JEE 2023 — Mathematics PYQ

Solution

Humein yeh dekhna hai ki 42923 se pehle kitne numbers aate hain. Hamare paas digits hain: $\{0,2,3,4,7,9\}$ (Total 6 digits).

1. Numbers starting with 2 and 3:

   Pehle place par 2 ya 3 ho sakta hai (2 options). Baaki 4 places par koi bhi 6 digits aa sakte hain.

   $$2\times 6\times 6\times 6\times 6=2\times 6^4=2592$$

2. Numbers starting with 40:

   Pehle do digits 4 aur 0 fix hain. Baaki 3 places ke liye:

   $$1\times 1\times 6\times 6\times 6=6^3=216$$

3. Numbers starting with 420, 422, 423, 424, 427:

   Yeh 5 cases hain. Har case mein baaki 2 places ke liye $6\times 6$ options hain:

   $$5\times (6\times 6)=5\times 36=180$$

4. Numbers starting with 4290:

   Baaki 1 place ke liye 6 options hain:

   $$1\times 1\times 1\times 1\times 6=6$$

5. Numbers starting with 4292:

   • 42920 (Serial no. 1)

   • 42922 (Serial no. 2)

   • 42923 (Serial no. 3)

Total Serial Number: