JEE 2023 Mathematics PYQ — The letters of the word OUGHT are written in all possible ways an… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is:
Choose the correct answer:
A.
84
B.
79
C.
89
(Correct Answer)
D.
86
Correct Answer:
89
Explanation
Step 1: Alphabetical Order
Word OUGHT ke letters ka alphabetical order hai:
G, H, O, T, U
Step 2: TOUGH tak pahunchne ke liye words count karna
G se shuru hone wale words:
Pahla letter G fix kar diya, baaki bache 4 letters (H,O,T,U) ko arrange karne ke tarike:
4!=24
H se shuru hone wale words:
Pahla letter H fix kiya, baaki bache 4 letters ko arrange karne ke tarike:
4!=24
O se shuru hone wale words:
Pahla letter O fix kiya, baaki bache 4 letters ko arrange karne ke tarike:
4!=24
T se shuru hone wale words:
Ab hum target word T tak pahunch gaye hain. Ab dusre letter par dhyan dete hain alphabetical order mein:
TG... se shuru hone wale words (3 letters bache): 3!=6
TH... se shuru hone wale words (3 letters bache): 3!=6
TO... ab hum target ke dusre letter tak pahunch gaye. Ab teesre letter par aate hain:
TOG... se shuru hone wale words (2 letters bache): 2!=2
TOH... se shuru hone wale words (2 letters bache): 2!=2
TOT... (Ye sambhav nahi kyunki 'T' ek baar use ho chuka hai).
TOU... hum target ke teesre letter tak pahunch gaye. Ab chauthe letter par:
TOUG... hum target ke chauthe letter tak pahunch gaye.
TOUGH (Ye wahi word hai jo hume chahiye). Iska number 1 hoga.
Step 3: Total Rank (Serial Number) calculate karna
Serial Number=24+24+24+6+6+2+2+1
Serial Number=72+12+4+1
Serial Number=89
Correct Option: (3) 89
Explanation
Step 1: Alphabetical Order
Word OUGHT ke letters ka alphabetical order hai:
G, H, O, T, U
Step 2: TOUGH tak pahunchne ke liye words count karna
G se shuru hone wale words:
Pahla letter G fix kar diya, baaki bache 4 letters (H,O,T,U) ko arrange karne ke tarike:
4!=24
H se shuru hone wale words:
Pahla letter H fix kiya, baaki bache 4 letters ko arrange karne ke tarike:
4!=24
O se shuru hone wale words:
Pahla letter O fix kiya, baaki bache 4 letters ko arrange karne ke tarike:
4!=24
T se shuru hone wale words:
Ab hum target word T tak pahunch gaye hain. Ab dusre letter par dhyan dete hain alphabetical order mein:
TG... se shuru hone wale words (3 letters bache): 3!=6
TH... se shuru hone wale words (3 letters bache): 3!=6
TO... ab hum target ke dusre letter tak pahunch gaye. Ab teesre letter par aate hain:
TOG... se shuru hone wale words (2 letters bache): 2!=2
TOH... se shuru hone wale words (2 letters bache): 2!=2
TOT... (Ye sambhav nahi kyunki 'T' ek baar use ho chuka hai).
TOU... hum target ke teesre letter tak pahunch gaye. Ab chauthe letter par:
TOUG... hum target ke chauthe letter tak pahunch gaye.
TOUGH (Ye wahi word hai jo hume chahiye). Iska number 1 hoga.
Step 3: Total Rank (Serial Number) calculate karna
