JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Application +4 | -1

Suppose

A_1, A_2, \ldots A_{30}

are thirty sets, each with five elements and

{B}_1, {~B}_2, \ldots, {B}_n

are

n

sets each with three elements Let

\bigcup_{i=1}^{30} {~A}_i=\bigcup_{j=1}^n {~B}_j={S}

If each elements of

{S}

belongs to exactly ten of the

{A}_i

's and exactly nine of the

{B}_j

's then

n=

View answer and explanation

Correct option: A

Option A (45) is correct because it equates the total number of elements counted in two different ways using the given information about the sets.

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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