UPLIFTjee
Question 37 — JEE Main 24 Jan 2026 (S I)
Question
The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits $0,1,2,5,9$, if the repetition of the digits is allowed, is $\_\_\_\_$ [JEE MAIN 24 Jan 2026 S I]
Solution
| 5 | x | y | z |
|---|
$\quad \mathrm{x}, \mathrm{y}, \mathrm{z} \in\{0,1,2,5,9\}$
\[
\frac{5+x+y+z}{3}=1+\frac{x+y+z+2}{3} \in I
\]
| $\mathrm{x}+\mathrm{y}+\mathrm{z}$ | $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ | ways |
|---|---|---|
| 1 | $0,0,1$ | $3!/ 2!=3$ |
| 4 | $0,2,2$ | $3!/ 2!=3$ |
| 4 | $1,1,2$ | $3!/ 2!=3$ |
| 7 | $0,2,5$ | $3!=6$ |
| 7 | $1,1,5$ | $3!/ 2!=3$ |
| 10 | $0,1,9$ | $3!=6$ |
| 10 | $0,5,5$ | $3!/ 2!=3$ |
| 13 | $9,2,2$ | $3!/ 2!=3$ |
| 16 | $2,5,9$ | $3!=6$ |
| 19 | $9,9,1$ | $3!/ 2!=3$ |
| 19 | $5,5,9$ | $3!/ 2!=3$ |
Total possible ways of $\mathrm{x}, \mathrm{y}, \mathrm{z}=42$ Answer(42)