NDA 2019 Maths · Mathematics · Sets, Relations and Functions · easy

Let A=\3,6,9,…,30\ and B=\5,10,15,…,30\. The number of elements in A∩ B is

Single correct option

Let

A=\{3,6,9,\ldots,30\}

and

B=\{5,10,15,\ldots,30\}

. The number of elements in

A\cap B

Show answer and solution

Answer: (D) $2$

The elements common to both sets are multiples of both

3

and

5

, i.e. multiples of

\operatorname{lcm}(3,5)=15

. Within

30

these are

15

and

30

, so

n(A\cap B)=2

. The trap is to stop at

15

alone, or to count

0

because

30

is the last element of each set; check that the end element belongs to both lists before deciding.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake