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JEE MATHEMATICS MCQ: SET THEORY

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From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is

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Correct option: D

14

Option D (14) is correct because it represents the largest possible number of students who could have passed all three examinations, derived from the given constraints on the number of students passing in pairs of subjects.

More Questions from SET THEORY

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S

be the set of all those 2007-place decimal integers

2 a_1 a_2 a_3 \ldots . . a_{2006}

which contain odd number of digit 9 in each sequence

a_1, a_2, a_3, \ldots ., a_{2006}

. The cardinal number of

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

are coprime, then Which of the following cannot be the number of elements in the power set of any finite set? If

A=\{x: x

is a multiple of 3

\}

B=\{x: x

is a multiple of 5}, then

A-B

F(n)

denotes the set of all divisors of

n

except 1 , what is the least value of y satisfying

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

? In a town of 10000 families, it was found that

40 \%

families buy newspaper

A, 20 \%

families buy newspaper B and

10 \%

families buy newspaper

C

, 5% families buy newspapers

A

and B, 3% buy newspapers B and

C

4 \%

A

C

2 \%

families buy all the three newspapers, then number of families which buy

A