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JEE 2023 Mathematics PYQ — Five digit numbers are formed using the digits with repetitions a… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Five digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example, the number $77777$ has serial number $1$ . Then the serial number of $35337$ is

Choose the correct answer:

A.
1436
(Correct Answer)
B.
1435
C.
1453

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1456

Correct Answer:
1436

Explanation

Solution

Numbers starting with $7$ (any, any, any, any): $5^4 = 625$

Numbers starting with $5$ (any, any, any, any): $5^4 = 625$

Numbers starting with $37$ : $5^3 = 125$

Numbers starting with $357$ : $5^2 = 25$

Numbers starting with $355$ : $5^2 = 25$

Numbers starting with $3537$ : $5^1 = 5$

Numbers starting with $3535$ : $5^1 = 5$

Next numbers: $35337$ (Serial No. $1$ )

Total Serial Number = $625 + 625 + 125 + 25 + 25 + 5 + 5 + 1 = 1436$

Explanation

Solution