NIMCET 2025 Paper

1. Total even numbersSequence: 100, 102, ..., 998This is an A.P. with $a=100, d=2$, last term 998 .$n=\frac{998-100}{2}+1=\frac{898}{2}+1=449+1=450 .$So, 450 even numbers.2. Even numbers divisible by $3 \rightarrow$ multiples of 6Between 100 and 998:- First multiple of $6 \geq 100$ is $102(6 \times 17)$- Last multiple of $6 \leq 998$ is $996(6 \times 166)$Count:$166-17+1=150$3. Even numbers divisible by $5 \rightarrow$ multiples of $1 0$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 $5 \rightarrow$ multiples of 30Between 100 and 998:- First: $120=30 \times 4$- Last: $990=30 \times 33$Count:$33-4+1=30$5. Use inclusion-exclusion on even numbersEven numbers divisible by 3 or 5 :$150+90-30=210 .$6. Not divisible by 3 or 5$450-210=240 .$