Q56 / 160 · TS EAMCET 2020 (10 Sep Shift 2) · Mathematics

Numbers between 1 and 10,000 are formed using the digits 2 and 3 only once and the digit 4 twice. If the numbers thus formed are arranged in increasing order and $x, y$ represent the ranks of 4324 and 324 respectively then $x-y=$

  • Correct answer
    A
    17
  • B
    31
  • C
    14
  • D
    16

Solution

Number between 1 and 10000 are formed using digit 2 and 3 only one and digit 4 twice $\text { one-digit }=\{2,3,4\}=3$ $\text { Two digit }=\{23,24,32,34,42,43,44\}=7$ Three digit number $=\{234,243,244,324,342,344$ $423,432,424,434,442,443\}=12$ Four digit number $=\{2344,2434,2443,3244,3424$, $3442,4234,4324 \ldots\}$ Rank of $324=14$ Rank of $4324=3+7+12+9=31$ $\therefore \quad x-y=31-14=17$

Hence, the correct answer is option: 'A'.

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