$A$ survey shows that $73 \%$ of the persons working in an office like coffee,whereas $65 \%$ like tea. If $x$ denotes the percentage of them who like both coffee and tea,then $x$ cannot be

$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey. $24$ played all three games. The number of boys who did not play any game is:

Let $A = \{n \in N : n \text{ is a } 3 \text{-digit number}\}$. Let $B = \{9k + 2 : k \in N\}$ and $C = \{9k + l : k \in N\}$ for some $l$ $(0 < l < 9)$. If the sum of all the elements of the set $A \cap (B \cup C)$ is $274 \times 400$,then $l$ is equal to:

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 . . . . .

Let $S = \{1, 2, 3, 4, 5, 6, 9\}$. Then the number of elements in the set $T = \{A \subseteq S : A \neq \phi \text{ and the sum of all the elements of } A \text{ is not a multiple of } 3\}$ is ..... .