Relations and Functions One Mark Online Test

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

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If \(n(A \\times B) = 6\) and \(A = \\{1, 3\\}\) then \(n(B)\) is

A.1 B.2 C.3 D.6

If \(A = \\{a, b, p\\}\), \(B = \\{2, 3\\}\), \(C = \\{p, q, r, s\\}\) then \(n((A \\cup C) \\times B)\) is

A.8 B.20 C.12 D.16

If \(A = \\{1, 2\\}\), \(B = \\{1, 2, 3, 4\\}\), \(C = \\{5, 6\\}\) and \(D = \\{5, 6, 7, 8\\}\) then state which of the following statement is true.

A.\((A \\times C) \\subset (B \\times D)\) B.\((B \\times D) \\subset (A \\times C)\) C.\((A \\times B) \\subset (A \\times D)\) D.\((D \\times A) \\subset (B \\times A)\)

If there are 1024 relations from a set \(A = \\{1, 2, 3, 4, 5\\}\) to a set \(B\), then the number of elements in \(B\) is

A.3 B.2 C.4 D.8

The range of the relation \(R = \\{(x, x^2) \\mid x \\text{ is a prime number less than } 13\\}\) is

A.\(\\{2, 3, 5, 7\\}\) B.\(\\{2, 3, 5, 7, 11\\}\) C.\(\\{4, 9, 25, 49, 121\\}\) D.\(\\{1, 4, 9, 25, 49, 121\\}\)

If the ordered pairs \((a+2, 4)\) and \((5, 2a+b)\) are equal then \((a, b)\) is

A.(2, -2) B.(5, 1) C.(2, 3) D.(3, -2)

Let \(n(A) = m\) and \(n(B) = n\) then the total number of non-empty relations that can be defined from \(A\) to \(B\) is

A.\(mn\) B.\(n^m\) C.\(2^{mn} - 1\) D.\(2^{mn}\)

If \(\\{(a, 8), (6, b)\\}\) represents an identity function, then the value of \(a\) and \(b\) are respectively

A.(8, 6) B.(8, 8) C.(6, 8) D.(6, 6)

Let \(A = \\{1, 2, 3, 4\\}\) and \(B = \\{4, 8, 9, 10\\}\). A function \(f: A \\to B\) given by \(f = \\{(1, 4), (2, 8), (3, 9), (4, 10)\\}\) is a

A.Many-one function B.Identity function C.One-to-one function D.Into function

Q10

If \(f(x) = 2x^2\) and \(g(x) = \\frac{1}{3x}\), then \(f \\circ g\) is

A.\(\\frac{3}{2x^2}\) B.\(\\frac{2}{3x^2}\) C.\(\\frac{2}{9x^2}\) D.\(\\frac{1}{6x^2}\)

Q11

If \(f: A \\to B\) is a bijective function and if \(n(B) = 7\), then \(n(A)\) is equal to

A.7 B.49 C.1 D.14

Q12

Let \(f\) and \(g\) be two functions given by \(f = \\{(0, 1), (2, 0), (3, -4), (4, 2), (5, 7)\\}\) and \(g = \\{(0, 2), (1, 0), (2, 4), (-4, 2), (7, 0)\\}\), then the range of \(f \\circ g\) is

A.\(\\{0, 2, 3, 4, 5\\}\) B.\(\\{-4, 1, 0, 2, 7\\}\) C.\(\\{1, 2, 3, 4, 5\\}\) D.\(\\{0, 1, 2\\}\)

Q13

Let \(f(x) = \\sqrt{1+x^2}\) then

A.\(f(xy) = f(x) \\cdot f(y)\) B.\(f(xy) \\ge f(x) \\cdot f(y)\) C.\(f(xy) \\le f(x) \\cdot f(y)\) D.None of these

Q14

If \(g = \\{(1, 1), (2, 3), (3, 5), (4, 7)\\}\) is a function given by \(g(x) = \\alpha x + \\beta\) then the values of \(\\alpha\) and \(\\beta\) are

A.(-1, 2) B.(2, -1) C.(-1, -2) D.(1, 2)

Q15

Let \(f(x) = (x+1)^3 - (x-1)^3\) represents a function which is

A.linear B.cubic C.reciprocal D.quadratic

Q16

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

Q17

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}

Q18

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

Q19

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)

Q20

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

Q21

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

Q22

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

Q23

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

Q24

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

Q25

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

Q26

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

Q27

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

Q28

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

Q29

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)}

Q30

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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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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