QJEEM22Mab3b2: JEE Main 2022 Mathematics - Class 11 JEEM22Mab3b2 Solution: The number of 3-digit odd numbers, whose sum of digits is a…

For odd number unit place shall be $1,3,5,7$ or 9 .

$\therefore$ x y 1, x y 3, x y 5, x y 7, x y 9 are the type of numbers. numbers.

If $x \,y\, 1$ then $x+y=6,13,20$ ... Cases are required

i.e., $6+6+0+\ldots=12$ ways

If $x \, y \,3$ then

$x+y=4,11,18, \ldots$ Cases are required

i.e., $4+8+1+0 \ldots=13$ ways

Similarly for $x \,y \,5$ , we have $x+y=2,9,16, \ldots$

i.e., $2+9+3=14$ ways

for $x \,y$ we have

$x+y=0,7,14, \ldots$

i.e., $0+7+5=12$ ways

And for $x$ y we have

$$x+y=5,12,19\dots$$

i.e., $5+7+0 \ldots=12$ ways

$\therefore$ Total 63 ways