Relation and Function Set-1

Q1. Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $a R b$ if $a$ is congruent to $b$, $a, b \in T$. Then $R$ is

Q2. The maximum number of equivalence relations on the set $A = \{2, 3, 4\}$ are

Q3. If $f : R \rightarrow R$ be the function defined by $f(x) = x^3 + 5$, then $f^{–1}(x)$ is

Q4. If a relation $R$ on the set $\{1, 2, 3\}$ be defined by $R = \{(1, 2)\}$, then $R$ is

Q5. If $f : R \rightarrow R$ be defined by $f(x) = 2/x$, $x \forall R$, then $f$ is

Q6. If $f : A \rightarrow B$ and $g : B \rightarrow C$ be the bijective functions, then $(gof)^{–1}$ is

Q7. Which of the following functions form $Z$ into $Z$ bijections?

Q8. If the set $A$ contains 7 elements and the set $B$ contains 8 elements, then number of one-one and onto mappings from $A$ to $B$ is

Q9. If $f : R – \{3/5\} \rightarrow R$ be defined by $f (x) = \frac{3x + 2}{5x - 3}$ then

Q10. Let $A = \{1, 2, 3, 4\}$. Let $R$ be the equivalence relation on $A \times A$ defined by $(a, b) R (c, d)$ if $a + d = b + c$. Then the equivalence class $[(1, 3)]$ is

Q11. Let $f : N \rightarrow R$ be the function defined by $f (x) = \frac{2x - 1}{2}$ and $g : Q \rightarrow R$ be another function defined by $g (x) = x + 2$. Then $(gof) \frac{3}{2}$ is

Q12. If $f: R\rightarrow R$ given by $f(x) =(3 − x^3)^{1/3}$, find $fof(x)$

Q13. Let $A = \{1,2,3\}$. The number of equivalence relations containing $(1,2)$ is

Q14. Let $f:R\rightarrow R$ defined by $f(x) = x^4$. Choose the correct answer

Q15. Let $f:R\rightarrow R$ defined by $f(x) = 3x$. Choose the correct answer