Correct Option (A)
The correct option is 1 and 2 only.
Based on the provided data:
- 60% of students play cricket.
- Students who do not play cricket (40% of the total) play football.
- Every football player possesses a two-wheeler. Therefore, 40% of the students have two-wheelers.
Let us evaluate each conclusion:
Conclusion 1: 60% of the students do not have two-wheelers.
- The data confirms that 40% of students (football players) have two-wheelers.
- The information does not specify whether the remaining 60% of students (cricket players) possess two-wheelers. They might or might not have them.
- Therefore, it cannot be definitively concluded that 60% of students do not have two-wheelers. This conclusion cannot be drawn from the given data.
Conclusion 2: No cricketer has a two-wheeler.
- The data states that every football player has a two-wheeler.
- It also implies that cricket players do not play football (as students who do not play cricket play football).
- However, the data does not provide any information to suggest that cricket players are prohibited from owning two-wheelers. A student can play cricket and still own a two-wheeler, as long as they are not a football player.
- Therefore, it cannot be definitively concluded that no cricketer has a two-wheeler. This conclusion cannot be drawn from the given data.
Conclusion 3: Cricket players do not play football.
- The statement "A student, who does not play cricket, plays football" establishes a clear distinction.
- This implies that the set of students who do not play cricket is identical to the set of students who play football.
- Consequently, if a student plays cricket, they belong to the group that is explicitly excluded from playing football.
- Therefore, this conclusion can be logically drawn from the given data.
Since the question asks for conclusions that *cannot* be drawn, conclusions 1 and 2 fit this criterion.
Incorrect Options:
Options 2, 3, and 4 are incorrect because they either exclude or incorrectly include Conclusion 3. Conclusion 3 ("Cricket players do not play football") can be directly inferred from the statement "A student, who does not play cricket, plays football." Therefore, any option suggesting that Conclusion 3 cannot be drawn, or that only 1 and 3, or 1, 2, and 3 cannot be drawn, is incorrect.