Sets And Relations - Algebra - Mathematics Previous Year Questions

On the set of positive rational, a binary operation * is defined by \(a * b=\frac{2 a b}{5}\). If \(2 * x=3^{-1}\), then \(x=\)

If \(A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}\), then the number of onto functions from \(A\) to \(B\) is

If \(U\) is the universal set with 100 elements; \(A\) and \(B\) are two set such that \(n(A)=50, n(B)=60, n(A \cap B)=20\) then \(n\left(A^{\prime} \cap B^{\prime}\right)=\)

If \(A=\{1,2,3,4,5,6\}\), then the number of subsets of A which contain at least two elements is

If \(n(A)=2\) and total number of possible relations from Set A to set B is 1024, then \(n(B)\) is

If \(A=\{a, b, c\}\), then the number of binary operations on \(A\) is

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,1)\}\), then \(R\) is

In a certain two \(65 \%\) families own cell phones, 15000 families own scooter and \(15 \%\) families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

Let the relation \(R\) is defined in \(N\) by \(a R b\), if \(3 a+2 b=27\) then \(R\) is

Suppose that the number of elements in set \(A\) is \(p\), the number of elements in set \(B\) is \(q\) and the number of elements in \(A \times B\) is 7, then \(p^2+q^2=\)

Which of the following is an empty set?

Let the relation \(R\) be defined in \(N\) by \(a R b\), if \(3 a+2 b=27\), then \(R\) is

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of $m$ and $n$, respectively are

Let $A=\{2,3,4,5, \ldots, 16,17,18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R(c, d)$ if and only if $a d=b c$ for all $(a, b),(c, d)$ in $A \times A$. Then, the number of ordered pairs of the equivalence class of $(3,2)$ is

If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$

$B=\{x: x$ is a natural number and $2 \leq x<5\}$

$\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a prime number $\leq 4\}$

Then $(B-C) \cup A$ is,

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.

Statement (I): Minimum number of elements in AUB is 3

Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

Consider the following statements :

Statement(I) : The set of all solutions of the linear inequalities $3 \mathrm{x}+8<17$ and $2 \mathrm{x}+8 \geq 12$ are $\mathrm{x}<3$ and $x \geq 2$ respectively.

Statement(II) : The common set of solutions of linear inequalities $3 x+8<17$ and $2 x+8 \geq 12$ is $(2,3)$ Which of the following is true?

$$\text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is }$$