JEE MATHEMATICS MCQ: SET THEORY

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Analyzing +4 | -1

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

View answer and explanation

Correct option: B

\frac{1}{2}\left(10^{2006}-8^{2006}\right)

Option A (

\frac{1}{2}(10^{2006}+8^{2006})

) is incorrect. The correct answer is

\frac{1}{2}(10^{2006}-8^{2006})

because it represents the number of 2007-place decimal integers with an odd number of 9s in each sequence.

More Questions from SET THEORY

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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

A=\{x: x

\}

B=\{x: x

A-B

F(n)

n

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

40 \%

A, 20 \%

10 \%

C

A

C

4 \%

A

C

2 \%

A

A

B

A

B

A \cup B

{A} \cap {B}