1
KCET 2024
MCQ (Single Correct Answer)
+1
-0

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

A
4
B
5
C
6
D
7
2
KCET 2023
MCQ (Single Correct Answer)
+1
-0

Which of the following is an empty set?

A
$$\left\{x: x^2+1=0, x \in R\right\}$$
B
$$\left\{x: x^2-9=0, x \in R\right\}$$
C
$$\left\{x: x^2=x+2, x \in R\right\}$$
D
$$\left\{x: x^2-1=0, x \in R\right\}$$
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

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

A
$$\left\{\left(0, \frac{27}{2}\right),(1,12),(3,9),(5,6),(7,3)\right\}$$
B
$$\{(1,12),(3,9),(5,6),(7,3),(9,0)\}$$
C
$$\{(2,1),(9,3),(6,5),(3,7)\}$$
D
$$\{(1,12),(3,9),(5,6),(7,3)\}$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0

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 $$p^2+q^2=$$

A
50
B
51
C
42
D
49
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