JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Analyzing +4 | -1

Consider the set

A

of all determinants of order 3 with entries 0 or 1 only. Let

B

be the subset of

A

consisting of all determinants with value 1. Let

C

be the subset of the set of all determinants with value

- 1.

Then

View answer and explanation

Correct option: B

B

has as many elements as

C

Option B (

B

has as many elements as

C

) is correct because interchanging two rows or columns in a determinant changes its sign, creating a one-to-one correspondence between determinants with value 1 and -1.

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