NIMCET 2025 Paper

Reason (simple and clear)- Elements of $A$ grow exponentially because of $5^n$.- Elements of $B$ grow linearly because $16(n-1)$.Exponential expressions rarely equal linear expressions except for very small values of $n$.Checking small $n$ :- $n=1$ : $A=5^1-4-1=0, B=16(0)=0 \rightarrow$ match- $n=2$ : $A=25-8-1=16, B=16(1)=16 \rightarrow$ match- $n=3$ : $A=125-12-1=112, B=16(2)=32 \rightarrow$ no match- For larger $n, 5^n$ grows too fast → no further matches.Thus, the intersection contains only a finite number of elements (in fact exactly two).So the correct conclusion:$A \cap B$ is a finite set