_2 a_3 \ldots . . a_{2006}

a_1, a_2, a_3, \ldots ., a_{2006}

S

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

b N \cap c N=d N

a, b, c \in N

b, c

A=\{x: x

\}

B=\{x: x

A-B

F(n)

n

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

40 \%

A, 20 \%

10 \%

C

A

C

4 \%

A

C

2 \%

A