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1.Set Theory
medium
ધારો કે $A=\{n \in N: H . C . F .(n, 45)=1\}$ અને ધારો કે $B=\{2 k: k \in\{1,2, \ldots, 100\}\}$.તો $A \cap B$ ના તમામ ઘટકોનો સરવાળો$\dots\dots\dots$
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
