JEE Main 2025 (Online) 24th January Evening ShiftQuestion 1
Number of functions $f:\{1,2,\ldots,100\}\to\{0,1\}$, that assign $1$ to exactly one of the positive integers less than or equal to $98$, is equal to $\_\_\_\_\_\_\_\_$ .
Permutation and Combination
Answer$392$
Solution
Concept. Only the numbers $1..98$ are restricted. $99$ and $100$ can map to $0$ or $1$ freely. Formulas used. (1) Multiplication principleStep 1 - Which of $1..98$ maps to 1. $98$ ways; the other 97 map to $0$. Step 2 - Values at 99 and 100. $2\cdot2=4$ ways. Step 3 - Total. $98\cdot4=392$. Answer: 392