JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Sets Relations and Functions

Let

⋃_{i = 1}^{50} X_{i} = ⋃_{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:

Answer: (B)

Solution

Let

T

have

R

elements. Counting memberships in the

X_{i}

, each of the

50

sets has

10

elements and each element of

T

lies in exactly

20

of them, so

50 \times 10 = 20 R

, giving

R = 25

. Counting memberships in the

Y_{i}

the same way, each of the

n

sets has

5

elements and each element lies in exactly

6

of them, so

5 n = 6 R = 6 \times 25 = 150

, hence

n = 30

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option