In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry,and $4$ in all the three subjects. The total number of students who have taken exactly one subject is

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

$A$ group of $40$ students appeared in an examination of $3$ subjects - Mathematics,Physics,and Chemistry. It was found that all students passed in at least one of the subjects. $20$ students passed in Mathematics,$25$ students passed in Physics,and $16$ students passed in Chemistry. At most $11$ students passed in both Mathematics and Physics,at most $15$ students passed in both Physics and Chemistry,and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all the three subjects is . . . . . . .

Let $A, B, C$ be three non-void subsets of set $S$. Let $(A \cap C) \cup (B \cap C^{\prime}) = \phi$, where $C^{\prime}$ denotes the complement of set $C$ in $S$. Then:

$A$ and $B$ are two sets having $3$ and $6$ elements respectively. Consider the following statements. Statement $(I)$: Minimum number of elements in $A \cup B$ is $6$. Statement $(II)$: Maximum number of elements in $A \cap B$ is $3$. Which of the following is correct?

In a study about a pandemic,data of $900$ persons was collected. It was found that:
$190$ persons had symptom of fever,
$220$ persons had symptom of cough,
$220$ persons had symptom of breathing problem,
$330$ persons had symptom of fever or cough or both,
$350$ persons had symptom of cough or breathing problem or both,
$340$ persons had symptom of fever or breathing problem or both,
$30$ persons had all three symptoms (fever,cough and breathing problem).
If a person is chosen randomly from these $900$ persons,then the probability that the person has at most one symptom is . . . . .