JEE Main 2026 Model Paper 1

(a) 5 ball are identical & 3 boxes are different so no. of ways each box can be filled such that no box remain empty.
=‌5−1C3−1=‌4C2=6
option s is correct match.
(b) Here balls are different & box are identical.
Case-1. 1.1.3 ⇒‌

‌5C1.‌4C1

2!

=10
Case-2. 1.2.2⇒‌

‌5C1.‌4C2

2!

=15
So total no. of ways =25
Option q is correct match.
(c) Balls as wall as boxes are identical
Case-1 1.1.3
Case-2 1.2.2
So there are two cases only
Option p is correct match.
(d)
‌35−‌3C125+‌3C21
‌243−96+3
‌=150