The number of elements in the set $\{n \in \{1, 2, 3, \ldots, 100\} \mid (11)^{n} > (10)^{n} + (9)^{n}\}$ is $.....$

In a certain town,$25\%$ of families own a phone,$15\%$ own a car,and $65\%$ of families own neither a phone nor a car. If $2000$ families own both a car and a phone,consider the following statements:
$1$. $10\%$ of families own both a car and a phone.
$2$. $35\%$ of families own either a car or a phone.
$3$. $40,000$ families live in the town.
Which of the above statements are correct?

Let $A = \{1, 6, 11, 16, \dots\}$ and $B = \{9, 16, 23, 30, \dots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A \cup B)$ is

In a class of $30$ pupils,$12$ take needle work,$16$ take physics,and $18$ take history. If all the $30$ students take at least one subject and no one takes all three,then the number of pupils taking exactly $2$ subjects is:

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Let $A = \{x : x \in R, |x| < 1\};$ $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D,$ then the set $D$ is