JEE Main 2023 — Mathematics Algebra

Given,

Five digit numbers are formed using the digits $1,2,3,5,7$1,2,3,5,7 with repetitions and are written in descending order with serial numbers,

Now number of $5$5 digit numbers starting with digit $1$1 will be $=5\times 5\times 5\times 5=625$=5×5×5×5=625

Number of $5$5 digit numbers starting with digit $2$2 will be $=5\times 5\times 5\times 5=625$=5×5×5×5=625

Number of $5$5 digit numbers starting with digit $31$31 will be $=5\times 5\times 5=125$=5×5×5=125

Number of $5$5 digit numbers starting with digit $32$32 will be $=5\times 5\times 5=125$=5×5×5=125

Number of $5$5 digit numbers starting with digit $33$33 will be $=5\times 5=25$=5×5=25

Number of $5$5 digit numbers starting with digit $351$351 will be$=5\times 5=25$=5×5=25

Number of $5$5 digit numbers starting with digit $352$352 will be $=5\times 5=25$=5×5=25

Number of $5$5 digit numbers starting with digit $3531$3531 will be $=5$=5

And number of $5$5 digit numbers starting with digit $3532$3532 will be $=5$=5

And before $35337$35337 will be $4$4 numbers, So rank of $35337$35337 will be $1690$1690

So, in descending order serial number will be

$$3125-1690+1=1436$$3125−1690+1=1436