JEE Main 2023 — Mathematics Algebra

Number of five-digit numbers formed using the digits $0,2,3,4,7,9$0,2,3,4,7,9 with $2$2 at the first place is

$$=6\times 6\times 6\times 6=1296$$=6×6×6×6=1296

Since, $2\underset{6}{+}\underset{6}{+}\underset{6}{+}\underset{6}{+}=1296$26+​6+​6+​6+​=1296

Number of five-digit numbers formed using the given digits with $3$3 at the first place is

$$=1296$$=1296

Since, $3\underset{6}{+}\underset{6}{+}\underset{6}{+}\underset{6}{+}=1296$36+​6+​6+​6+​=1296

Number of five-digit numbers formed using the given digits with $40$40 at the first place is

$$=216$$=216

Since, $40\underset{6}{+}\underset{6}{+}\underset{6}{+}=216$406+​6+​6+​=216

And,

$$420\underset{6}{+}\underset{6}{+}=36$$4206+​6+​=36

$$422\underset{6}{+}\underset{6}{+}=36$$4226+​6+​=36

$$423\underset{6}{+}\underset{6}{+}=36$$4236+​6+​=36

$$424\underset{6}{+}\underset{6}{+}=36$$4246+​6+​=36

$$427\underset{6}{+}\underset{6}{+}=36$$4276+​6+​=36

$$4290\underset{6}{+}=6$$42906+​=6

$$42920=1$$42920=1

$$42922=1$$42922=1

$$42923=1$$42923=1

Required serial number is

$$=1296\times 2+216+5\times 36+6+1+1+1=2997$$=1296×2+216+5×36+6+1+1+1=2997