JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q27

MathematicsInteger+4 / -1Question 27 of 90

The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

Your answer

Answer and worked solution

Official answer: 243

Patterns AAB, ABA, BAA with $A\ne B$ and no leading zero.

Count. All such strings: $3\times10\times9=270$ ; those starting with 0: AAB with A = 0 (9), ABA with A = 0 (9), BAA with B = 0 (9), i.e. 27.

Total. $270-27=243$ (checked by enumeration).

Answer: 243

JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 27