Relations and Functions Additional One Mark Online Test

Relations and Functions Additional One Mark Online Test (10th Standard Mathematics)

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If n(A) = 3 and n(B) = 4, how many relations can be defined from set A to set B?

A.12 B.64 C.1024 D.4096

If A x B = {(a, 1), (b, 2), (a, 2), (b, 1)}, then which of the following is set A?

A.{1, 2} B.{a, b} C.{a, b, 1, 2} D.{a, 1}

If n(A) = 4 and n(B) = 3, what is the total number of functions that can be defined from set A to set B?

A.12 B.64 C.81 D.128

For any two non-empty sets A and B, which of the following statements is always true regarding the cardinality of their Cartesian products?

A.n(A x B) > n(B x A) B.n(A x B) < n(B x A) C.n(A x B) = n(B x A) D.n(A x B) is not equal to n(B x A)

Let A = {1, 2} and B = {3, 4}. If a relation R from A to B contains no elements, what is this relation called?

A.Identity relation B.Null relation C.Universal relation D.Reflexive relation

A function f from X to Y is defined as f(x) = c for all x in X, where c is a fixed element in Y. What type of function is f?

A.Identity function B.Constant function C.One-one function D.Onto function

What is the domain of the real-valued function f(x) \(= 1/(x^2 - 9)\)?

A.The set of all real numbers B.The set of all real numbers except 3 C.The set of all real numbers except -3 and 3 D.The set of all positive real numbers

If a function f from A to B is both one-one and onto, then what is it called?

A.Constant function B.Identity function C.Bijection D.Into function

If f(x) = 2x + 1 and g(x) \(= x^2 - 2\), what is the value of the composition (g o f)(1)?

A.1 B.3 C.7 D.9

Q10

If f(x) = x + 2 and g(x) = 3x - 1, then which of the following represents (f o g)(x)?

A.3x + 1 B.3x + 5 C.3x + 2 D.3x - 1

Q11

If f from A to B is a constant function and n(B) = 5, what is the cardinality of the range of f?

A.0 B.1 C.5 D.Cannot be determined

Q12

If the function f(x) = ax + b represents the identity function on the set of real numbers, then what are the values of a and b?

A.a = 0, b = 1 B.a = 1, b = 1 C.a = 1, b = 0 D.a = 0, b = 0

Q13

If f, g, and h are three real-valued functions, then which of the following properties is always true for their compositions?

A.Compositions are always commutative B.Compositions are always associative C.Compositions are neither commutative nor associative D.Compositions are commutative but not associative

Q14

If A = {1, 2, 3} and B = {4}, what is the set A x B?

A.{(1, 4), (2, 4), (3, 4)} B.{(4, 1), (4, 2), (4, 3)} C.{1, 2, 3, 4} D.{(1, 4), (4, 2), (3, 4)}

Q15

What is the nature of the function f(x) \(= x^3\) defined from the set of real numbers to the set of real numbers?

A.Linear function B.Quadratic function C.Cubic function D.Reciprocal function

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About this Relations and Functions test

This free online practice test covers Relations and Functions from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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