Set theory practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

1 Hard

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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.

Revision notes and key takeaways

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Key Takeaways

✓ This set contains 1 single-correct-answer MCQs on SET THEORY.
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