Ten books are arranged in a row following a certain sequence. Among them 3 are History , 3 are Economics, 2 are Maths and 2 are English. From the left, there is an English book between a History and Maths book, a history book between a Maths and an English book, an Economics book between an English and a Maths Book. a Maths book between two Economics books and two Economics two Economics book between a Maths and a History book. Book of which subject is at the sixth position from the left?
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ক
English
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খ
Economics
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গ
History
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ঘ
Mathematics
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ঙ
None of the above
Mathematics is at the sixth position from the left.
Let’s decode the conditions step by step and build a consistent pattern.
We have 10 books:
- H = 3 (History)
- E = 3 (Economics)
- M = 2 (Maths)
- Eng = 2 (English)
Given relational rules (key idea: “between” constraints):
Key deductions:
- An English book is between a History and Maths book
→ Pattern: H – Eng – M or M – Eng – H - A History book is between a Maths and English book
→ M – H – Eng or Eng – H – M - An Economics book is between an English and Maths book
→ Eng – E – M or M – E – Eng - A Maths book is between two Economics books
→ E – M – E - Two Economics books are between a Maths and a History book
→ M – E – E – H or H – E – E – M
Strong structure emerges:
From rule (4):
E – M – E (fixed pattern)
From rule (5):
M – E – E – H or H – E – E – M
So combining consistent overlaps, the core block becomes:
H – E – E – M – E – E – H (core structure)
Now we still need:
- 2 English
- 1 Maths
- 1 History (extra placements)
Fitting remaining constraints, valid arrangement centers around:
H – E – E – M – E – H – E – M – H – E
Now check 6th position:
Positions:
1 H
2 E
3 E
4 M
5 E
6 H
7 E
8 M
9 H
10 E
Final Answer: C. History
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