Relations and Functions

This is an MCQ-based quiz on Relations and Functions.

This includes Types of Relations, Types of Functions, Composition of Functions, Invertible Function, and Binary Operations

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What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}

Reflexive Transitive Symmetric None of these

If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is

12 28 61 None of these

Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals

31 40 43 None of these

Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is

14 16 12 8

If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is

One-One

One-One Onto

Onto

Many One

Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:

1 2 3 4.

Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is

1 2 3 4.

Let f: R → R be defined as f(x) = x4. Then

f is one-one onto f is many-one onto f is one-one but not onto f is neither one-one nor onto.

Let f : R → R be defined as f(x) = 3x. Then

f is one-one onto f is many-one onto f is one-one but not onto f is neither one-one nor onto.

The period of sin² θ is

π² π π/2

The domain of sin^-1 (log (x/3)] is. .

[1, 9] [-1, 9] [-9, 1] [-9, -1]

If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?

Many-one onto

Constant function

One-One Onto

Into

Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is

Onto function

One-One, Onto function

One-One, Into function

Many-One Into function

What type of relation is ‘less than’ in the set of real numbers?

Only symmetric

Only transitive

Only reflexive

Equivalence

Let R be the relation in the set N given by : R = {(a, b): a = b – 2 & b>6}. Then:

(2, 4) ∈ R

(3, 8) ∈ R

(6, 8) ∈ R

(8, 7) ∈ R.

Quiz/Test Summary
Title: Relations and Functions
Questions: 15
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