UPSC Prelims 2005 Q112: Science & Technology – Quantitative Aptitude
- (a) 60
- (b) 72
- (c) 120
- (d) None of the above
Answer: (d) None of the above
Explanation
> Note for students: As printed, the question has one condition (B never ahead of A), which gives 360 arrangements, so the correct option is (d) None of the above. Some sources show a second condition about C, which gives 120. Read the stem in your paper carefully.
Seating six persons with B never ahead of A
| Step | Result |
|---|---|
| Total arrangements | 6! = 720 |
| Condition | B is never ahead of A, so in every arrangement A precedes B |
| Valid arrangements | Exactly half of the 720, as A-before-B and B-before-A are equally many: 720 / 2 = 360 |
With only the condition that B never sits ahead of A, half of the 720 arrangements qualify, which gives 360; this is not among 60, 72 and 120, so the answer is 'None of the above'. (Some copies add a second condition that C never sits ahead of B, which would give 120, but that is not in the stem as printed.)
Answer: (d) None of the above (the correct count is 360).
Why each option is right or wrong
- (a) Incorrect. 60 is far below 360.
- (b) Incorrect. 72 is far below 360.
- (c) Incorrect. 120 would need a second ordering condition on C.
- (d) CORRECT. The count is 360, which is none of the listed numbers.
Key point
One fixed order between two persons halves the arrangements; between three persons divides by 6.
Remember
With B never ahead of A among six persons there are 360 arrangements.
Common mistakes
- Dividing by 6 as if three persons had a fixed order.
- Counting positions for A and B separately.
- Not reading the stem for how many conditions there are.
Exam tip
Two persons in fixed relative order: n! / 2.
Sources
- NCERT Class XI Mathematics — Permutations and Combinations
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Permutations and Combinations)