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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to_______.

Choose the correct answer:

A.
26664
(Correct Answer)
B.
26564
C.
24656
D.
None

Correct Answer:

26664

Explanation

Digits: ${1, 2, 2, 3}$

Total numbers formed = $\frac{4 !}{2 !} = \frac{24}{2} = 12$

Sum of digits at each place = $\frac{12}{4} \times (1 + 2 + 2 + 3) = 3 \times 8 = 24$

Total Sum = $24 \times (1000 + 100 + 10 + 1) = 24 \times 1111 = 26664$

Explanation

Digits: ${1, 2, 2, 3}$

Total numbers formed = $\frac{4 !}{2 !} = \frac{24}{2} = 12$

Sum of digits at each place = $\frac{12}{4} \times (1 + 2 + 2 + 3) = 3 \times 8 = 24$

Total Sum = $24 \times (1000 + 100 + 10 + 1) = 24 \times 1111 = 26664$

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