If $A = \{x \in \mathbb{R} : |x - 2| > 1\}$,$B = \{x \in \mathbb{R} : \sqrt{x^2 - 3} > 1\}$,$C = \{x \in \mathbb{R} : |x - 4| \geq 2\}$,and $\mathbb{Z}$ is the set of all integers,then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is .... .

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

In a cinema hall,the charge per person is $₹ 200$. On the first day,only $60 \%$ of the seats were filled. The owner decided to reduce the price by $20 \%$ and there was an increase of $50 \%$ in the number of spectators on the next day. The percentage increase in the revenue on the second day was (in $\%$)

Let $A = \{ x \in R : | x + 1 | < 2 \}$ and $B = \{ x \in R : | x - 1 | \geq 2 \}$. Then which one of the following statements is $NOT$ true?

An integer is chosen at random from the integers $\{1, 2, 3, \ldots, 50\}$. The probability that the chosen integer is a multiple of at least one of $4, 6,$ and $7$ is

If the probabilities of a student succeeding in the entrance tests for institutes $A$, $B$ and $C$ are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both $A$ and $B$ is $0.3$, in both $B$ and $C$ is $0.2$, in both $A$ and $C$ is $0.2$, and in all three is $0.1$, then the probability that the student succeeds in exactly one of these tests is......