Logic: If we try to consider each of the house who like bull dogs and Samoyeds as independent of each other, we would get a total of

1000+750=1750 houses.

However, we have a total of only 1500 houses in the colony and hence, there has tp be a minimum interference of at least 250 houses who like both bull dogs and Samoyeds.

Therefore 250 houses is the Answer

Hence, option c is the correct Answer

In this case, the number of houses who like bull dogs and German shepherds can be separate from each other since there is no interference required between the houses who like bull dogs and the houses who like German shepherds as their individual sum

(1000+300) is smaller than the 1500 available houses in the colony. Therefore there are 0 houses who like both bull dogs and German shepherds.

Hence, option d is the correct Answer

For this to occur, the following situation would give the required solution:

As we can clearly see from the figure, all the requirements of each category of breeds is fulfilled by the given allocation of 1000 houses. In this situation, the maximum number of houses who do not like any of the three dog breeds is visible as 1500-1000=500.

Hence, option b is the correct Answer

6 students cleared the cut-off in all the three sections.

Hence option b is the correct answer.

The figure now becomes:

Total students who cleared the cut-off from only one section =

Hence option b is the correct answer.

Hence option a is the correct answer.