All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS
Answer: 553
Solution
Letters of GTWENTY sorted alphabetically: E, G, N, T, T, W, Y (7 letters, T repeated twice).
Words starting with E: fix E, arrange the remaining 6 letters (G, N, T, T, W, Y): .
Words starting with G, second letter before the actual T: remaining letters after G are E, N, T, T, W, Y.
Words starting with GT (matches actual), third letter before the actual W: remaining after G, T are E, N, T, W, Y.
Words starting with GTW (matches actual): remaining letters E, N, T, Y, and the actual continuation E-N-T-Y is already the smallest ordering at each remaining position, so no further words precede GTWENTY.
Total words before GTWENTY: . Adding the word itself:
Key confirmed: 553.
Words starting with E: fix E, arrange the remaining 6 letters (G, N, T, T, W, Y): .
Words starting with G, second letter before the actual T: remaining letters after G are E, N, T, T, W, Y.
- second letter E:
- second letter N:
Words starting with GT (matches actual), third letter before the actual W: remaining after G, T are E, N, T, W, Y.
- third letter E:
- third letter N:
- third letter T:
Words starting with GTW (matches actual): remaining letters E, N, T, Y, and the actual continuation E-N-T-Y is already the smallest ordering at each remaining position, so no further words precede GTWENTY.
Total words before GTWENTY: . Adding the word itself:
Key confirmed: 553.
JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Integer answer