JEE MATHEMATICS MCQ: SET THEORY

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Application +4 | -1

Let

X

and

Y

be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then,

n\left( {X \cap Y} \right)

is equal to

View answer and explanation

Correct option: D

Option D (12) is correct because the intersection of the sets of divisors of 400 and 1000 is the set of divisors of their greatest common divisor (GCD), which is 200, and 200 has 12 divisors.

More Questions from SET THEORY

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Let

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

is If

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

and

b N \cap c N=d N

, where

a, b, c \in N

and

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

\}

and

B=\{x: x

is a multiple of 5}, then

A-B

is equal to If

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

and

4 \%

buy newspapers

A

and

C

. If

2 \%

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

A

only is