• 072920 77839
  • info@smartachievers.in
Menu
Back
  • JEE ADVANCE
  • JEE MAIN
  • NEET
  • BITSAT
  • CBSE BOARD
  • UP BOARD
  • CUET
JEE ADVANCE
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
JEE MAIN
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
NEET
  • CLASS XI - XII
  • CRASH COURSE
BITSAT
  • CLASS XI - XII
CBSE BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
  • CLASS VI
  • CLASS VII
  • CLASS VIII
UP BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
CUET
  • CRASH COURSE
Courses


Solution


Q.

Number of functions f:{1,2,...,100}→{0,1}, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to __________.          [2025]

Ans.

(392)

Given : f:{1,2,...,100}→{0,1}

Number of ways to connect {1, 2, ..., 98} to 1 = 98

Number 99 can connect either 0 or 1 ⇒ 2 ways

Similarly, 100 can connect either 0 or 1 ⇒ 2 ways

∴   Total number of functions for the given condition that assign 1 to exactly one of positive integers ≤ 98 is given by 98×2×2 = 392.