QJEEM22Ma66d2: JEE Main 2022 Mathematics - Class 11 JEEM22Ma66d2 Solution: The number of 5-digit natural numbers, such that the product of …

Factors of 36 = 2² . 3² . 1

Five-digit combinations can be

(1, 2, 2, 3, 3) (1, 4, 3, 3, 1), (1, 9, 2, 2, 1)

(1, 4, 9, 11) (1, 2, 3, 6, 1) (1, 6, 6, 1, 1)

i.e., total numbers

${{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {3!}} + {{5!} \over {2!}} + {{5!} \over {3!2!}}$

$= (30 \times 3) + 20 + 60 + 10 = 180$ .