1.Set Theory
medium

माना $A =\{ n \in N :$ म.स.प. $( n , 45)=1\}$ तथा माना $B =\{2 k : k \in\{1,2, \ldots, 100\}\}$ है। तब $A \cap B$ के सभी अवयवों का योगफल है

A

$5264$

B

$5265$

C

$5255$

D

$5235$

(JEE MAIN-2022)

Solution

Sum of elements in $A \cap B$

$=\underbrace{(2+4+6+\ldots+200)}_{\text {Multiple of } 2}-\underbrace{(6+12+\ldots+198)}_{\text {Multiple of } 2 \; and\; 3 \text { i.e. } 6}$

$\quad-\underbrace{(10+20+\ldots+200)}_{\text {Multiple of } 5 \; and \; 2 \text { i.e. } 10}+\underbrace{(30+60+\ldots+180)}_{\text {Multiple of } 2,5 \; and \;3 \text { i.e. } 30}$

$=5264$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.