List of top Mathematics Questions on sets asked in JEE Main

If $ R $ is the smallest equivalence relation on the set $ \{1, 2, 3, 4\} $ such that $ \{(1,2), (1,3)\} \subseteq R $, then the number of elements in $ R $ is ______.

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if \[(A \cap B^c) \cup (B \cap A^c) = ,\]and $A R_2 B$ if\[A \cup B^c = B \cup A^c,\]for all $A, B \in P(S)$. Then:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

If the set $\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)$ is equal to the interval (α,β), then 24(β-α) is equal to

Let S = {1, 2, 3, 4, 5}
if f : S → P(S), where P(S) is power set of S. Then number of one-one functions f can be made is

Negation of (p⇒q)⇒(q⇒p) is

For n ∈ N let $S_n$={z∈C:|z−3+2i|=$\frac{n}{4}$} and $T_n$={z ∈ C:|z−2+3i|=$\frac{1}{n}$}.Then the number of elements in the set

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of $A∩B$ is ___________

Let
$f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}$
Then, the value of ∑_n∈S f(n) is equal to ________.

For any two statements

p

and

q

, the negation of the expression

p \lor (\sim p \land q)

is:

Let $S=x: x∈R$ and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to