JEE Main 2026 — Jan 24, Shift 1 — Mathematics solution

JEE Main2026Jan 24, Shift 1Mathematics

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits $0, 1, 2, 5, 9$ , if the repetition of the digits is allowed, is _____ .

Your answer

Solution

$(1) all different$

$5,0,1,9 \Rightarrow |3 = 6\text{ ways}$

$(2) 2 alike, 2 different$

$5,0,0,1 \Rightarrow 3\text{ ways}$

$5,1,1,2 \Rightarrow 3\text{ ways}$

$5,2,2,0 \Rightarrow 3\text{ ways}$

$5,2,2,9 \Rightarrow 3\text{ ways}$

$5,5,0,2 \Rightarrow 6\text{ ways}$

$5,5,2,9 \Rightarrow 6\text{ ways}$

$5,1,9,9 \Rightarrow 3\text{ ways}$

$(3) 3 alike, 1 different$

$5,5,5,0 \Rightarrow 3\text{ ways}$

$5,5,5,9 \Rightarrow 3\text{ ways}$

$(4) 2 alike, 2 other alike$

$5,5,1,1 \Rightarrow 3\text{ ways}$

$Total ways = 42$

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