List of top Mathematics Questions on Sets asked in JEE Main

Let \[ A = \{x : |x^2 - 10| \le 6\} \quad \text{and} \quad B = \{x : |x - 2| > 1\}. \] Then 

Let \(S\) be the set of the first 11 natural numbers. Then the number of elements in \[ A = \{ B \subseteq S : n(B) \ge 2 \text{ and the product of all elements of } B \text{ is even} \} \] is ____________.
Let \( A = \{ n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of 3 nor a multiple of 4} \} \).
Then the number of elements in \( A \) is:
Let \[f(x) =\begin{cases} x-1, & x \text{ is even, } \, x \in \mathbb{N}, \\2x, & x \text{ is odd, } \, x \in \mathbb{N}.\end{cases}\]If for some $a \in \mathbb{N}$, $f(f(f(a))) = 21$, then \[\lim_{x \to a^-} \left\{ \frac{|x|^3}{a} - \left\lfloor \frac{x}{a} \right\rfloor \right\},\]where $\lfloor t \rfloor$ denotes the greatest integer less than or equal to $t$, is equal to:
The distance of the point \( (2, 3) \) from the line \( 2x - 3y + 28 = 0 \), measured parallel to the line \( \sqrt{3}x - y + 1 = 0 \), is equal to
Let \( \alpha \beta \gamma = 45 \); \( \alpha, \beta, \gamma \in \mathbb{R} \). If \( x(\alpha, 1, 2) + y(1, \beta, 2) + z(2, 3, \gamma) = (0, 0, 0) \) for some \( x, y, z \in \mathbb{R} \), \( xyz \neq 0 \), then \( 6\alpha + 4\beta + \gamma \) is equal to ______.
If \[ S(x) = (1 + x) + 2(1 + x)^2 + 3(1 + x)^3 + \ldots + 60(1 + x)^{60}, \, x \neq 0, \] and \[ (60)^2 S(60) = a(b)^b + b, \] where $a, b \in \mathbb{N}$, then $(a + b)$ is equal to ________.
If \( f(x) = \frac{4x + 5}{6x - 4}, \, x \neq \frac{2}{3} \) and \( (fof)(x) = g(x) \), where \( g : \mathbb{R} - \left\{ \frac{2}{3} \right\} \rightarrow \mathbb{R} - \left\{ \frac{2}{3} \right\} \), then \( (gogogog)(4) \) is equal to
If \(S = \{z \in C : |z – i| = |z + i| = |z–1|\}\), then, n(S) is:
Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Suppose \( M \) is the set of all the subsets of \( S \), then the relation \( R = \{ (A, B): A \cap B \neq \phi; A, B \in M \} \) is:
The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is
Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?
Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

Consider two sets A and B. Set A has 5 elements whose mean & variance are 5 and 8 respectively. Set B has also 5 elements whose mean & variance are 12 & 20 respectively. A new set C is formed by subtracting 3 from each element of set A and by adding 2 to each element of set B. The sum of mean & variance of the set C is

The number of  \(\theta \in(0,4 \pi) \)for which the system of linear equations \(3(\sin 3 \theta) x-y+z=2\)  \(3(\cos 2 \theta) x+4 y+3 z=3\)  \(6 x+7 y+7 z=9\) has no solution is :

For \(n \in N\), let \(S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}\) and \(T_n=\left\{z \in C:|z-2+3 i|=\frac{1}{n}\right\}\) Then the number of elements in the set \(\left\{ n \in N : S _{ n } \cap T _{ n }=\phi\right\}\) is :
Let A = {1, a1, a2…a18, 77} be a set of integers with 1 <a1<a2<….<a18< 77. Let the set A + A = {x + y :x, y∈A} contain exactly 39 elements. Then, the value of a1 + a2 +…+a18 is equal to _____.
Let 
\(S=\left\{x∈[-6,3]-\left\{-2,2 \right\} :\frac{|x+3|-1}{|x|-2}>=0 \right\} \space and \space \left\{T={x∈Z:x^2-7|x|+9<=0}\right\}\)
Then the number of elements in S ⋂ T is
In a class of $140$ students numbered $1$ to $140$, all even numbered students opted mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :
Let $Z$ be the set of integers. If $A \, = \, \{ x \in Z : 2^{ (x+2) (x^2 - 5x + 6)} \}=1$ and $B \, = \, \{ \, x \in Z: -3 <2x -1 <9 \}$, then the number of subsets of the set $A \times B$, is :
The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, is :
In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,
Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .
Let R be the set of real numbers A = {(x, y) $\in$ R $\times$ R : y - x is an integer} is an equivalence relation on R. B = {(x, y) $\in$ R $\times$ R : x = $\alpha$y for some rational number $\alpha$} is an equivalence relation on R.
The variance of first n even natural numbers is $\frac{n^2 - 1}{4}$. The sum of first n natural numbers is $\frac{n(n + 1)}{2}$ and the sum of squares of first n natural numbers is $\frac{n(n + 1)(2n +1)}{6}$.