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Mathematics · Permutations and Combinations

JEE Main 2026 — 24 January, Morning Shift — Question 22

The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits 0,1,2,5,90,1,2,5,9, if the repetition of the digits is allowed, is ____\_\_\_\_

Answer: 42

Numerical answer — enter this value.

Step-by-step solution

all different 5,0,1,9⇒⌊3=65,0,1,9 \Rightarrow\lfloor 3=6 ways 2 alike, 2 different

5,0,0,1⇒35,0,0,1 \Rightarrow 3 ways

5,1,1,2⇒35,1,1,2 \Rightarrow 3 ways

5,2,2,0⇒35,2,2,0 \Rightarrow 3 ways

5,2,2,9⇒35,2,2,9 \Rightarrow 3 ways

5,5,0,2⇒65,5,0,2 \Rightarrow 6 ways

5,5,2,9⇒65,5,2,9 \Rightarrow 6 ways

5,1,9,9⇒35,1,9,9 \Rightarrow 3 ways 3 alike, 1 different

5,5,5,0⇒35,5,5,0 \Rightarrow 3 ways

5,5,5,9⇒35,5,5,9 \Rightarrow 3 ways 2 alike, 2 other alike

5,5,1,1⇒35,5,1,1 \Rightarrow 3 ways

Total ways =42=42

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
24 January, Morning Shift
Subject
Mathematics
Chapter
Permutations and Combinations
Topic
Combinations
The number of numbers greater than 5000 , less than 9000 and… | JEE Main 2026 PYQ with Solution · DhiX AI