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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

If A B are two sets such that n(A × B) = 60 n(A) = 12 also n(A B) =...

If

A B

are two sets such that

n\left(A \times B\right) = 60 n\left(A\right) = 12

also

n\left(A \cap B\right) = K

, then the sum of maximum & minimum possible value of

K

is

Options

A $17$
B $12$
C $5$
D $7$

Correct answer

C. $5$

Step-by-step solution

n \left(B\right) = \dfrac{n \left(A \times B\r right)}

{n\left(A\right)} =5

∴n\left(A \cap B\right)

has minimum value

= 0

and

n \left(A \cap B\right)

has maximum value

= n\left(B\right) =5

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