**Q.1. Let P = {(x, y) : x ^{2}+y^{2}=1, x, y ∈ R}. Then, P is **

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) Anti-symmetric

## Answer

Answer: (b)**Q.2. Let S be the set of all real numbers. Then, the relation R = {(a, b) : 1 +ab > 0} on S is **

(a) Reflexive and symmetric but not transitive

(b) Reflexive and transitive but not symmetric

(c) Symmetric, transitive but not reflexive

(d) reflexive, transitive and symmetric

## Answer

Answer: (a)**Q.3. The relation R = {(1,1), (2, 2), (3, 3)} on set {1, 2, 3} is:**

(a) symmetric only

(b) reflexive only

(c) an equivalence relation

(d) transitive only

## Answer

Answer: (b)**Q.4. If R is a relation in a set A such that (a, a) ∈ R for every a ∈ A, then the relation R is called **

(a) symmetric

(b) reflexive

(c) transitive

(d) symmetric or transitive

## Answer

Answer: (b)**Q.5. Let A = {1, 2, 3} and R={(1, 2), (2, 3)} be a relation in A. Then, the minimum number of ordered pairs may be added, so that R becomes an equivalence relation, is **

(a) 7

(b) 5

(c) 1

(d) 4

## Answer

Answer: (a)**Q.6. Let f : R → R be defined as f(x) = x ^{4}, then **

(a) f is one-one onto

(b) f is many-one onto

(c) f is one-one but not onto

(d) f is neither one-one nor onto

## Answer

Answer: (d)**Q.7. Let A={1, 2, 3} and B={a, b, c}, and let f = {(1, a), (2, b), (P, c)} be a function from A to B. For the function f to be one-one and onto, the value of P = **

(a) 1

(b) 2

( c) 3

(d) 4

## Answer

Answer: (c)**Q.8. If **

**then f (x) is**

(a) one to one and onto

(b) many to one and onto

(c) one to one and into

(d) many to one and into

## Answer

Answer: (a)**Q.9. The function F : R → R defined by f(x) = (x-1) (x-2) (x-3) is **

(a) one-one but not onto

(b) onto but not one-one

(c) both one-one and onto

(d) neither one-one and onto

## Answer

Answer: (b)**Q.10. For real x, let f(x) = x ^{3}+5x+1, then **

(a) f is one-one but not onto R

(b) f is onto R but not one-one

(c) f is one-one and onto R

(d) f is neither one-one nor onto R