List of top Mathematics Questions on sets asked in KEAM

The number of elements in the set \(\{(x,y): 2x^2 + 3y^2 = 35, x,y \in \mathbb{Z}\}\), where \(\mathbb{Z}\) is the set of all integers, is
If \( y = \frac{1}{3\sqrt{x}} \left( \frac{2}{x} - 3 \right) \), find the interval in which \( y \) is strictly decreasing.
Solve \( 6(2x+3) + x>53 - 2x \).
Let \( A = \{x : x \text{ is a positive multiple of } 2 \text{ less than } 36\},\)
\(B = \{x : x \text{ is a positive multiple of } 3 \text{ greater than } 16\}, \text{ and }\)
\(C = \{x : x \text{ is a positive multiple of } 4 \text{ less than } 42\}. \text{ Then } (A \cap B) \cap C =\)
Let \(A = \{a,b,c,d,e,f\}\) Then the number of subsets of \(A\) with an odd number of elements is
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
Let \( X \) and \( Y \) be subsets of \( \mathbb{R} \). If \( f : X \rightarrow Y \) given by \( f(x) = -8(x + 5)^2 \) is one-to-one, then the codomain \( Y \) is:
Let \( P \) and \( Q \) be two finite sets having 3 elements each. The total number of mappings from \( P \) to \( Q \) is

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to
If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to
The number of subsets containing exactly 4 elements of the set {2, 4, 6, 8, 10, 12, 14, 16, 18) is equal to
If $A=\{1,2,3,4,5\}$ and $B=\{2,4,6\}$, then $A-B=$
Let $A$ and $B$ be finite sets such that $n(A-B)=18$, $n(A \cap B)=25$ and $n(A \cup B)=70$. Then $n(B)$ is equal to
If set \( S \) has 10 elements and \( A=\{(x,y):x,y\in S, x\ne y\} \), number of elements in \( A \)
If set \( S \) has 10 elements and \( A=\{(x,y):x,y\in S, x\ne y\} \), number of elements in \( A \)
Let \( S = \{1, 2, 3, \dots, 10\} \). The number of subsets of \( S \) containing only odd numbers is:
In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak at least one of the two languages is:
If $A \setminus B = \{a, b\}$, $B \setminus A = \{c, d\}$ and $A \cap B = \{e, f\}$, then the set $B$ is equal to:
In a class of 80 students numbered 1 to 80, all odd numbered students opt for Cricket, students divisible by 5 opt for Football, and those divisible by 7 opt for Hockey. The number of students who do not opt any of the three games is
The set \( (A \setminus B) \cup (B \setminus A) \) is equal to
Let \( X \) and \( Y \) be two non-empty sets such that \( X \cap A = Y \cap A = \emptyset \) and \( X \cup A = Y \cup A \) for some non-empty set \( A \). Then