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JEE MATHEMATICS MCQ: SET THEORY

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\left\{ {n\left( {n + 1} \right)\left( {2n + 1} \right):n \in Z} \right\} \subset

subset

View answer and explanation

Correct option: A

\left\{ {6k\;:k \in Z} \right\}

Option A (

\{ {6k\;:\;k \in Z} \}

) is correct because the expression

n(n+1)(2n+1)

is always divisible by 6 for any integer n.

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