JEE MATHEMATICS MCQ: SET THEORY

1 Hard

1 of 1

Analyzing +4 | -1

Suppose

{A_1},\;{A_2}, \ldots ,{A_{30}}

are thirty sets, each having 5 elements and

{B_1},\;{B_2},\; \ldots ,\;{B_n}

are

n

sets each with 3 elements, let

\mathop \cup \nolimits_{i = 1}^{30} {A_i} = \mathop \cup \nolimits_{j = 1}^n {B_j} = S

and each element of S belongs to exactly 10 of the

{A_i}{\,^\prime }s

and exactly 9 of the

{B_j}

's. Then,

n

is equal to

View answer and explanation

Correct option: C

Option C (45) is correct because by equating the total number of elements counted in sets A_i and B_j, we can solve for n, the number of sets B_j.

More Questions from SET THEORY

Practice All Chapter MCQs →

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