QJEEM22Ma73a1: JEE Main 2022 Mathematics - Class 11 JEEM22Ma73a1 Solution: Let A = {n N : H.C.F. (n, 45) = 1} and Let B = {2k : k {1, 2,…

Sum of all elements of A $\cap$ B = 2 [Sum of natural numbers upto 100 which are neither divisible by 3 nor by 5]

$= 2\left[ {{{100 \times 101} \over 2} - 3\left( {{{33 \times 34} \over 2}} \right) - 5\left( {{{20 \times 21} \over 2}} \right) + 15\left( {{{6 \times 7} \over 2}} \right)} \right]$

$= 10100 - 3366 - 2100 + 630$

$= 5264$