Syllogism UPSC Questions

Consider the following Statements and Conclusions:
Statements:
1. Some rats are cats.
2. Some cats are dogs.
3. No dog is a cow.
Conclusions:
I. No cow is a cat.
II. No dog is a rat.
III. Some cats are rats.
Which of the above conclusions is/are drawn from the statements?

Consider two Statements and four Conclusions given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all Conclusions and then decide which of Half of the villagers of a certain village have the given Conclusion(s) logically follows/follow from the Statements, disregarding the commonly known facts.
Statement-1: Some greens are blues.
Statement 2: Some blues are blacks.
Conclusion-1: Some greens are blacks.
Conclusion 2: No green is black.
Conclusion 3: All greens are blacks.
Conclusion-4: All blacks are greens.
Which one of the following is correct?

A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts.
Statement:
Some cats are almirahs.
Some almirahs are chairs.
All chairs are tables.
Conclusion-I: Certainly some almirahs are tables,
Conclusion-II: Some cats may not be chairs.
Which one of the following is correct?

A Statement followed by Conclusion-1 and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(a) logically follows/follow from the Statement. disregarding the commonly known facts.
Statement:
Some radios are mobiles.
All mobiles are aeroplanes.
Some aeroplanes are watches.
Conclusion-1: Certainly some radios are watches.
Conclusion II: Certainly some mobiles are watches.
Which one of the following is correct?

Two Statements are given followed by two Conclusions:
Statements:
All cats are dogs.
All cats are black.
Conclusion-1: All dogs are black.
Conclusion-II: Some dogs are not black.
Which of the above Conclusions two given Statements, disregarding commonly known facts?

Two Statements are given followed by two Conclusions:
Statements:
All numbers are divisible by 2.
All numbers are divisible by 3.
Conclusion-I: All numbers are divisible by 6.
Conclusion-II: All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?