JEE MATHEMATICS MCQ: SET THEORY

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Analyzing +4 | -1

Let

Z

denote the set of all integers and

A = \left\{ {\left( {a,b} \right):{a^2} + 3{b^2} = 28,\;\;a,\;b \in Z} \right\}

and

B = \{ \left( {a,\;b} \right):a > b,\;a,\;b \in Z\}

. Then, the number of elements in

A \cap B

View answer and explanation

Correct option: D

Option D (6) is correct because by finding all possible integer pairs (a, b) satisfying the equation and then filtering those where a > b, we arrive at a total of 6 elements in the intersection.

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