The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ is

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

If $U$ is the universal set with $100$ elements; $A$ and $B$ are two sets such that $n(A)=50$,$n(B)=60$,and $n(A \cap B)=20$,then find $n(A^{\prime} \cap B^{\prime})$.

$A$ market research group conducted a survey of $1000$ consumers and reported that $720$ consumers like product $A$ and $450$ consumers like product $B$. What is the least number of consumers that must have liked both products?

If $A = \{1, 2, 3, 4, 5, 6\}$,then the number of subsets of $A$ which contain at least two elements is

In a certain examination,a candidate has to pass in each of the $5$ subjects. The number of ways in which the candidate can fail is: