Sets — NDA Mathematics PYQs

A set $S$ contains $(2n+1)$ elements. If the number of subsets of $S$ which contain at most $n$ elements is $1024$, then what is the value of $n$ ?

What is $(((A\cap B)\cup (A-B))-((A\cap B)\cup (B-A)))\cup A$ equal to ?

Let $A$ and $B$ be two sets. For some set $C$, both $A\cap C$ and $B\cap C$ are empty sets and $A\cup C=B\cup C$. Which of the following is/are true ?
I. $C=\varphi$
II. $A=B$
III. $A\cup B=C$
Select the answer using the code given below :

If $A$ and $B$ are non-empty subsets of a set, and $A^c$ and $B^c$ represent their complements, then which of the following is/are correct?
I. $A-B=B^c-A^c$
II. $A-B^c=A^c-B$
Select the answer using the code given below.

In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at least one of the two games. How many students like to play exactly one game?

Set $X$ contains $3n$ elements and set $Y$ contains $2n$ elements, and they have $n$ elements in common. How many elements does $(X-Y)\times (Y-X)$ have?

For any three non-empty sets $A$, $B$, $C$, what is
$(A\cup B)-\{(A-B)\cup (B-A)\cup (A\cap B)\}$
equal to?

Consider the following statements :

I. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set.

II. The set of all odd integers less than 1000 is a finite set.

Which of the statements given above is/are correct?

If $A$ and $B$ are two non-empty sets having 10 elements in common, then how many elements do $A\times B$ and $B\times A$ have in common?

In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?