NIMCET 2025 Paper

1. Total even numbers
Sequence: 100, 102, ..., 998
This is an A.P. with $\mathit{a}=100,\mathit{d}=2$, last term 998 .
$\mathit{n}=\frac{998-100}{2}+1=\frac{898}{2}+1=449+1=450.$
So, 450 even numbers.
2. Even numbers divisible by $3⟶$ multiples of 6
Between 100 and 998:
- First multiple of $6\ge 100$ is $102\left(6\times 17\right)$
- Last multiple of $6\le 998$ is $996\left(6\times 166\right)$
Count:
$166-17+1=150$
3. Even numbers divisible by $5⟶$ multiples of $10$
Between 100 and 998:
- First: $100=10\times 10$
- Last: $990=10\times 99$
Count:
$99-10+1=90$

4. Even numbers divisible by both 3 and $5⟶$ multiples of 30
Between 100 and 998:
- First: $120=30\times 4$
- Last: $990=30\times 33$
Count:
$33-4+1=30$
5. Use inclusion-exclusion on even numbers
Even numbers divisible by 3 or 5 :
$150+90-30=210.$
6. Not divisible by 3 or 5
$450-210=240.$